We consider finite two-player normal form games with random payoffs. Player A's payoffs are i.i.d. from a uniform distribution. Given p in [0, 1], for any action profile, player B's payoff coincides with player A's payoff with probability p and is i.i.d. from the same uniform distribution with probability 1-p. This model interpolates the model of i.i.d. random payoff used in most of the literature and the model of random potential games. First we study the number of pure Nash equilibria in the above class of games. Then we show that, for any positive p, asymptotically in the number of available actions, best response dynamics reaches a pure Nash equilibrium with high probability.

翻译：考虑有限双人正则型博弈，其支付为随机变量。玩家A的支付独立同分布于均匀分布。给定p∈[0,1]，对任意行动组合，玩家B的支付以概率p与玩家A的支付相同，以概率1-p独立同分布于同一均匀分布。该模型对大多数文献采用的独立同分布随机支付模型与随机势博弈模型进行了插值。首先研究上述博弈类别中纯纳什均衡的数量。随后证明，对于任意正数p，当可用行动数量渐近增加时，最佳响应动力学以高概率收敛于纯纳什均衡。