Logarithmic Query Complexity for Approximate Nash Computation in Large Games

Abstract

We investigate the problem of equilibrium computation for “large” n-player games where each player has two pure strategies. Large games have a Lipschitz-type property that no single player’s utility is greatly affected by any other individual player’s actions. In this paper, we assume that a player can change another player’s payoff by at most \(\frac{1}{n}\) by changing her strategy. We study algorithms having query access to the game’s payoff function, aiming to find \(\varepsilon \)-Nash equilibria. We seek algorithms that obtain \(\varepsilon \) as small as possible, in time polynomial in n.