2022/09/26 by Hlafo Alfie Mimun, Mimun, Hlafo Alfie, Matteo Quattropani +3
Decision Sciences · Physics and Astronomy · Social Sciences · #Game Theory and Applications #Opinion Dynamics and Social Influence #Evolutionary Game Theory and Cooperation
paper · pdf · doi:10.48550/arxiv.2209.12967
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.