New results on the complexity of uniformly mixed nash equilibria

  • Authors:

  • Vincenzo Bonifaci;Ugo Di Iorio;Luigi Laura

  • Affiliations:

  • Department of Computer and System Sciences, University of Rome “La Sapienza”, Rome, Italy;Department of Computer and System Sciences, University of Rome “La Sapienza”, Rome, Italy;Department of Computer and System Sciences, University of Rome “La Sapienza”, Rome, Italy

  • Venue:
  • WINE'05 Proceedings of the First international conference on Internet and Network Economics
  • Year:
  • 2005

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Abstract

We are interested in the complexity of finding Nash equilibria with one uniformly mixed strategy (that is, equilibria in which at least one of the players plays a uniform probability distribution over some set of pure strategies). We show that, even in imitation bimatrix games, where one player has a positive payoff if he plays the same pure strategy as the opponent, deciding the existence of such an equilibrium is an NP-complete problem. We derive this result from the NP-completeness of graph-theoretical problems strictly related to this class of equilibria.