Logarithmic Query Complexity for Approximate Nash Computation in Large Games

Paul W. Goldberg, Francisco J. Marmolejo-Cossío, Zhiwei Steven Wu

Research output: Contribution to journalArticlepeer-review

Abstract

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 1n. 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 18 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 18, 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.

Original languageEnglish (US)
Pages (from-to)26-53
Number of pages28
JournalTheory of Computing Systems
Volume63
Issue number1
DOIs
StatePublished - Jan 15 2019

Bibliographical note

Funding Information:
Francisco J. Marmolejo-Cossío supported by the Mexican National Council of Science and Technology (CONACyT)

Keywords

  • Equilibrium computation
  • Game theory
  • Lipschitz games
  • Multi-player games
  • Uncoupled dynamics

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