Best-Response dynamics in two-person random games with correlated payoffs

TL;DR

This paper studies two-player finite games with correlated random payoffs, analyzing the existence of pure Nash equilibria and showing that best response dynamics efficiently finds such equilibria as the number of actions grows.

Contribution

It introduces a model interpolating between i.i.d. and potential games, and proves that best response dynamics converges to pure Nash equilibria with high probability for positive correlation.

Findings

Number of pure Nash equilibria analyzed in the model.

Best response dynamics reaches equilibrium with high probability as actions increase.

Model bridges i.i.d. and potential game frameworks.

Abstract

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.