Finding any nontrivial coarse correlated equilibrium is hard

Siddharth Barman, Katrina Ligett

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

8 Scopus citations

Abstract

One of the most appealing aspects of the (coarse) correlated equilibrium concept is that natural dynamics quickly arrive at approximations of such equilibria, even in games with many players. In addition, there exist polynomial-time algorithms that compute exact (coarse) correlated equilibria. In light of these results, a natural question is how good are the (coarse) correlated equilibria that can arise from any efficient algorithm or dynamics. In this paper we address this question, and establish strong negative results. In particular, we show that in multiplayer games that have a succinct representation, it is NP-hard to compute any coarse correlated equilibrium (or approximate coarse correlated equilibrium) with welfare strictly better than the worst possible. The focus on succinct games ensures that the underlying complexity question is interesting; many multiplayer games of interest are in fact succinct. Our results imply that, while one can efficiently compute a coarse correlated equilibrium, one cannot provide any nontrivial welfare guarantee for the resulting equilibrium, unless P = NP. We show that analogous hardness results hold for correlated equilibria, and persist under the egalitarian objective or Pareto optimality. To complement the hardness results, we develop an algorithmic framework that identifies settings in which we can efficiently compute an approximate correlated equilibrium with near-optimal welfare. We use this framework to develop an efficient algorithm for computing an approximate correlated equilibrium with near-optimal welfare in aggregative games.

Original languageAmerican English
Title of host publicationEC 2015 - Proceedings of the 2015 ACM Conference on Economics and Computation
PublisherAssociation for Computing Machinery, Inc
Pages815-816
Number of pages2
ISBN (Electronic)9781450334105
DOIs
StatePublished - 15 Jun 2015
Externally publishedYes
Event16th ACM Conference on Economics and Computation, EC 2015 - Portland, United States
Duration: 15 Jun 201519 Jun 2015

Publication series

NameEC 2015 - Proceedings of the 2015 ACM Conference on Economics and Computation

Conference

Conference16th ACM Conference on Economics and Computation, EC 2015
Country/TerritoryUnited States
CityPortland
Period15/06/1519/06/15

Keywords

  • Coarse correlated equilibrium
  • Complexity of equilibria
  • Price of anarchy
  • Welfare maximization

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