In game theory the large poisson game is a game with a random number of players. More exactly, N, the number of players is a Poisson random variable. The type of each player is selected randomly independently of other players types from a given set T. Each player selects an action and then the payoffs are determined.
Contents 
Large Poisson game  the collection (n,T,r,C,u),
where:
n  the average number of
players in the game
T  the set of all possible
types for a player, (same for each player).
r  the probability
distribution over T according
to which the types are selected.
C  the set of all possible
pure choices, (same for each player, same for each type).
u  the payoff (utility)
function.
The total number of players, N is a poisson distributed random
variable:
Stategy 
Nash equilibrium 
Environmental equivalence  from the perspective of each player the number of other players is a Poisson random varible with mean n.
Decomposition property for types  the number of players of the type t is a Poisson random variable with mean nr(t)
Decomposition property for choices  the number of players who have chosen the choice c is a Poisson random variable with mean ...
Pivotal probability ordering Every limit of the form
is equal to 0 or to infinity. This means that all pivotal
probability may be ordered from the most important to the least
important.
Magnitude .
This has a nice form: twice geometric mean minus arithmetic
mean.
Theorem 1. Nash equilibrium exists.
Theorem 2. Nash equilibrium in undominated strategies exists.
Mainly large poisson games are used as models for voting procedures.
