Approximate well-supported nash equilibria below two-thirds

  • Authors:

  • John Fearnley;Paul W. Goldberg;Rahul Savani;Troels Bjerre Sørensen

  • Affiliations:

  • Department of Computer Science, University of Liverpool, UK;Department of Computer Science, University of Liverpool, UK;Department of Computer Science, University of Liverpool, UK;Department of Computer Science, University of Warwick, UK

  • Venue:
  • SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
  • Year:
  • 2012

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Abstract

In an ε-Nash equilibrium, a player can gain at most ε by changing his behaviour. Recent work has addressed the question of how best to compute ε-Nash equilibria, and for what values of ε a polynomial-time algorithm exists. An ε-well-supported Nash equilibrium (ε-WSNE) has the additional requirement that any strategy that is used with non-zero probability by a player must have payoff at most ε less than a best response. A recent algorithm of Kontogiannis and Spirakis shows how to compute a 2/3-WSNE in polynomial time, for bimatrix games. Here we introduce a new technique that leads to an improvement to the worst-case approximation guarantee.