Logarithmic Query Complexity for Approximate Nash Computation in Large Games

  • Paul W. Goldberg
  • Francisco J. Marmolejo Cossío
  • Zhiwei Steven Wu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9928)

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.

Our main result is a randomised algorithm that achieves \(\varepsilon \) approaching \(\frac{1}{8}\) 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 \(\frac{1}{8}\), by introducing a small amount of communication between the players.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Paul W. Goldberg
    • 1
  • Francisco J. Marmolejo Cossío
    • 1
  • Zhiwei Steven Wu
    • 2
  1. 1.University of OxfordOxfordUK
  2. 2.University of PennsylvaniaPhiladelphiaUSA

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