Large Poisson Games

Existence of equilibria is proven for Poisson games with compact type sets and finite action sets. Then three theorems are introduced for characterizing limits of probabilities in Poisson games when the expected number of players becomes large. The magnitude theorem characterizes the rate at which probabilities of events go to zero. The offset theorem characterizes the ratios of probabilities of events that differ by a finite additive translation. The hyperplane theorem estimates probabilities of hyperplane events. These theorems are applied to derive formulas for pivot probabilities in binary elections, and to analyze a voting game that was studied by Ledyard. Journal of Economic Literature Classification Numbers: C63, C70.