The complexity of pure Nash equilibria

  • Authors:
  • Alex Fabrikant;Christos Papadimitriou;Kunal Talwar

  • Affiliations:
  • UC Berkeley, CA;UC Berkeley, CA;UC Berkeley, CA

  • Venue:
  • STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
  • Year:
  • 2004

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Abstract

We investigate from the computational viewpoint multi-player games that are guaranteed to have pure Nash equilibria. We focus on congestion games, and show that a pure Nash equilibrium can be computed in polynomial time in the symmetric network case, while the problem is PLS-complete in general. We discuss implications to non-atomic congestion games, and we explore the scope of the potential function method for proving existence of pure Nash equilibria.