Probability of a pure equilibrium point in n-person games

Abstract

A “random” n-person non-cooperative game—the game that prohibits communication and therefore coalitions among the n players—is shown to have with high probability a pure strategy solution. Such a solution is by definition an equilibrium point or a set of strategies, one for each player, such that if n−1 players use their equilibrium strategies then the n-th player has no reason to deviate from his equilibrium strategy. It is shown that the probability of a solution in pure strategies for large random n-person games converges to (1−1/e) for all n≥2.