Random Bimatrix Games Are Asymptotically Easy to Solve

摘要

We focus on the problem of computing approximate Nash equilibria and well-supported approximate Nash equilibria in random bi-matrix games, where each player's payoffs are bounded and independent random variables, not necessarily identically distributed, but with common expectations. We show that the completely mixed uniform strategy profile, i.e. the combination of mixed strategies (one per player) where each player plays with equal probability each one of her available pure strategies, is with high probability a {the square root of}(ln n/n)-Nash equilibrium and a {the square root of}(3 ln n/n)-well supported Nash equilibrium, where n is the number of pure strategies available to each player. This asserts that the completely mixed, uniform strategy profile is an almost Nash equilibrium for random bimatrix games, since it is, with high probability, an ∈-well-supported Nash equilibrium where ∈ tends to zero as n tends to infinity.