Probability of a Pure Equilibrium Point in n-Person Games

by Melvin Dresher

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A random n-person noncooperative game — that game that prohibits communication and therefore coalitions among n players — is shown to have a pure strategy solution with a high probability. A solution of a game is an equilibrium point or set of strategies, one for each player, such that if n-1 players use their equilibrium strategies, then the nth 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 games converges to 1-1/e for all n greater than or equal to 2.

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