From Wikipedia, the free encyclopedia
.^ In biology, game theory has been used to understand many different phenomena.
^ Game theory From Wikipedia, the free encyclopedia Game theory is a branch of applied mathematics that is used in the social sciences, most notably in economics, as well as in biology, engineering, political science, international relations, computer science, and philosophy.
^ The use of game theory in the social sciences has expanded, and game theory has been applied to political, sociological, and psychological behaviors as well.
.^ Game theory and individual motivation . Trust in Game Theory  Unpublished Talk, May, 1997 8 January 2010 4:14 UTC philosophy.wisc.edu [Source type: FILTERED WITH BAYES]
^ Would this be considered a game theory situation? A Conversation with Len Fisher  Popular Science 8 January 2010 4:14 UTC www.popsci.com [Source type: General]
^ Recall that in games, fitness also depends on the frequency of other behaviors. Introduction to Game Theory  simple, twostrategy examples 8 January 2010 4:14 UTC www.holycross.edu [Source type: FILTERED WITH BAYES]
.^ While initially developed to analyze competitions in which one individual does better at another's expense (zero sum games), it has been expanded to treat a wide class of interactions, which are classified according to several criteria.
^ Business is a NONzero sum game . Game Theory 8 January 2010 4:14 UTC www.12manage.com [Source type: FILTERED WITH BAYES]
^ Poker exemplifies a zerosum game (ignoring the possibility of the house's cut), because one wins exactly the amount one's opponents lose.
.^ Game theory in computer science . Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
^ Today, "game theory is a sort of umbrella or 'unified field' theory for the rational side of social science, where 'social' is interpreted broadly, to include human as well as nonhuman players (computers, animals, plants)" (Aumann 1987).
^ I call game theory and rational choice theory that includes this assumption "vulgar." Trust in Game Theory  Unpublished Talk, May, 1997 8 January 2010 4:14 UTC philosophy.wisc.edu [Source type: FILTERED WITH BAYES]
.^ Traditional applications of game theory attempt to find equilibria in these games.
^ The lack of a dynamical theory in the traditional theory of games . Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Developed by John von Neumann, the theory has applications to real games (cards, chess, etc. In a few words... from Interactive Mathematics Miscellany and Puzzles 8 January 2010 4:14 UTC www.cuttheknot.org [Source type: Reference]
.^ Matrices, unlike trees, simply show the outcomes, represented in terms of the players' utility functions, for every possible combination of strategies the players might use. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ Nash's idea, based on the idea of equilibrium in a physical system, was that players would adjust their strategies until no player could benefit from changing. Sample Chapter for Camerer, C.F.: Behavioral Game Theory: Experiments in Strategic Interaction. 8 January 2010 4:14 UTC press.princeton.edu [Source type: FILTERED WITH BAYES]
^ Game theory started on this idea that you try to put yourself in the other person's head and think for them, 'What's they're best strategy going to be?' A Conversation with Len Fisher  Popular Science 8 January 2010 4:14 UTC www.popsci.com [Source type: General]
.^ Nash's idea, based on the idea of equilibrium in a physical system, was that players would adjust their strategies until no player could benefit from changing. Sample Chapter for Camerer, C.F.: Behavioral Game Theory: Experiments in Strategic Interaction. 8 January 2010 4:14 UTC press.princeton.edu [Source type: FILTERED WITH BAYES]
^ Such remarks ignore the fact that the concept 'Nash equilibrium strategy' is not necessarily synonymous to 'optimal play'.
^ The basic idea behind the concept of a Nash Equilibrium is that for wide classes of games there are ways for the players to play the game, sometimes as pure strategies and sometimes as mixed strategies so that if a player deviates from the Nash Equilibrium strategy, he/she can not improve his/her payoff. Feature Column from the AMS 8 January 2010 4:14 UTC www.ams.org [Source type: FILTERED WITH BAYES]
.^ In fact, the behaviorist needs the concept of equilibrium in beliefs too, but for different purposes. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ Although the gametheoretic equilibrium of zero is a poor guess about initial choices, players are inexorably drawn toward zero as they learn. Sample Chapter for Camerer, C.F.: Behavioral Game Theory: Experiments in Strategic Interaction. 8 January 2010 4:14 UTC press.princeton.edu [Source type: FILTERED WITH BAYES]
^ The movement patterns (or "personalities" as they are often labelled) of the enemy ghosts are different for each ghost and quite complex (Mateas, 2003). Game Studies  The Games Economists Play  Implications of Economic Game Theory for the Study of Computer Games 8 January 2010 4:14 UTC gamestudies.org [Source type: FILTERED WITH BAYES]
.^ So which refinement is more appropriate as a solution concept? Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ One limitation with this paper is that Shubik worked within the confines of TU games whereas Edgeworth's idea is more appropriately modelled as an NTU game.
^ The introduction of trembling hand perfect equilibria occurred in the paper Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games by Reinhard Selten.
.^ See economic game theory. HalfReal: A Dictionary of Video Game Theory 8 January 2010 4:14 UTC www.halfreal.net [Source type: General]
^ Games and Economic Behavior 1: 6079. Trust in Game Theory  Unpublished Talk, May, 1997 8 January 2010 4:14 UTC philosophy.wisc.edu [Source type: FILTERED WITH BAYES]
^ They published the Theory of Games and Economic Behavior in 1944. Game Theory 8 January 2010 4:14 UTC www.12manage.com [Source type: FILTERED WITH BAYES]
.^ Many game development methods call for extensive testing of a game on users during all phases of game development. HalfReal: A Dictionary of Video Game Theory 8 January 2010 4:14 UTC www.halfreal.net [Source type: General]
.^ The most welldeveloped game theory software package is Gambit , a software library developed primarily by Richard McKelvey, Andrew McLennan and Theodore Turocy. Resources 8 January 2010 4:14 UTC www.hss.cmu.edu [Source type: FILTERED WITH BAYES]
^ Developed by John von Neumann, the theory has applications to real games (cards, chess, etc. In a few words... from Interactive Mathematics Miscellany and Puzzles 8 January 2010 4:14 UTC www.cuttheknot.org [Source type: Reference]
^ In the preface to Evolution and the Theory of Games , Maynard Smith notes that “[p]aradoxically, it has turned out that game theory is more readily applied to biology than to the field of economic behaviour for which it was originally designed.” It is perhaps doubly paradoxical, then, that the subsequent development of evolutionary game theory has produced a theory which holds great promise for social scientists, and is as readily applied to the field of economic behaviour as that for which it was originally designed. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
.^ It is important to distinguish games from game theory . Sample Chapter for Camerer, C.F.: Behavioral Game Theory: Experiments in Strategic Interaction. 8 January 2010 4:14 UTC press.princeton.edu [Source type: FILTERED WITH BAYES]
^ In the early 1950s, John Nash generalized their results and provided the basis of the modern field of Game Theory. Game Theory 8 January 2010 4:14 UTC www.12manage.com [Source type: FILTERED WITH BAYES]
^ Interest in data also suffered from the fact that so many interesting mathematical puzzles were open for solution in game theory for such a long time. Sample Chapter for Camerer, C.F.: Behavioral Game Theory: Experiments in Strategic Interaction. 8 January 2010 4:14 UTC press.princeton.edu [Source type: FILTERED WITH BAYES]
.^ Game theory in computer science . Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
^ What, then, do these economic game theorists do? Game Studies  The Games Economists Play  Implications of Economic Game Theory for the Study of Computer Games 8 January 2010 4:14 UTC gamestudies.org [Source type: FILTERED WITH BAYES]
^ Iyt is interesting that advanced Game Theory was developed by John Nash and he won the Nobel Prize for it. How Israel Wages Game Theory Warfare « INTIFADA 8 January 2010 4:14 UTC intifadapalestine.com [Source type: Original source]
Representation of games
.^ "Game theory" is also a mathematical method of decisionmaking in which a competitive situation is analyzed to determine the optimal course of action for an interested party. ArtLex's GGl page 8 January 2010 4:14 UTC www.artlex.com [Source type: FILTERED WITH BAYES]
^ Interest in data also suffered from the fact that so many interesting mathematical puzzles were open for solution in game theory for such a long time. Sample Chapter for Camerer, C.F.: Behavioral Game Theory: Experiments in Strategic Interaction. 8 January 2010 4:14 UTC press.princeton.edu [Source type: FILTERED WITH BAYES]
^ This broad definition applies to most of the social sciences, but game theory applies mathematical models to this interaction under the assumption that each person's behavior impacts the wellbeing of all other participants in the game. Game Theory 8 January 2010 4:14 UTC www.12manage.com [Source type: FILTERED WITH BAYES]
.^ Outcome : an assignment of a set of payoffs, one to each player in the game. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ A strategy for a player, in this game, consists of an amount of cake that he would like. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Figure 11 illustrates the state space under the continuous replicator dynamics for the senderreceiver game consisting of two states of the world, two signals, and two responses, where players are restricted to using one of the previous four strategies. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
.^ Matrix games are referred to as ‘normalform’ or ‘strategicform’ games, and games as trees are referred to as ‘extensiveform’ games. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ Keywords: experiments, game theory, extensive form, presentation effects. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ This paper also introduced the extensive form of a game.
Extensive form
.^ Keywords: experiments, game theory, order of play, extensive form. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ These experiments have worked with the centipede game in extensive form as well as in recent work that gets new insights from using a normal form for the centipede game. Feature Column from the AMS 8 January 2010 4:14 UTC www.ams.org [Source type: FILTERED WITH BAYES]
^ For now, we have described it just in order to use it to introduce one of the two types of mathematical objects used to represent games: gametrees . Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
.^ First, however, here are definitions of some concepts that will be helpful in analyzing gametrees: . Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
.^ Node : A point at which a player takes an action. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ Strategy : a program instructing a player which action to take at every node in the tree where she could possibly be called on to make a choice. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ If the subgame descending from node 3 is played, then Player II will face a choice between a payoff of 4 and a payoff of 3. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
.^ The player is specified by a number listed by the vertex.
^ Each player has two strategies, which are specified by the number of rows and the number of columns.
.^ The lines out of the vertex represent a possible action for that player.
^ Matrices, unlike trees, simply show the outcomes, represented in terms of the players' utility functions, for every possible combination of strategies the players might use. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ Of course, not all paths will be possible because the other player has a role in selecting paths too, and won't take actions that lead to less preferred outcomes for him. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
.^ The payoffs are specified at the bottom of the tree.
^ The numbers in the parentheses at the bottom of the tree are the payoffs at each respective point, in the format (Player 1, Player 2).
.^ This game involves two players. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ Note there are two waveforms here. Game Theory 8 January 2010 4:14 UTC blogs.msdn.com [Source type: General]
^ In the game pictured here, there are two players.
.^ Player 1 moves first and chooses either F or U. Player 2 sees Player 1's move and then chooses A or R. Suppose that Player 1 chooses U and then Player 2 chooses A, then Player 1 gets 8 and Player 2 gets 2.
^ Consider what happens if one modifies the oneshot prisoner's dilemma above by having A move first with the knowledge that what she chooses will be common knowledge before B moves. Trust in Game Theory  Unpublished Talk, May, 1997 8 January 2010 4:14 UTC philosophy.wisc.edu [Source type: FILTERED WITH BAYES]
^ Game Theory predicts that Player 1 will choose D in his first move and thus both players will receive payoff of 1! EconPort  Handbook  Game Theory  Centipede Game 8 January 2010 4:14 UTC www.econport.org [Source type: FILTERED WITH BAYES]
.^ Player 1 moves first and chooses either F or U. Player 2 sees Player 1's move and then chooses A or R. Suppose that Player 1 chooses U and then Player 2 chooses A, then Player 1 gets 8 and Player 2 gets 2.
^ Game Theory predicts that Player 1 will choose D in his first move and thus both players will receive payoff of 1! EconPort  Handbook  Game Theory  Centipede Game 8 January 2010 4:14 UTC www.econport.org [Source type: FILTERED WITH BAYES]
^ The top number at the end of each vertical line is a payoff for player 1 and the bottom number is a payoff for player 2.Player 1 has the first move: if she chooses D, both players get 1; if she chooses A, the opportunity to make a decision passes to player 2. EconPort  Handbook  Game Theory  Centipede Game 8 January 2010 4:14 UTC www.econport.org [Source type: FILTERED WITH BAYES]
Suppose that
Player 1 chooses
U and then
Player 2 chooses
A, then
Player 1 gets 8 and
Player 2 gets 2.
.^ When the "moves" and payoffs for a game are displayed in this form, the game is said to be described in "extensive form." Feature Column from the AMS 8 January 2010 4:14 UTC www.ams.org [Source type: FILTERED WITH BAYES]
^ This paper also introduced the extensive form of a game.
^ These experiments have worked with the centipede game in extensive form as well as in recent work that gets new insights from using a normal form for the centipede game. Feature Column from the AMS 8 January 2010 4:14 UTC www.ams.org [Source type: FILTERED WITH BAYES]
.^ When players do know each other, they might know what their respective values might be as well as the way they think about situations involved in the game. Feature Column from the AMS 8 January 2010 4:14 UTC www.ams.org [Source type: FILTERED WITH BAYES]
^ An event is common knowledge among a set of agents if all know it and all know that they all know it and so on ad infinitum.
^ In a series of three papers, Games with Incomplete Information Played by 'Bayesian' Players, Parts I, II and III , John Harsanyi constructed the theory of games of incomplete information.
Normal form

Player 2
chooses Left 
Player 2
chooses Right 
Player 1
chooses Up 
4, 3 
–1, –1 
Player 1
chooses Down 
0, 0 
3, 4 
Normal form or payoff matrix of a 2player, 2strategy game 
.^ Matrix games are referred to as ‘normalform’ or ‘strategicform’ games, and games as trees are referred to as ‘extensiveform’ games. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ Now consider the strategic form of this game: . Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ Now we can represent your entire situation on a matrix; this is the strategic form of your game: . Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
.^ Matrices, unlike trees, simply show the outcomes, represented in terms of the players' utility functions, for every possible combination of strategies the players might use. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ In other words, in zerosum games the total benefit to all players in the game, for every combination of strategies, always adds to zero. Game Theory 8 January 2010 4:14 UTC www.12manage.com [Source type: FILTERED WITH BAYES]
^ Each bridge should be thought of as a lottery over the fugitive's possible outcomes, in which each lottery has a different expected payoff in terms of the items in his utility function. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
.^ It will be convenient to refer to the two players involved in a game as Row and Column. Feature Column from the AMS 8 January 2010 4:14 UTC www.ams.org [Source type: FILTERED WITH BAYES]
^ So depending on the perceived probability of those two events it becomes a matter of assessing how the other players view their own sense of "greed".
^ Since each player chooses between two actions at each of two information sets here, each player has four strategies in total. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
.^ This number is typically the payoff to the row player. Feature Column from the AMS 8 January 2010 4:14 UTC www.ams.org [Source type: FILTERED WITH BAYES]
^ It will be convenient to refer to the two players involved in a game as Row and Column. Feature Column from the AMS 8 January 2010 4:14 UTC www.ams.org [Source type: FILTERED WITH BAYES]
^ Each player has two strategies, which are specified by the number of rows and the number of columns.
.^ The payoffs are provided in the interior.
.^ The first number represents the payoff to A , and the second represents the payoff to B . Trust in Game Theory  Unpublished Talk, May, 1997 8 January 2010 4:14 UTC philosophy.wisc.edu [Source type: FILTERED WITH BAYES]
^ For each outcome, Row's payoff is always listed first, followed by Column's. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ Player I's payoff appears as the first number of each pair, Player II's as the second. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
Suppose that Player 1 plays
Up and that Player 2 plays
Left. Then Player 1 gets a payoff of 4, and Player 2 gets 3.
.^ Games in the normal form; 6. Political Game Theory  Cambridge University Press 8 January 2010 4:14 UTC www.cambridge.org [Source type: Reference]
^ This representation of the game is called the normal form . Egwald Operations Research  Game Theory  Introduction 8 January 2010 4:14 UTC www.egwald.ca [Source type: FILTERED WITH BAYES]
^ When a game is presented in normal form, it is presumed that each player acts simultaneously or, at least, without knowing the actions of the other.
.^ Games in the extensive form. GAME THEORY Outline 8 January 2010 4:14 UTC www.nes.ru [Source type: Reference]
^ In other games, each player's role is different. Game theory  encyclopedia article  Citizendium 8 January 2010 4:14 UTC en.citizendium.org [Source type: FILTERED WITH BAYES]
^ If players have some information about the choices of other players, the game is usually presented in extensive form.
Characteristic function form
.^ As well as expounding twoperson zero sum theory this book is the seminal work in areas of game theory such as the notion of a cooperative game, with transferable utility (TU), its coalitional form and its von NeumannMorgenstern stable sets.
^ More specifically, in a social dilemma "each individual always receives a higher payoff for defecting than for cooperating, but all are better off if all cooperate than if all defect" (Dawes and Messick, 2000, p. Game Studies  The Games Economists Play  Implications of Economic Game Theory for the Study of Computer Games 8 January 2010 4:14 UTC gamestudies.org [Source type: FILTERED WITH BAYES]
^ Consequently, no single unit is useful in all circumstances, although the distribution of units in a given game is rarely equal due to production costs, etcetera. Game Studies  The Games Economists Play  Implications of Economic Game Theory for the Study of Computer Games 8 January 2010 4:14 UTC gamestudies.org [Source type: FILTERED WITH BAYES]
Instead, the characteristic function determines the payoff of each coalition. The standard assumption is that the empty coalition obtains a payoff of 0.
.^ A game played against the computer is considered a single player game. HalfReal: A Dictionary of Video Game Theory 8 January 2010 4:14 UTC www.halfreal.net [Source type: General]
^ In the opening pages of their seminal book, von Neumann and Morgenstern (1944, p. Sample Chapter for Camerer, C.F.: Behavioral Game Theory: Experiments in Strategic Interaction. 8 January 2010 4:14 UTC press.princeton.edu [Source type: FILTERED WITH BAYES]
^ Neumann, John von and Oskar Morgenstern. HalfReal: A Dictionary of Video Game Theory 8 January 2010 4:14 UTC www.halfreal.net [Source type: General]
The equilibrium payoff of
C is
characteristic.
.^ Now consider the strategic form of this game: . Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ After all, there is little risk in the game since the worst consequence is merely leaving with $0, which is what you started with.
^ We cannot solve this game, as before, simply on the basis of knowing the players' ordinal utility functions, since the intensities of their respective preferences will now be relevant to their strategies. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
.^ Outcome : an assignment of a set of payoffs, one to each player in the game. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ The bargaining set includes the core but unlike it, is never empty for TU games.
^ At a given time, a player has a repertoire of skills for playing a given game. HalfReal: A Dictionary of Video Game Theory 8 January 2010 4:14 UTC www.halfreal.net [Source type: General]
.^ As well as expounding twoperson zero sum theory this book is the seminal work in areas of game theory such as the notion of a cooperative game, with transferable utility (TU), its coalitional form and its von NeumannMorgenstern stable sets.
^ We cannot solve this game, as before, simply on the basis of knowing the players' ordinal utility functions, since the intensities of their respective preferences will now be relevant to their strategies. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ We can solve this new game if we make certain assumptions about the two players' utility functions. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
Partition function form
The characteristic function form ignores the possible
externalities of coalition formation.
.^ Costs may be assigned either positive or negative values depending on the form of the payoff equation. Introduction to Game Theory  simple, twostrategy examples 8 January 2010 4:14 UTC www.holycross.edu [Source type: FILTERED WITH BAYES]
^ I do not believe that one can explain how people choose if one supposes that their preferences depend only on the material payoffs. Trust in Game Theory  Unpublished Talk, May, 1997 8 January 2010 4:14 UTC philosophy.wisc.edu [Source type: FILTERED WITH BAYES]
^ (This form does not require that the payoffs for each player be symmetric, only that the proper ordering of the payoffs obtains. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
Application and challenges
.^ Now that's good behavioral game theory! Sample Chapter for Camerer, C.F.: Behavioral Game Theory: Experiments in Strategic Interaction. 8 January 2010 4:14 UTC press.princeton.edu [Source type: FILTERED WITH BAYES]
^ The results are used to create behavioral game theory. Sample Chapter for Camerer, C.F.: Behavioral Game Theory: Experiments in Strategic Interaction. 8 January 2010 4:14 UTC press.princeton.edu [Source type: FILTERED WITH BAYES]
^ Evolutionary game theory has been used to explain a number of aspects of human behavior. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
.^ In economics, game theory is used to analyze behavior of firms that worry about what their competitors will do. Sample Chapter for Camerer, C.F.: Behavioral Game Theory: Experiments in Strategic Interaction. 8 January 2010 4:14 UTC press.princeton.edu [Source type: FILTERED WITH BAYES]
^ Behavioral game theory uses a concept of limited iterated reasoning to understand initial choices and a theory of learning to explain movement across rounds. Sample Chapter for Camerer, C.F.: Behavioral Game Theory: Experiments in Strategic Interaction. 8 January 2010 4:14 UTC press.princeton.edu [Source type: FILTERED WITH BAYES]
^ Some Dynamics of a Strategic Market Game with a Large Number of Agents,” Journal of Economics , 60: 1–28. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
.^ Keywords: experiments, game theory, psychological game theory. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Keywords: experiments, game theory, public, voting, political science. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ This broad definition applies to most of the social sciences, but game theory applies mathematical models to this interaction under the assumption that each person's behavior impacts the wellbeing of all other participants in the game. Game Theory 8 January 2010 4:14 UTC www.12manage.com [Source type: FILTERED WITH BAYES]
.^ Game theory can be defined as the study of how people interact and make decisions. Game Theory 8 January 2010 4:14 UTC www.12manage.com [Source type: FILTERED WITH BAYES]
^ If one seeks to use an evolutionary game theoretic model to explain the normativity attached to a social rule, one must explain how such an approach avoids committing the socalled “naturalistic fallacy” of inferring an oughtstatement from a conjunction of isstatements. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Since evolutionary game theory successfully explains the predominance of certain behaviors of insects and animals, where strong rationality assumptions clearly fail, this suggests that rationality is not as central to game theoretic analyses as previously thought. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
.^ It is important to distinguish games from game theory . Sample Chapter for Camerer, C.F.: Behavioral Game Theory: Experiments in Strategic Interaction. 8 January 2010 4:14 UTC press.princeton.edu [Source type: FILTERED WITH BAYES]
^ In the early 1950s, John Nash generalized their results and provided the basis of the modern field of Game Theory. Game Theory 8 January 2010 4:14 UTC www.12manage.com [Source type: FILTERED WITH BAYES]
^ Interest in data also suffered from the fact that so many interesting mathematical puzzles were open for solution in game theory for such a long time. Sample Chapter for Camerer, C.F.: Behavioral Game Theory: Experiments in Strategic Interaction. 8 January 2010 4:14 UTC press.princeton.edu [Source type: FILTERED WITH BAYES]
.^ Keywords: experiments, game theory, evolution. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Evolution and the Theory of Games” Journal of Theoretical Biology , 1: 382–403. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ See economic game theory. HalfReal: A Dictionary of Video Game Theory 8 January 2010 4:14 UTC www.halfreal.net [Source type: General]
.^ Now that's good behavioral game theory! Sample Chapter for Camerer, C.F.: Behavioral Game Theory: Experiments in Strategic Interaction. 8 January 2010 4:14 UTC press.princeton.edu [Source type: FILTERED WITH BAYES]
^ The results are used to create behavioral game theory. Sample Chapter for Camerer, C.F.: Behavioral Game Theory: Experiments in Strategic Interaction. 8 January 2010 4:14 UTC press.princeton.edu [Source type: FILTERED WITH BAYES]
^ Evolutionary game theory has been used to explain a number of aspects of human behavior. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
.^ See economic game theory. HalfReal: A Dictionary of Video Game Theory 8 January 2010 4:14 UTC www.halfreal.net [Source type: General]
^ They published the Theory of Games and Economic Behavior in 1944. Game Theory 8 January 2010 4:14 UTC www.12manage.com [Source type: FILTERED WITH BAYES]
^ Now that's good behavioral game theory! Sample Chapter for Camerer, C.F.: Behavioral Game Theory: Experiments in Strategic Interaction. 8 January 2010 4:14 UTC press.princeton.edu [Source type: FILTERED WITH BAYES]
.^ Fisher's argument can be understood game theoretically, but he did not state it in those terms. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Let's see how we formally analyze a game  how we make theoretical calculations of relative fitness that are based on benefits, costs and frequencies of various types of outcomes. Introduction to Game Theory  simple, twostrategy examples 8 January 2010 4:14 UTC www.holycross.edu [Source type: FILTERED WITH BAYES]
^ Depending on the type of explanation it seeks to provide, are evolutionary game theoretic explanations of social phenomena irrelevant or mere vehicles for the promulgation of preexisting values and biases? Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^{[1]}
Political science
.^ Keywords: experiments, game theory, public, social dilemmas. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Keywords: experiments, game theory, public. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Keywords: experiments, game theory, public, voting, political science. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
.^ Gametheoretic models of bargaining. Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
^ These game types also inspire sudden alliances since one player constructing a wonder will immediately mean a certain convergence of interests of all other players. Game Studies  The Games Economists Play  Implications of Economic Game Theory for the Study of Computer Games 8 January 2010 4:14 UTC gamestudies.org [Source type: FILTERED WITH BAYES]
^ An equilibrium, then, may be thought of as a game state to which the game is likely to gravitate and once reached the players will generally not change their strategies. Game Studies  The Games Economists Play  Implications of Economic Game Theory for the Study of Computer Games 8 January 2010 4:14 UTC gamestudies.org [Source type: FILTERED WITH BAYES]
.^ See economic game theory. HalfReal: A Dictionary of Video Game Theory 8 January 2010 4:14 UTC www.halfreal.net [Source type: General]
^ Keywords: experiments, game theory, public, voting, political science. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ In the early 1950s, John Nash generalized their results and provided the basis of the modern field of Game Theory. Game Theory 8 January 2010 4:14 UTC www.12manage.com [Source type: FILTERED WITH BAYES]
.^ Few corporations nowadays think about their strategy without adding some game theory models or game elements into their strategy process. Game Theory 8 January 2010 4:14 UTC www.12manage.com [Source type: FILTERED WITH BAYES]
^ Smith, Vernon L. (1992) Game Theory and Experimental Economics: Beginnings and Early Influences, History of Political Economy , 24:Special Issue 241282. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Abstract: This book surveys and develops models of learning and dynamic adjustment in economic games. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
.^ Figure 3 illustrates one way of representing the replicator dynamical model of the prisoner's dilemma, known as a statespace diagram. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
The theorist shows how the political candidates will converge to the ideology preferred by the median voter.
.^ Messages are more effective in the treatment where the receiver also sees that sender's message/action decisions from the most recent matching, as compared with a baseline treatment where only the sender's previous action is revealed. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ (Note: a more common type of game is probably "playing the field" (see Maynard Smith, 1982 ) or "nperson game" by Riechert and Hammerstein 1983 ), but we will not consider this model. Introduction to Game Theory  simple, twostrategy examples 8 January 2010 4:14 UTC www.holycross.edu [Source type: FILTERED WITH BAYES]
^ (See, for example, the socalled ‘continuous double auction’ experiments discussed in Plott and Smith 1978 and Smith 1962 , 1964 , 1965 , 1976 , 1982 ). Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
.^ One should however be cautious about extrapolating this explanation to other games where other factors might be involved. Trust in Game Theory  Unpublished Talk, May, 1997 8 January 2010 4:14 UTC philosophy.wisc.edu [Source type: FILTERED WITH BAYES]
^ However, many have already indicated far lower values which, once again, illustrates the problem when there is imperfect information regarding the other players.
^ If at least one node shares its information set with another, while others are alone, the game involves both simultaneous and sequential play, and so is still a game of imperfect information. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
.^ In contrast, it is difficult to know the intentions of nondemocratic leaders, what effect concessions will have, and if promises will be kept.
^ Bobbob321, immediately upon entering, wants to know of rushing is allowed, practically asking for a promise that may or may not be kept once the game starts. Game Studies  The Games Economists Play  Implications of Economic Game Theory for the Study of Computer Games 8 January 2010 4:14 UTC gamestudies.org [Source type: FILTERED WITH BAYES]
Thus there will be mistrust and unwillingness to make concessions if at least one of the parties in a dispute is a nondemocracy (Levy & Razin
2003).
Economics and business
.^ See economic game theory. HalfReal: A Dictionary of Video Game Theory 8 January 2010 4:14 UTC www.halfreal.net [Source type: General]
^ Keywords: experiments, game theory, trust game, fairness, social history. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Keywords: experiments, game theory, fairness. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
.^ This research usually focuses on particular sets of strategies known as equilibria in games.
^ For each player in a twoperson zerosum matrix game, the set of optimal mixed strategies is a closed, convex set (Karlin, 36). Egwald Operations Research  Game Theory  Introduction 8 January 2010 4:14 UTC www.egwald.ca [Source type: FILTERED WITH BAYES]
^ The focus of attention is usually not so much on what is the best way to play such a game, but simply on whether one or the other player has a winning strategy.
.^ These "solution concepts" are usually based on what is required by norms of rationality.
^ There is no more ‘refined’ concept of rationality of which this can be argued to be true in general ; and so, according to behaviorists, refinements of NE based on refinements of rationality are likely to be of merely occasional interest. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ This is a persuasive solution concept because, again unlike the refinements of Section 2.5, it does not demand ‘more’ rationality of agents, but less . Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
.^ If all people know that these incentives hold for most others, then cooperation will not only be possible, but will be the expected norm, and the war of all against all becomes a general peace. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ We will demonstrate this shortly by reference to the most famous (though not the most typical) game, the socalled Prisoner's Dilemma , and to other, more typical, games. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ In 1982, Maynard Smith's seminal text Evolution and the Theory of Games appeared, followed shortly thereafter by Robert Axelrod's famous work The Evolution of Cooperation in 1984. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
.^ A set of strategies is a Nash equilibrium if each represents a best response to the other strategies.
^ A selection of strategies by a group of agents is said to be in a Nash equilibrium if each agent's strategy is a bestresponse to the strategies chosen by the other players. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Since a Nash equilibrium Cooperate 1, 1 10, 0 of a game constitutes one's best response to the actions of the other players, playing a Defect 0, 10 5, 5 strategy that is part of a Nash equilibrium seems appropriate.
.^ A selection of strategies by a group of agents is said to be in a Nash equilibrium if each agent's strategy is a bestresponse to the strategies chosen by the other players. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ In other words, in zerosum games the total benefit to all players in the game, for every combination of strategies, always adds to zero. Game Theory 8 January 2010 4:14 UTC www.12manage.com [Source type: FILTERED WITH BAYES]
^ Each power will recognize this incentive on the part of the other, and so will anticipate an attack if they don't preempt it. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
.^ In general, then, a game is partly defined by the payoffs assigned to the players. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ Matrices, unlike trees, simply show the outcomes, represented in terms of the players' utility functions, for every possible combination of strategies the players might use. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ Outcome : an assignment of a set of payoffs, one to each player in the game. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
.^ Often in modeling situations the payoffs represent money, which presumably corresponds to an individual's utility.
^ The payoffs of the game are generally taken to represent the utility of individual players.
^ The number in the upper triangle of each pair indicates the payoff for Player B; the lower triangle, Player A. Higher numbers represent greater payoff for the individual. http://www.beyondintractability.org/essay/prisoners_dilemma/ 8 January 2010 4:14 UTC www.beyondintractability.org [Source type: FILTERED WITH BAYES]
.^ This assumption, however, can be faulty.
.^ A prototypical paper on game theory in economics begins by presenting a game that is an abstraction of some particular economic situation.
^ See economic game theory. HalfReal: A Dictionary of Video Game Theory 8 January 2010 4:14 UTC www.halfreal.net [Source type: General]
^ Questions about economic or game theory?
.^ Game for more than one player . HalfReal: A Dictionary of Video Game Theory 8 January 2010 4:14 UTC www.halfreal.net [Source type: General]
^ One or more solution concepts are chosen, and the author demonstrates which strategy sets in the presented game are equilibria of the appropriate type.
^ So which refinement is more appropriate as a solution concept? Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
.^ Naturally one might wonder to what use should this information be put.
^ One natural game to use for investigating the evolution of fairness is dividethecake (this is the simplest version of the Nash bargaining game). Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ I tried to spark the use of the term "design economics" in my 2002 manifesto , which might have more naturally included all the things that economists can help design (e.g. Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
Economists and business professors suggest two primary uses:
descriptive and
prescriptive.
Descriptive
.^ It all depends, of course, on how accurately the replicator dynamics models the primary evolutionary forces (cultural or biological) acting on human populations. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ First we will need a complete description of the strategy  how does it behave in regards to other known strategies? Introduction to Game Theory  simple, twostrategy examples 8 January 2010 4:14 UTC www.holycross.edu [Source type: FILTERED WITH BAYES]
.^ Some scholars believe that by finding the equilibria of games they can predict how actual human populations will behave when confronted with situations analogous to the game being studied.
^ Game theory is a technique for analysing how people, firms and governments should behave in strategic situations (in which they must interact with each other), and in deciding what to do must take into account what others are likely to do and how others might respond to what they do. Economics AZ  Economist.com 8 January 2010 4:14 UTC www.economist.com [Source type: FILTERED WITH BAYES]
^ Game theorists study the predicted and actual behaviour of individuals in games, as well as optimal strategies. Game theory  Theories Used in IS Research 8 January 2010 4:14 UTC www.fsc.yorku.ca [Source type: Academic]
.^ However, this use for game theory has also come under criticism.
^ This is where game theory comes in. Advanced NFL Stats: Game Theory and Run/Pass Balance 8 January 2010 4:14 UTC www.advancednflstats.com [Source type: General]
^ Recent developments in game theory. Game Theory Books: A Core Collection & More  Business Library  University of Florida 8 January 2010 4:14 UTC www.uflib.ufl.edu [Source type: Academic]
.^ First, it is criticized because the assumptions made by game theorists are often violated.
^ Shmuel Zamir at the Hebrew University is the last game theorist I know in alphabetical order (but one of the first game theorists I knew). Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
^ What we should therefore expect, because it is the only NE of the game, is a race between the two powers to be the first to attack. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
.^ While it is true that every noncooperative game in which players may use mixed strategies has a Nash equilibrium, some have questioned the significance of this for real agents. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Why has classical game theory helped to predict nonhuman animal behavior more straightforwardly than it has done most human behavior? Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ Also, in darkened arcades many Space Invaders players will have considered their scores highly gratifying even though the game may be technically impossible to win. Game Studies  The Games Economists Play  Implications of Economic Game Theory for the Study of Computer Games 8 January 2010 4:14 UTC gamestudies.org [Source type: FILTERED WITH BAYES]
.^ There are many models that use altruism to explain apparent cooperation, especially in more complicated games. Trust in Game Theory  Unpublished Talk, May, 1997 8 January 2010 4:14 UTC philosophy.wisc.edu [Source type: FILTERED WITH BAYES]
.^ Game theorists respond by comparing their assumptions to those used in physics.
^ Thus while their assumptions do not always hold, they can treat game theory as a reasonable scientific ideal akin to the models used by physicists.
^ Game theorists achieve this mathematically by determining which strategies are numerically dominant and using randomly mixed strategies. A Game Theory Guide to Negotiations  Digital Tonto 8 January 2010 4:14 UTC www.digitaltonto.com [Source type: General]
.^ For this reason, economists use ‘overlapping generations’ models when modeling distribution games. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ Thus while their assumptions do not always hold, they can treat game theory as a reasonable scientific ideal akin to the models used by physicists.
^ The purpose of the course is to introduce basic concepts and results of the modern game theory which are increasingly used in Economics. GAME THEORY Outline 8 January 2010 4:14 UTC www.nes.ru [Source type: Reference]
.^ Keywords: experiments, game theory, mixed strategies. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Keywords: experiments, game theory, 2x2 games. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Keywords: experiments, game theory, evolution. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
.^ Other games with these characteristics such as the game Guess 2/3 of the average and Traveler's dilemma invariably lead to experimental results that deviate markedly from the gametheoretical (Nash equilibrium) predictions.
^ It highlights the fact that one hasn't specified what game people are playing until one specifies the players' preferences and perspective. Trust in Game Theory  Unpublished Talk, May, 1997 8 January 2010 4:14 UTC philosophy.wisc.edu [Source type: FILTERED WITH BAYES]
^ To see this, first notice that there are an infinite number of Nash equilibria for this game. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
.^ There is an ongoing debate regarding the importance of these experiments.
^{[2]}
.^ Alternatively, some authors claim that Nash equilibria do not provide predictions for human populations, but rather provide an explanation for why populations that play Nash equilibria remain in that state.
^ One cannot ask why people play as they do without attributing to them subjective states of belief and preference. Trust in Game Theory  Unpublished Talk, May, 1997 8 January 2010 4:14 UTC philosophy.wisc.edu [Source type: FILTERED WITH BAYES]
^ Human communities evolve cultural norms to select equilibria in these games, and many of these equilibria will be compatible with high levels of apparently altruistic behavior in some (but not all) games. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
.^ However, the question of how populations reach those points remains open.
^ The problem of how the difference [min j max i t ij ]  [max min t ij ] ³ 0 should be subdivided between the players thus remains open. ZeroSum Games with Applications 8 January 2010 4:14 UTC home.ubalt.edu [Source type: Academic]
^ Notice however, that f rom the point of view of A, interactions with B are extremely rare as compared to those with A. Thus, we will assume that we can ignore the fitness contribution of A vs. B interactions to the overall fitness of strat. Introduction to Game Theory  simple, twostrategy examples 8 January 2010 4:14 UTC www.holycross.edu [Source type: FILTERED WITH BAYES]
.^ These are the times that " Game Theory " has been played: . Breakfast of Champions Search Engine 8 January 2010 4:14 UTC wmbr.org [Source type: FILTERED WITH BAYES]
^ VirtualLabs in evolutionary game theory has some tutorials. Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
^ What, then, do these economic game theorists do? Game Studies  The Games Economists Play  Implications of Economic Game Theory for the Study of Computer Games 8 January 2010 4:14 UTC gamestudies.org [Source type: FILTERED WITH BAYES]
.^ Modeling bounded rationality. Game Theory Books: A Core Collection & More  Business Library  University of Florida 8 January 2010 4:14 UTC www.uflib.ufl.edu [Source type: Academic]
^ These models presume either no rationality or bounded rationality on the part of players.
^ There is no bound on the number of offers that can be made but there is a cost to delay for each player.
.^ Despite the name, evolutionary game theory does not necessarily presume natural selection in the biological sense.
^ First, the ‘evolution’ treated by evolutionary game theory need not be biological evolution. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Applications of Evolutionary Game Theory 4.1 A sense of fairness 4.2 The emergence of language. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
.^ Keywords: experiments, game theory, learning, evolution, replicator dynamics. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Keywords: experiments, game theory, evolution. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Keywords: experiments, game theory, learning, dynamics, equilibrium selection. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
Prescriptive or normative analysis

Cooperate 
Defect 
Cooperate 
1, 1 
10, 0 
Defect 
0, 10 
5, 5 
The Prisoner's Dilemma 
.^ Prescriptive or normative analysis Cooperate Defect On the other hand, some scholars see game theory not as a predictive tool for the behavior of human beings, but as a suggestion for how people ought to behave.
^ See economic game theory. HalfReal: A Dictionary of Video Game Theory 8 January 2010 4:14 UTC www.halfreal.net [Source type: General]
^ Now that's good behavioral game theory! Sample Chapter for Camerer, C.F.: Behavioral Game Theory: Experiments in Strategic Interaction. 8 January 2010 4:14 UTC press.princeton.edu [Source type: FILTERED WITH BAYES]
.^ Game for more than one player . HalfReal: A Dictionary of Video Game Theory 8 January 2010 4:14 UTC www.halfreal.net [Source type: General]
^ A selection of strategies by a group of agents is said to be in a Nash equilibrium if each agent's strategy is a bestresponse to the strategies chosen by the other players. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Game for one player . HalfReal: A Dictionary of Video Game Theory 8 January 2010 4:14 UTC www.halfreal.net [Source type: General]
.^ However, this use for game theory has also come under criticism.
^ This is where game theory comes in. Advanced NFL Stats: Game Theory and Run/Pass Balance 8 January 2010 4:14 UTC www.advancednflstats.com [Source type: General]
^ This particular view of game theory has come under recent criticism.
.^ First, in some cases it is appropriate to play a non The Prisoner's Dilemma equilibrium strategy if one expects others to play nonequilibrium strategies as well.
^ If not, one strategy will be increasing relative to the other . Introduction to Game Theory  simple, twostrategy examples 8 January 2010 4:14 UTC www.holycross.edu [Source type: FILTERED WITH BAYES]
^ Since a Nash equilibrium Cooperate 1, 1 10, 0 of a game constitutes one's best response to the actions of the other players, playing a Defect 0, 10 5, 5 strategy that is part of a Nash equilibrium seems appropriate.
For an example, see
Guess 2/3 of the average.
.^ Abstract: The prisoner's dilemma is modified by adding an initial stage in which players can precommit to reward the other one for a cooperative decision in the second stage. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ As an example of the second approach, consider the wellknown Prisoner's Dilemma. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
.^ In the Prisoner's Dilemma, each player pursuing his own self interest leads both players to be worse off than had they not pursued their own selfinterests.
^ Most classical game theoretical analyses predict that rational, selfinterested players will make decisions to reach outcomes, known as Nash equilibria ( 4 ), from which no player can increase his or her own payoff unilaterally. Social DecisionMaking: Insights from Game Theory and Neuroscience  Sanfey 318 (5850): 598  Science 8 January 2010 4:14 UTC www.sciencemag.org [Source type: Academic]
^ More specifically, in a social dilemma "each individual always receives a higher payoff for defecting than for cooperating, but all are better off if all cooperate than if all defect" (Dawes and Messick, 2000, p. Game Studies  The Games Economists Play  Implications of Economic Game Theory for the Study of Computer Games 8 January 2010 4:14 UTC gamestudies.org [Source type: FILTERED WITH BAYES]
Biology

Hawk 
Dove 
Hawk 
v−c, v−c 
2v, 0 
Dove 
0, 2v 
v, v 
The hawkdove game 
.^ Zauner, K. G. (1999) A Payoff Uncertainty Explanation of Results in Experimental Centipede Games, Games and Economic Behavior , 26:1 (January), 157185. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ On Interpreting Payoffs: Morality and Efficiency in Games . Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
.^ Again, one may wonder what has been gained by the evolutionary modelwould it not have been just as easy to determine the cultural dynamics and initial conditions beforehand, constructing the model afterwards? Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ As we will see after discussing evolutionary game theory in a later section, it is possible to maintain this understanding of equilibria in the case of game theory. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ Institutions and evolutionary processes build many environments, and what counts as rational procedure in one environment may not be favoured in another. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
.^ The first approach derives from the work of Maynard Smith and Price and employs the concept of an evolutionarily stable strategy as the principal tool of analysis. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ In 1972, Maynard Smith defined the concept of an evolutionarily stable strategy (hereafter ESS) in the article “Game Theory and the Evolution of Fighting.” However, it was the publication of “The Logic of Animal Conflict,” by Maynard Smith and Price in 1973 that introduced the concept of an ESS into widespread circulation. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Maynard Smith, John and George Price (1973). Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
.^ Although its initial motivation did not involve any of the mental requirements of the Nash equilibrium, every ESS is a Nash equilibrium.
^ These equilibrium concepts are motivated differently depending on the field of application, although they often overlap or coincide.
^ Although the gametheoretic equilibrium of zero is a poor guess about initial choices, players are inexorably drawn toward zero as they learn. Sample Chapter for Camerer, C.F.: Behavioral Game Theory: Experiments in Strategic Interaction. 8 January 2010 4:14 UTC press.princeton.edu [Source type: FILTERED WITH BAYES]
.^ Evolutionary game theory has been used to explain many seemingly incongruous phenomena in nature.
^ In biology, game theory has been used to understand many different phenomena.
^ Some other theorists understand the point of game theory differently. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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.^ It was first used to explain the evolution (and stability) of the approximate 1:1 sex ratios.
^ This theory of the evolution of the sex ratio is normally attributed to R. A. Fisher (The Genetical Theory of Natural Selection.
^ Using the expression for B vs. A that you just wrote and the matrix above , explain whether or not B is stable against invasion by A. (ANS) . Introduction to Game Theory  simple, twostrategy examples 8 January 2010 4:14 UTC www.holycross.edu [Source type: FILTERED WITH BAYES]
.^ We can think of each lineage as ‘trying’ to maximize its reproductive fitness (= expected number of grandchildren) through finding strategies that are optimal given the strategies of other lineages. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ It all depends, of course, on how accurately the replicator dynamics models the primary evolutionary forces (cultural or biological) acting on human populations. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Fisher pointed out that, in such a situation, the evolutionary dynamics lead to the sex ratio becoming fixed at equal numbers of males and females. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
.^ Evolutionary game theory has been used to explain a number of aspects of human behavior. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Evolutionary game theory owes its explicit genesis to Maynard Smith (1982) (**). Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ Applications of Evolutionary Game Theory 4.1 A sense of fairness 4.2 The emergence of language. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
.^ Here are some of the main insights from the game: . Game Theory in The Dark Knight: the opening scene (spoilers)  Mind Your Decisions 8 January 2010 4:14 UTC mindyourdecisions.com [Source type: General]
^ The analysis of signaling games and other communication games has provided some insight into the evolution of communication among animals.
^ The employees in CEE regard the corporate environment as a conflict zone, a zero sum game (in which the gains by some equal the losses to others). Game Theory Applied to Economics 8 January 2010 4:14 UTC samvak.tripod.com [Source type: Original source]
For example, the
mobbing behavior of many species, in which a large number of prey animals attack a larger predator, seems to be an example of spontaneous emergent organization.
.^ Games and Economic Behavior has a web page from which you can see tables of contents. Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
.^ The following subsections provide a brief illustration of the use of evolutionary game theoretic models to explain two areas of human behavior. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Abstract: This paper uses the Luce probabilistic choice rule to analyze behavior in matrix games. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Seminal texts in neuroeconomics, with extensive use of and implications for behavioral game theory, are Montague and Berns (2002) , Glimcher 2003 (**), and Camerer, Loewenstein and Prelec (2005) . Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^{[citation needed]}
.^ Keywords: experiments, game theory, evolution. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Evolutionary game theory has been used to explain a number of aspects of human behavior. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Evolution and the Theory of Games” Journal of Theoretical Biology , 1: 382–403. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^{[3]}
One such phenomenon is known as biological altruism.
.^ They thus acted so as to create situations in which this was true for other Serbs (Hutus) as well. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ There is no way of applying game theory ‘all by itself’, independently of other modelling technologies. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ Briefly, the Prisoner's Dilemma is a situation in which two people are faced with a temptation to act in their personal interest disregarding the interest of the other person. Game Studies  The Games Economists Play  Implications of Economic Game Theory for the Study of Computer Games 8 January 2010 4:14 UTC gamestudies.org [Source type: FILTERED WITH BAYES]
.^ The topic that has received most attention from evolutionary game theorists is altruism , defined as any behaviour by an organism that decreases its own expected fitness in a single interaction but increases that of the other interactor. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ This is so because in such games (as long as the games are finite, that is, terminate after a known number of actions) players and analysts can use a straightforward procedure for predicting outcomes. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
.^ It can be raised with respect to any number of examples, but we will borrow an elegant one from C. Bicchieri ( 1993 ), who also provides the most extensive treatment of the problem found in the literature. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ When they ran this game under hyperscanning, the KingCasas and Montague group obtained the following results. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ The puzzle Fisher faced was this: why is it that the sex ratio is approximately equal in many species where the majority of males never mate? Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^{[4]} .^ Then standing and fighting is each soldier's individually rational course of action after all, because the cost of running is sure to be at least as high as the cost of staying. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ The coordination failure occurs because the Sender and Receiver only pair the appropriate action with the state of the world in one instance, as with 〈Sender 1, Receiver 1〉, or not at all, as with 〈Sender 2, Receiver 3〉. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
.^ Keywords: experiments, game theory, altruism. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ The explanatory irrelevance of evolutionary game theory . Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ The principles of evolutionary game theory are best explained through examples. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
Altruists discriminate between the individuals they help and favor relatives.
.^ As we saw, the puzzle in that game consists in the fact that if the fugitive's reasoning selects a particular bridge as optimal, his pursuer must be assumed to be able to duplicate that reasoning. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
.^ Here are two papers on the early history of experimental economics (and its close relation to game theory): . Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
^ Because they are more difficult for other players to infer, their use increases the probability of miscommunication. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ Often, of course, more than two players compete for the same resource. Game Studies  The Games Economists Play  Implications of Economic Game Theory for the Study of Computer Games 8 January 2010 4:14 UTC gamestudies.org [Source type: FILTERED WITH BAYES]
.^ Distrust towards newcomers is an unfortunate consequence of having any degree of persistent identities, which, as mentioned above, is in itself an essential feature for ensuring trust in many interactions [5] . Game Studies  The Games Economists Play  Implications of Economic Game Theory for the Study of Computer Games 8 January 2010 4:14 UTC gamestudies.org [Source type: FILTERED WITH BAYES]
Helping a sibling for example, has a coefficient of ½, because an individual shares ½ of the alleles in its sibling's offspring. Ensuring that enough of a sibling’s offspring survive to adulthood precludes the necessity of the altruistic individual producing offspring.
^{[4]} .^ The strategic dynamics may be quite different between games which are only played once (singleshot games) and games that are repeated. Game Studies  The Games Economists Play  Implications of Economic Game Theory for the Study of Computer Games 8 January 2010 4:14 UTC gamestudies.org [Source type: FILTERED WITH BAYES]
^ If all people know that these incentives hold for most others, then cooperation will not only be possible, but will be the expected norm, and the war of all against all becomes a general peace. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ This is obviously only dangerous in freeforall games or team games where players can switch between teams. Game Studies  The Games Economists Play  Implications of Economic Game Theory for the Study of Computer Games 8 January 2010 4:14 UTC gamestudies.org [Source type: FILTERED WITH BAYES]
epigenetics, religion, science, etc) persisted through time the playing field becomes larger still, and the discrepancies smaller.
Computer science and logic
.^ Game theory in computer science . Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
^ Game theory plays a leading role in neuroeconomics at two levels. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ Combinatorial Game Theory : Some game theory with connections to operations research and computer science can be found at Combinatorial Game Theory maintained by David Eppstein at UC Irvine. Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
.^ Gintis (2000) (**) has provided a text crammed with terrific problem exercises, which is also unique in that it treats evolutionary game theory as providing the foundational basis for game theory in general. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ Prior to the advent of game theory, therefore, economists were severely limited in the class of circumstances to which they could neatly apply their models. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ Our last point above opens the way to a philosophical puzzle, one of several that still preoccupy those concerned with the logical foundations of game theory. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
.^ Researchers in matching and market design: (game theorists, experimenters and computer scientists interested in matching, auctions and market design) Alphabetically by last name: . Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
^ First, game theory has been used to predict the computations that individual neurons and groups of neurons serving the reward system must perform. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ For this reason, economists use ‘overlapping generations’ models when modeling distribution games. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
.^ Second, the rationality assumptions underlying evolutionary game theory are, in many cases, more appropriate for the modelling of social systems than those assumptions underlying the traditional theory of games. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Moreover, most of the evolutionary game theoretic models developed to date have provided the crudest approximations of the real cultural dynamics driving the social phenomenon in question. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Keywords: experiments, game theory, principal agent model, contracts, linear contracts, inequality aversion, fairness. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
.^ Game theory plays a leading role in neuroeconomics at two levels. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ With the use of game theory algorithms, those responses become predictable, even foreseeable—within an acceptable range of probabilities. How Israel Wages Game Theory Warfare « INTIFADA 8 January 2010 4:14 UTC intifadapalestine.com [Source type: Original source]
^ Keywords: experiments, game theory, coordination, suggested play. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
.^ According to Binmore's ( 1994 , 1998 , 2005a ) model,the basic class of strategic problems facing noneusocial social animals are coordination games. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ Budescu, David V.*, and Amnon Rapoport (1994) Subjective Randomization in One and TwoPerson Games, Journal of Behavioral Decision Making , 7261278. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Game Theory, Rationality and Evolution,” in M. L. Dalla Chiara et al . Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
.^ Ross (2005a) studies the gametheoretic foundations of microeconomics in general, but especially behavioral economics and neuroeconomics, from the perspective of cognitive science. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ We begin our backwardinduction analysis—using a technique called Zermelo's algorithm —with the subgames that arise last in the sequence of play. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ A useful highlevel principle for sorting the literature indexes it to the different auxiliary assumptions with which gametheoretic axioms are applied. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
.^ Frdrick Asselin maintains a list of researchers in Game Theory or Economics and Computer Science . Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
^ Game theory in computer science . Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
^ I n 2005, the Nobel Prize in Economic Science was awarded to Israeli mathematician and game theory specialist Robert J. Aumann, cofounder of the Center for Rationality at Hebrew University. How Israel Wages Game Theory Warfare « INTIFADA 8 January 2010 4:14 UTC intifadapalestine.com [Source type: Original source]
.^ That is, a player can find a set of systems of beliefs for the other players such that any history of the game along an equilibrium path is consistent with that set of systems. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ Researchers in matching and market design: (game theorists, experimenters and computer scientists interested in matching, auctions and market design) Alphabetically by last name: . Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
^ Keywords: experiments, game theory, mixed strategies, posted offer auctions, markets, risk aversion, capacity constraints, cost asymmetries. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^{[5]}
Philosophy

Stag 
Hare 
Stag 
3, 3 
0, 2 
Hare 
2, 0 
2, 2 
Stag hunt 
.^ With the use of game theory algorithms, those responses become predictable, even foreseeable—within an acceptable range of probabilities. How Israel Wages Game Theory Warfare « INTIFADA 8 January 2010 4:14 UTC intifadapalestine.com [Source type: Original source]
^ Evolutionary game theory has been used to explain a number of aspects of human behavior. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Yaw Nyarko is at NYU. Barry O'Neill , at UCLA uses game theory in innovative ways in political science. Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
.^ However, the philosopher who wants game theory to serve as a descriptive and/or normative theory of strategic rationality cannot rest content with this answer. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ At this point, one may see little difference between the two approaches to evolutionary game theory. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Abstract: This paper reports a series of twoperson coordination game experiments in which the outcomes are generally well organized by the notion of risk dominance. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
.^ Keywords: experiments, game theory, coordination, suggested play. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ The first approach can thus be thought of as providing a static conceptual analysis of evolutionary stability. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Abstract: Subjects play several finite prisoner's dilemma games simultaneously, which allows rejection of the common notion that players can be categorized into distinct "types." Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
.^ Shmuel Zamir at the Hebrew University is the last game theorist I know in alphabetical order (but one of the first game theorists I knew). Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
^ First, the game must be repeated, with uncertainty as to which round is the last one. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ It is natural, as a first approximation, to think of sequentialmove games as being ones in which players choose their strategies one after the other, and of simultaneousmove games as ones in which players choose their strategies at the same time. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
.^ Some exciting applications of evolutionary game theory to a range of philosophical issues, on which this article has drawn heavily, is Skyrms (1996) (**). Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ Lewis (1969) (**) puts gametheoretic equilibrium concepts to wider application in philosophy, a program that is carried a good deal further in Skyrms (1996) (**). Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ For a selection of some discussion see, in particular, D'Arms (1996, 2000); D'Arms et al ., 1998; Danielson (1998); Bicchieri (1999); Kitcher (1999); Gintis (2000); Harms (2000); Krebs (2000); Alexander and Skyrms (1999); and Alexander (2000, 2007). Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
.^ Keywords: experiments, game theory, coordination, convention. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Keywords: experiments, game theory, coordination. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Keywords: experiments, game theory, entry games, coordination, mixed strategies. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^{[6]}
.^ However, the philosopher who wants game theory to serve as a descriptive and/or normative theory of strategic rationality cannot rest content with this answer. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ Keywords: experiments, game theory, beliefs, scoring rule, elicitation. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Second, the rationality assumptions underlying evolutionary game theory are, in many cases, more appropriate for the modelling of social systems than those assumptions underlying the traditional theory of games. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
.^ It can be raised with respect to any number of examples, but we will borrow an elegant one from C. Bicchieri ( 1993 ), who also provides the most extensive treatment of the problem found in the literature. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ Philosophical puzzles at this foundational level are critically discussed in Bicchieri (1993) (**). Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^{[9]}
.^ In the Prisoner's Dilemma, each player pursuing his own self interest leads both players to be worse off than had they not pursued their own selfinterests.
^ Thus, people's choices in the UG do not conform to a model in which decisions are driven by financial selfinterest, and neuroscience has begun to offer clues as to the mechanisms underlying these decisions. Social DecisionMaking: Insights from Game Theory and Neuroscience  Sanfey 318 (5850): 598  Science 8 January 2010 4:14 UTC www.sciencemag.org [Source type: Academic]
.^ We will demonstrate this shortly by reference to the most famous (though not the most typical) game, the socalled Prisoner's Dilemma , and to other, more typical, games. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ Keywords: experiments, game theory, prisoner's dilemma, communication, gender effects. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Game theorists objected that MAD was mad, because it set up a Prisoner's Dilemma as a result of the fact that the reciprocal threats were incredible. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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.^ For example, two firms might commit to their marketing strategies independently and in secrecy from one another, but thereafter engage in pricing competition in full view of one another. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ Précis of Evolution of the Social Contract ,” Philosophy and Phenomenological Research , 59 (1): 217–220. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Critical Notice: Evolution of the Social Contract ,” Canadian Journal of Philosophy , 28 (4): 627–652. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^{[10]}
.^ Evolutionary game theory has been used to explain a number of aspects of human behavior. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ The model is used to explain behavior in games with unique mixed strategies. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Other game theory servers: . Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
.^ We will demonstrate this shortly by reference to the most famous (though not the most typical) game, the socalled Prisoner's Dilemma , and to other, more typical, games. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ It's useful to start the discussion here from the case of the Prisoner's Dilemma because it's unusually simple from the perspective of these puzzles. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ To see this, first notice that there are an infinite number of Nash equilibria for this game. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
.^ Keywords: experiments, game theory, psychological game theory. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ However, the philosopher who wants game theory to serve as a descriptive and/or normative theory of strategic rationality cannot rest content with this answer. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ Second, the rationality assumptions underlying evolutionary game theory are, in many cases, more appropriate for the modelling of social systems than those assumptions underlying the traditional theory of games. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
(
see Psychological egoism#Criticism)
Types of games
Cooperative or noncooperative
.^ In this game, individuals choose one of two strategies, typically called “Cooperate” and “Defect.” Here is the general form of the payoff matrix for the prisoner's dilemma: . Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ The two sorts of games are not equivalent, because extensiveform games contain information—about sequences of play and players' levels of information about the game structure—that strategicform games do not. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ The former provides a setwise generalization of the concept of an evolutionarily stable strategy, and the latter extends the concept of an evolutionarily stable strategy to the context of twoplayer extensive form games. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
For instance the legal system requires them to adhere to their promises. In noncooperative games this is not possible.
.^ It is also one of the landmarks of "cooperative" game theory. Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
^ Outcome : an assignment of a set of payoffs, one to each player in the game. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ Abstract: The experiment introduces costless preplay communication into a multiplayer coordination game with multiple Paretoranked equilibria. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
This classification on two binary criteria has been rejected (
Harsanyi 1974).
.^ Moreover, even if an evolutionary game theoretic model indicated that a single historical sequence was capable of producing a given social phenomenon, there remains the important question of why we ought to take this result seriously. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ For now, we have described it just in order to use it to introduce one of the two types of mathematical objects used to represent games: gametrees . Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ Abstract: The paper uses Rabin's fairness model as a basis for explaining results of a standard trust game. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
.^ In this game, the basin of attraction for defection is large unless there is a high proportion of cooperators in round one. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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Considerable efforts have been made to link the two approaches.
.^ As a result, when set into what is intended to be a oneshot PD in the experimental laboratory, people tend to initially play as if the game were a single round of a repeated PD. The repeated PD has many Nash equilibria that involve cooperation rather than defection. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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.^ The Prisoner's Dilemma and Dynamical Systems Associated to Noncooperative Games,” Econometrica , 48: 1617–1634. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Noncooperative Games.’ Annals of Mathematics Journal 54:286295. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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.^ As the values of these two variables increase, game behavior shifts (weakly) in the direction of Nash equilibrium play. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ The Prisoner's Dilemma and Dynamical Systems Associated to Noncooperative Games,” Econometrica , 48: 1617–1634. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Figure 1: The HawkDove Game (The payoffs listed in the matrix are for that of a player using the strategy in the appropriate row, playing against someone using the strategy in the appropriate column. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
Symmetric and asymmetric

E 
F 
E 
1, 2 
0, 0 
F 
0, 0 
1, 2 
An asymmetric game 
Main article:
Symmetric game
.^ If player I plays strategy 2, his payoff depends on which strategy player II has chosen to play. Egwald Operations Research  Game Theory  Introduction 8 January 2010 4:14 UTC www.egwald.ca [Source type: FILTERED WITH BAYES]
^ The fate (or the payoff) of a player in a game depends not only on the actions of that player but also on the other players! Microeconomics  Oligopoly Game Theory 8 January 2010 4:14 UTC www.tutor2u.net [Source type: FILTERED WITH BAYES]
^ E F Symmetric and asymmetric E 1, 2 0, 0 Main article: Symmetric game F 0, 0 1, 2 A symmetric game is a game where the payoffs for playing a particular strategy depend only An asymmetric game on the other strategies employed, not on who is playing them.
.^ In an equilibrium, each player of the game has adopted a strategy that they are unlikely to change.
^ If the identities of the players can be changed without changing the payoff to the strategies, then a game is symmetric.
^ TwoPerson Zero Sum Game In a twoperson zero sum game , each of the two players is given a choice between several prescribed strategies at each turn, and each player's loss is equal to the other player's gain. Chapter G Summary Finite 8 January 2010 4:14 UTC people.hofstra.edu [Source type: FILTERED WITH BAYES]
.^ Many of the commonly studied 2×2 games are symmetric.
^ Most commonly studied asymmetric games are games where there are not identical strategy sets for both players.
^ But many aspects of strategy can be studied and systematized into a science  game theory. American Experience  A Brilliant Madness  Special Features 8 January 2010 4:14 UTC www.pbs.org [Source type: FILTERED WITH BAYES]
.^ We will demonstrate this shortly by reference to the most famous (though not the most typical) game, the socalled Prisoner's Dilemma , and to other, more typical, games. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ Keywords: experiments, game theory, prisoner's dilemma, communication, gender effects. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Game theorists objected that MAD was mad, because it set up a Prisoner's Dilemma as a result of the fact that the reciprocal threats were incredible. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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.^ Human communities evolve cultural norms to select equilibria in these games, and many of these equilibria will be compatible with high levels of apparently altruistic behavior in some (but not all) games. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ For some games, these adjustment paths lead to equilibria that are ruled out by the intuitive criterion and other refinements. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ These “failures of the transitivity of preference” would not occur if people had a welldefined consistent set of preferences. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
.^ However, most games do not have this property. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ However, for most games of reasonable complexity (and hence interest), the extensive form of the game quickly becomes unmanageable. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Clearly, however, if this is applied then a theory of games that incorporated it would not be descriptively true of most people. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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.^ For example, the game pictured to the right is asymmetric despite having identical strategy sets for both players.
^ Most commonly studied asymmetric games are games where there are not identical strategy sets for both players.
^ It is possible, however, for a game to have identical strategies for both players, yet be asymmetric.
.^ For instance, the ultimatum game and similarly the dictator game have different strategies for each player.
^ Game theory is a branch of applied mathematics that studies strategic situations where players choose different actions in an attempt to maximize their returns. Game Theory  Nicolae Sfetcu 8 January 2010 4:14 UTC www.sfetcu.com [Source type: General]
^ TwoPerson Zero Sum Game In a twoperson zero sum game , each of the two players is given a choice between several prescribed strategies at each turn, and each player's loss is equal to the other player's gain. Chapter G Summary Finite 8 January 2010 4:14 UTC people.hofstra.edu [Source type: FILTERED WITH BAYES]
.^ For example, the game pictured to the right is asymmetric despite having identical strategy sets for both players.
^ Most commonly studied asymmetric games are games where there are not identical strategy sets for both players.
^ It is possible, however, for a game to have identical strategies for both players, yet be asymmetric.
.^ For example, the game pictured to the right is asymmetric despite having identical strategy sets for both players.
^ Most commonly studied asymmetric games are games where there are not identical strategy sets for both players.
^ It is possible, however, for a game to have identical strategies for both players, yet be asymmetric.
Zerosum and nonzerosum

A 
B 
A 
–1, 1 
3, –3 
B 
0, 0 
–2, 2 
A zerosum game 
.^ We were able to solve this game straightforwardly because we set the utility functions in such a way as to make it zerosum , or strictly competitive . Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ First, there is the problem that in most nonzerosum games, there is more than one NE, but not all NE look equally plausible as the solutions upon which strategically rational players would hit. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ In an inspection game, one player faces a series of choices either to work for a reward, in which case he is sure to receive it, or to perform another, easier action ("shirking"), in which case he will receive the reward only if the other player (the "inspector") is not monitoring him. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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.^ All other possible combinations of strategies result in the players failing to coordinate. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Each player in a game faces a choice among two or more possible strategies . Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ Matrices, unlike trees, simply show the outcomes, represented in terms of the players' utility functions, for every possible combination of strategies the players might use. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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.^ Because nodes 13 and 14 fall inside a common information set, Selten's Horse has only one subgame (namely, the whole game). Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ We were able to solve this game straightforwardly because we set the utility functions in such a way as to make it zerosum , or strictly competitive . Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ First, there is the problem that in most nonzerosum games, there is more than one NE, but not all NE look equally plausible as the solutions upon which strategically rational players would hit. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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.^ The game “Matching Pennies” illustrates this problem. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Figure 7: Payoff matrix for the game of Matching Pennies (Row wins if the two coins do not match, whereas Column wins if the two coins match). Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Keywords: experiments, game theory, bounded rationality, procedural rationality, coordination games, matching pennies, mixed strategies. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
.^ For this purpose, we'll use the most famous game: the Prisoner's Dilemma. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ Game theorists objected that MAD was mad, because it set up a Prisoner's Dilemma as a result of the fact that the reciprocal threats were incredible. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ We will demonstrate this shortly by reference to the most famous (though not the most typical) game, the socalled Prisoner's Dilemma , and to other, more typical, games. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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.^ Another famous nonzero sum strategy game is The Prisoner's Dilemma: .
^ In this case the sum is not fixed; the game is nonzero sum (or variable sum), as the total sum of gains and losses experienced by the players is not necessarily zero. Game Studies  The Games Economists Play  Implications of Economic Game Theory for the Study of Computer Games 8 January 2010 4:14 UTC gamestudies.org [Source type: FILTERED WITH BAYES]
^ Such games are termed zerosum , as the total sum of the players' gains and losses equals zero. Game Studies  The Games Economists Play  Implications of Economic Game Theory for the Study of Computer Games 8 January 2010 4:14 UTC gamestudies.org [Source type: FILTERED WITH BAYES]
.^ Keywords: experiments, game theory, centipede games, constantsum games. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Keywords: experiments, game theory, learning, constant sum games. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Mookherjee, Dilip, and Barry Sopher (1997) Learning and Decision Costs in Experimental Constant Sum Games, Games and Economic Behavior , 19:1 (April), 97132. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
.^ Abstract: The experiment introduces costless preplay communication into a multiplayer coordination game with multiple Paretoranked equilibria. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ We were able to solve this game straightforwardly because we set the utility functions in such a way as to make it zerosum , or strictly competitive . Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ First, there is the problem that in most nonzerosum games, there is more than one NE, but not all NE look equally plausible as the solutions upon which strategically rational players would hit. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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Simultaneous and sequential
.^ For example, if two competing businesses are both planning marketing campaigns, one might commit to its strategy months before the other does; but if neither knows what the other has committed to or will commit to when they make their decisions, this is a simultaneousmove game. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ But you will recall from earlier in this section that this is just what defines two moves as simultaneous. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ We can solve this new game if we make certain assumptions about the two players' utility functions. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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.^ We can solve this new game if we make certain assumptions about the two players' utility functions. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ Chess, by contrast, is normally played as a sequentialmove game: you see what your opponent has done before choosing your own next action. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ That is, a player might intend to take an action but then slip up in the execution and send the game down some other path instead. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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.^ Matrices, unlike trees, simply show the outcomes, represented in terms of the players' utility functions, for every possible combination of strategies the players might use. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ The simplest games (from the perspective of logical structure) are those in which agents have perfect information , meaning that at every point where each agent's strategy tells her to take an action, she knows everything that has happened in the game up to that point. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ Strategy : a program instructing a player which action to take at every node in the tree where she could possibly be called on to make a choice. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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.^ In the first case, nodes at the top of the page are interpreted as coming earlier in the sequence of actions. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ If what the Receiver does is the correct response, given the state of the world, then both players receive a payoff of 1; if the Receiver performed an incorrect response, then both players receive a payoff of 0. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ For example, if two competing businesses are both planning marketing campaigns, one might commit to its strategy months before the other does; but if neither knows what the other has committed to or will commit to when they make their decisions, this is a simultaneousmove game. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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.^ The difference between simultaneous and sequential games is captured in the different representations discussed above.
^ More interestingly, one could contrast the sequential game described above, in which A knows that her move will be common knowledge before B moves, with a different sequential game in which A is not told that B will know how she moved before he gets to move. Trust in Game Theory  Unpublished Talk, May, 1997 8 January 2010 4:14 UTC philosophy.wisc.edu [Source type: FILTERED WITH BAYES]
^ If at least one node shares its information set with another, while others are alone, the game involves both simultaneous and sequential play, and so is still a game of imperfect information. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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.^ Matrix games are referred to as ‘normalform’ or ‘strategicform’ games, and games as trees are referred to as ‘extensiveform’ games. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ Email Contact: stahl@eco.utexas.edu Stahl, Dale O. (1999) RuleLearning in Symmetric NormalForm Games: Theory and Evidence, Games and Economic Behavior , forthcoming. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ If one seeks to use an evolutionary game theoretic model to explain the normativity attached to a social rule, one must explain how such an approach avoids committing the socalled “naturalistic fallacy” of inferring an oughtstatement from a conjunction of isstatements. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
Perfect information and imperfect information
A game of imperfect information (the dotted line represents ignorance on the part of player 2)
.^ We will assume that the games involved are games of perfect information . Feature Column from the AMS 8 January 2010 4:14 UTC www.ams.org [Source type: FILTERED WITH BAYES]
^ Perfect information and imperfect information A game of imperfect information (the dotted line represents ignorance on the part of player 2) Main article: Perfect information An important subset of sequential games consists of games of perfect information.
^ Most games studied in game theory are imperfectinformation games, although there are some interesting examples of perfectinformation games, including the ultimatum game and centipede game.
.^ Only if all information sets are inhabited by just one node do we have a game of perfect information. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ Game for more than one player . HalfReal: A Dictionary of Video Game Theory 8 January 2010 4:14 UTC www.halfreal.net [Source type: General]
^ A game is one of perfect information if all players know the moves previously made by all other players.
.^ Thus, only sequential games can be games of perfect information, since in simultaneous games not every player knows the actions of the others.
^ The fate (or the payoff) of a player in a game depends not only on the actions of that player but also on the other players! Microeconomics  Oligopoly Game Theory 8 January 2010 4:14 UTC www.tutor2u.net [Source type: FILTERED WITH BAYES]
^ A game is one of perfect information if all players know the moves previously made by all other players.
.^ Other servers devoted to game theory (including some blogs) . Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
^ By contrast, the example of the bridgecrossing game from Section 1 above illustrates a game of imperfect information , since the fugitive must choose a bridge to cross without knowing the bridge at which the pursuer has chosen to wait, and the pursuer similarly makes her decision in ignorance of the actions of her quarry. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ Only if all information sets are inhabited by just one node do we have a game of perfect information. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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.^ The setting is a twostage game with perfect information. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Rosenthal, Robert W. (1981) Games of Perfect Information, Predatory Pricing and the Chain Store Paradox, Journal of Economic Theory , 2592100. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
Perfect information is often confused with
complete information, which is a similar concept.
.^ Own strategies/decisions  Other players' strategies/decisions . Game theory  Theories Used in IS Research 8 January 2010 4:14 UTC www.fsc.yorku.ca [Source type: Academic]
^ The fate (or the payoff) of a player in a game depends not only on the actions of that player but also on the other players! Microeconomics  Oligopoly Game Theory 8 January 2010 4:14 UTC www.tutor2u.net [Source type: FILTERED WITH BAYES]
^ Complete information requires that every player know the strategies and payoffs of the other players but not necessarily the actions.
Infinitely long games
Main article:
Determinacy
.^ For this reason, economists use ‘overlapping generations’ models when modeling distribution games. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ A number of game theory papers and abstracts are available from the webpages of the Center for mathematical studies in economics and management science at Northwestern, and from the CentER for Economic Research at Tilburg. Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
^ There's even a band named Game Theory , and a Game Theory Guild for World of Warcraft players. Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
.^ To see this, first notice that there are an infinite number of Nash equilibria for this game. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ We see that eventually the population, for this particular set of initial conditions, converges to one of the pure Lewisian signalling systems identified above. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Game theorists objected that MAD was mad, because it set up a Prisoner's Dilemma as a result of the fact that the reciprocal threats were incredible. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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.^ Figure 11 illustrates the state space under the continuous replicator dynamics for the senderreceiver game consisting of two states of the world, two signals, and two responses, where players are restricted to using one of the previous four strategies. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Matrices, unlike trees, simply show the outcomes, represented in terms of the players' utility functions, for every possible combination of strategies the players might use. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ Outcome : an assignment of a set of payoffs, one to each player in the game. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
.^ Each player in a game faces a choice among two or more possible strategies . Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ Figure 11 illustrates the state space under the continuous replicator dynamics for the senderreceiver game consisting of two states of the world, two signals, and two responses, where players are restricted to using one of the previous four strategies. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ While it is true that every noncooperative game in which players may use mixed strategies has a Nash equilibrium, some have questioned the significance of this for real agents. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
)
.^ Keywords: experiments, game theory, mixed strategies. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ However, the philosopher who wants game theory to serve as a descriptive and/or normative theory of strategic rationality cannot rest content with this answer. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ Keywords: experiments, game theory, mixed strategies, posted offer auctions, markets, risk aversion, capacity constraints, cost asymmetries. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
Discrete and continuous games
.^ Outcome : an assignment of a set of payoffs, one to each player in the game. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ This brings us right up to the moving frontier of experimental / behavioral applications of classical game theory. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ Evolutionary game theory has been used to explain a number of aspects of human behavior. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
Many concepts can be extended, however.
.^ Figure 11 illustrates the state space under the continuous replicator dynamics for the senderreceiver game consisting of two states of the world, two signals, and two responses, where players are restricted to using one of the previous four strategies. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Outcome : an assignment of a set of payoffs, one to each player in the game. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ That is, a player can find a set of systems of beliefs for the other players such that any history of the game along an equilibrium path is consistent with that set of systems. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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.^ How should we interpret the processes being modeled by computations of NE strategy mixes in games like the rivercrossing one? Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ In this figure, the cake is of size C =10 but all strategies between 0 and 10 inclusive are permitted for either player (including fractional demands). Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ It is natural, as a first approximation, to think of sequentialmove games as being ones in which players choose their strategies one after the other, and of simultaneousmove games as ones in which players choose their strategies at the same time. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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Oneplayer and manyplayer games
.^ Keywords: experiments, game theory, entry game, individual decisions. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Keywords: experiments, game theory, decisions. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ It is also one of the landmarks of "cooperative" game theory. Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
.^ This game involves two players. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ Each player in a game faces a choice among two or more possible strategies . Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ Now the two leaders can do nothing but watch in dismay as the world is blown up—due to a gametheoretic mistake. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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.^ In some games, players can improve their outcomes by taking actions that makes it impossible for them to take what would be her best actions in the corresponding simultaneousmove games. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ It is natural, as a first approximation, to think of sequentialmove games as being ones in which players choose their strategies one after the other, and of simultaneousmove games as ones in which players choose their strategies at the same time. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ They are cases where the signaling system would not work in a population of players who are pairwise randomly assigned to play the senderreceiver game. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
.^ This game involves two players. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ We can solve this new game if we make certain assumptions about the two players' utility functions. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ In this game, individuals choose one of two strategies, typically called “Cooperate” and “Defect.” Here is the general form of the payoff matrix for the prisoner's dilemma: . Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
.^ Abstract: Subjects play several finite prisoner's dilemma games simultaneously, which allows rejection of the common notion that players can be categorized into distinct "types." Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Abstract: Each subject in the game chooses a number, with a prize going to the person whose choice is closest to twothirds of the average of all chosen numbers. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ (Chess can be turned into a simultaneousmove game if the players each call moves while isolated from the common board; but this is a very different game from conventional chess. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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Metagames
.^ If at least one node shares its information set with another, while others are alone, the game involves both simultaneous and sequential play, and so is still a game of imperfect information. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ For some games, these adjustment paths lead to equilibria that are ruled out by the intuitive criterion and other refinements. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Abstract: Subjects play several finite prisoner's dilemma games simultaneously, which allows rejection of the common notion that players can be categorized into distinct "types." Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
Metagames seek to maximize the utility value of the rule set developed.
.^ The 2007 Nobel Prize for "foundations of mechanism design theory " was awarded to Leonid Hurwicz , Eric S. Maskin , and Roger B. Myerson . Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
^ Other market design links (researchers, 2007 Nobel Prize for "foundations of mechanism design theory", other designed markets, class materials, presentations, software, conferences... Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
^ This is natural: just as chemical engineering is related to but different from chemistry, we can expect "microeconomic engineering" and economic design to be different from but related to game theory. Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
.^ We mean merely that the action was taken when an alternative action was available, in some sense of ‘available’ normally established by the context of the particular analysis. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ I tried to spark the use of the term "design economics" in my 2002 manifesto , which might have more naturally included all the things that economists can help design (e.g. Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
^ Matrix games are referred to as ‘normalform’ or ‘strategicform’ games, and games as trees are referred to as ‘extensiveform’ games. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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Subsequent developments have led to the formulation of
drama theory.
History
.^ Keywords: experiments, game theory, mixed strategies. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Keywords: experiments, game theory, minimax theory. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Keywords: experiments, game theory, entry games, coordination, mixed strategies. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
.^ Now the two leaders can do nothing but watch in dismay as the world is blown up—due to a gametheoretic mistake. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ However, two agents in one game, or one agent under different sorts of circumstances, may display very different attitudes to risk. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ A useful highlevel principle for sorting the literature indexes it to the different auxiliary assumptions with which gametheoretic axioms are applied. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^{[11]}^{[12]}
.^ Keywords: experiments, game theory, altruism, intergenerational transfers. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ On the Applicability of Game Theory to Evolution,” Journal of Theoretical Biology , 75 (1): 245–247. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Evolution and the Theory of Games” Journal of Theoretical Biology , 1: 382–403. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
.^ The concept of a Nash equilibrium (see the entry on game theory ) has been the most used solution concept in game theory since its introduction by John Nash in 1950. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Yet a difficulty arises with the use of Nash equilibrium as a solution concept for games: if we restrict players to using pure strategies, not every game has a Nash equilbrium. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Unfortunately, so many refinements of the notion of a Nash equilibrium have been developed that, in many games which have multiple Nash equilibria, each equilibrium could be justified by some refinement present in the literature. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
.^ The following paper grew out of our work on game theory: . Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
^ The mathematical theory of games was invented by John von Neumann and Oskar Morgenstern ( 1944 ). Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ In the preface to Evolution and the Theory of Games , Maynard Smith notes that “[p]aradoxically, it has turned out that game theory is more readily applied to biology than to the field of economic behaviour for which it was originally designed.” It is perhaps doubly paradoxical, then, that the subsequent development of evolutionary game theory has produced a theory which holds great promise for social scientists, and is as readily applied to the field of economic behaviour as that for which it was originally designed. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
.^ A crucial aspect of von Neumann & Morgenstern's (1947) work was the solution to this problem. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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^ At the end of the first chapter of Theory of Games and Economic Behavior , von Neumann and Morgenstern write: . Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Prior to the work of von Neumann & Morgenstern (1947) , situations of this sort were inherently baffling to analysts. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
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.^ At the end of the first chapter of Theory of Games and Economic Behavior , von Neumann and Morgenstern write: . Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ The mathematical theory of games was invented by John von Neumann and Oskar Morgenstern ( 1944 ). Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ Keywords: experiments, game theory, decisions, psychology, behavioral economics. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
.^ That is, a player can find a set of systems of beliefs for the other players such that any history of the game along an equilibrium path is consistent with that set of systems. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ Abstract: This paper reports a series of twoperson coordination game experiments in which the outcomes are generally well organized by the notion of risk dominance. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ In twoperson matrix games with three strategies, the data patterns do not correspond to either Nash or maximin play. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
.^ Keywords: experiments, game theory, cooperation. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Game theory and individual motivation . Trust in Game Theory  Unpublished Talk, May, 1997 8 January 2010 4:14 UTC philosophy.wisc.edu [Source type: FILTERED WITH BAYES]
^ Keywords: experiments, game theory, cooperative games. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
.^ Keywords: experiments, game theory, prisoner's dilemma, incomplete information. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Keywords: experiments, game theory, prisoner's dilemma, number of strategies. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Keywords: experiments, game theory, prisoner's dilemma, probability of continuation. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
.^ The mathematical theory of games was invented by John von Neumann and Oskar Morgenstern ( 1944 ). Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ A strategy for a player, in this game, consists of an amount of cake that he would like. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Abstract: An unprofitable game is one in which maximin strategies do not constitute a Nash equilibrium, yet they guarantee the same payoff as players earn in a Nash equilibrium. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
.^ It is also one of the landmarks of "cooperative" game theory. Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
^ One strategy is ‘better’ than another if it is likely to leave more copies of itself in the next generation, when the game will be played again. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ We can specify one class of games in which NE is always not only necessary but sufficient as a solution concept. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
.^ Keywords: experiments, game theory, prisoner's dilemma, repeated play. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Keywords: experiments, game theory, extensive form, presentation effects. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Keywords: experiments, game theory, reciprocity, trust, extensive form game. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
.^ Game theory in computer science . Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
^ Rebecca Morton at NYU applies game theory to political science. Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
^ Keywords: experiments, game theory, public, voting, political science. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
.^ So which refinement is more appropriate as a solution concept? Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ Thus even behaviorists who aren't impressed with the project of refinements might make use of the concept of subgameperfect equilibrium (SPE), as discussed in Section 2.6 , if they think they're dealing with agents who are very well informed (say, because they're in a familiar institutional setting). Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ Here, we will restrict our attention to the least refined equilibriuminbelief concept, that obtained when we require players to reason in accordance with Bayes's rule. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
.^ We need a ‘cousin’ concept to SPE that we can apply in cases of imperfect information, and we need a new solution procedure to replace Zermelo's algorithm for such games. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ The concept of a Nash equilibrium (see the entry on game theory ) has been the most used solution concept in game theory since its introduction by John Nash in 1950. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
.^ Smith, Vernon L. (1992) Game Theory and Experimental Economics: Beginnings and Early Influences, History of Political Economy , 24:Special Issue 241282. Y2K Bibliography of Experimental Economics and Social Science: Game Theory Experiments 8 January 2010 4:14 UTC people.virginia.edu [Source type: Academic]
^ Frdrick Asselin maintains a list of researchers in Game Theory or Economics and Computer Science . Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
^ For Paul Walker's outline History of game theory see history of game theory (updated to reflect the 2005 Nobel award to Bob Aumann and Tom Schelling ). Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
.^ In the preface to Evolution and the Theory of Games , Maynard Smith notes that “[p]aradoxically, it has turned out that game theory is more readily applied to biology than to the field of economic behaviour for which it was originally designed.” It is perhaps doubly paradoxical, then, that the subsequent development of evolutionary game theory has produced a theory which holds great promise for social scientists, and is as readily applied to the field of economic behaviour as that for which it was originally designed. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ The former provides a setwise generalization of the concept of an evolutionarily stable strategy, and the latter extends the concept of an evolutionarily stable strategy to the context of twoplayer extensive form games. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ The first approach derives from the work of Maynard Smith and Price and employs the concept of an evolutionarily stable strategy as the principal tool of analysis. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
In addition, the concepts of
correlated equilibrium, trembling hand perfection, and
common knowledge^{[13]} were introduced and analyzed.
.^ Robert Aumann and Thomas Schelling shared the Nobel Memorial Prize in Economic Science in 2005 . Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
^ For Paul Walker's outline History of game theory see history of game theory (updated to reflect the 2005 Nobel award to Bob Aumann and Tom Schelling ). Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
^ But now consider the threeplayer imperfectinformation game below known as ‘Selten's horse’ (for its inventor, Nobel Laureate Reinhard Selten, and because of the shape of its tree; taken from Kreps (1990) , p. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
.^ The lack of a dynamical theory in the traditional theory of games . Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
^ Schelling worked on dynamic models, early examples of evolutionary game theory.
^ Evolution, evolutionary game theory, learning, and dynamics . Al Roth's game theory, experimental economics, and market design page 8 January 2010 4:14 UTC kuznets.fas.harvard.edu [Source type: FILTERED WITH BAYES]
.^ Equilibrium selection issues are often more fruitfully addressed in the context of extensiveform games. Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ The news for the fans of justice gets more cheerful still if we introduce correlated play . Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]
 Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC setis.library.usyd.edu.au [Source type: FILTERED WITH BAYES]
^ Furthermore, experiments with a class of games known as a “beauty pageant” show, quite dramatically, the failure of common knowledge assumptions typically invoked to solve games. Evolutionary Game Theory (Stanford Encyclopedia of Philosophy) 8 January 2010 4:14 UTC plato.stanford.edu [Source type: Academic]
See also
Notes
 ^ Ross, Don. "Game Theory". The Stanford Encyclopedia of Philosophy (Spring 2008 Edition). Edward N. Zalta (ed.). http://plato.stanford.edu/archives/spr2008/entries/gametheory/. Retrieved 20080821.
 ^ Experimental work in game theory goes by many names, experimental economics, behavioral economics, and behavioural game theory are several. For a recent discussion on this field see Camerer (2003).
 ^ Evolutionary Game Theory (Stanford Encyclopedia of Philosophy)
 ^ ^{a} ^{b} Biological Altruism (Stanford Encyclopedia of Philosophy)
 ^ Algorithmic Game Theory. http://www.cambridge.org/journals/nisan/downloads/Nisan_Nonprintable.pdf.
 ^ E. Ullmann Margalit, The Emergence of Norms, Oxford University Press, 1977. C. Bicchieri, The Grammar of Society: the Nature and Dynamics of Social Norms, Cambridge University Press, 2006.
 ^ "SelfRefuting Theories of Strategic Interaction: A Paradox of Common Knowledge ", Erkenntnis 30, 1989: 6985. See also Rationality and Coordination, Cambridge University Press, 1993.
 ^ The Dynamics of Rational Deliberation, Harvard University Press, 1990.
 ^ "Knowledge, Belief, and Counterfactual Reasoning in Games." In Cristina Bicchieri, Richard Jeffrey, and Brian Skyrms, eds., The Logic of Strategy. New York: Oxford University Press, 1999.
 ^ For a more detailed discussion of the use of Game Theory in ethics see the Stanford Encyclopedia of Philosophy's entry game theory and ethics.
 ^ James Madison, Vices of the Political System of the United States, April, 1787. Link
 ^ Jack Rakove, "James Madison and the Constitution", History Now, Issue 13 September 2007. Link
 ^ Although common knowledge was first discussed by the philosopher David Lewis in his dissertation (and later book) Convention in the late 1960s, it was not widely considered by economists until Robert Aumann's work in the 1970s.
References
Textbooks and general references
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