Logarithmic Query Complexity for Approximate Nash Computation in Large Games

摘要

We investigate the problem of equilibrium computation for large n-player games. 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 mostly focus on the case where any change of strategy by a player causes other players' payoffs to change by at most. We study algorithms having query access to the game's payoff function, aiming to find epsilon-Nash equilibria. We seek algorithms that obtain epsilon as small as possible, in time polynomial in n. Our main result is a randomised algorithm that achieves epsilon approaching for 2-strategy games in a completely uncoupled setting, where each player observes her own payoff to a query, and adjusts her behaviour independently of other players' payoffs/actions. O(log n) rounds/queries are required. We also show how to obtain a slight improvement over , by introducing a small amount of communication between the players. Finally, we give extension of our results to large games with more than two strategies per player, and alternative largeness parameters.