Probability of a Pure Equilibrium Point in n-Person Games

Melvin Dresher

ResearchPublished 1968

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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Dresher, Melvin, Probability of a Pure Equilibrium Point in n-Person Games. Santa Monica, CA: RAND Corporation, 1968. https://www.rand.org/pubs/research_memoranda/RM5768.html.
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