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 1/n by changing her strategy. We study algorithms having query access to the game’s payoff function, aiming to find ε-Nash equilibria. We seek algorithms that obtain ε as small as possible, in time polynomial in n. Our main result is a randomised algorithm that achieves ε approaching 1/8 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 1/8, by introducing a small amount of communication between the players.
|Original language||English (US)|
|Title of host publication||Algorithmic Game Theory - 9th International Symposium, SAGT 2016, Proceedings|
|Editors||Martin Gairing, Rahul Savani|
|Number of pages||12|
|State||Published - 2016|
|Event||9th International Symposium on Algorithmic Game Theory, SAGT 2016 - Liverpool, United Kingdom|
Duration: Sep 19 2016 → Sep 21 2016
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Other||9th International Symposium on Algorithmic Game Theory, SAGT 2016|
|Period||9/19/16 → 9/21/16|
Bibliographical notePublisher Copyright:
© Springer-Verlag Berlin Heidelberg 2016.