Polynomial algorithms for approximating nash equilibria of bimatrix games

  • Authors:

  • Spyros C. Kontogiannis;Panagiota N. Panagopoulou;Paul G. Spirakis

  • Affiliations:

  • Computer Science Department, University of Ioannina, Ioannina, Greece;Department of Computer Engineering and Informatics, Patras University, Greece;Department of Computer Engineering and Informatics, Patras University, Greece

  • Venue:
  • WINE'06 Proceedings of the Second international conference on Internet and Network Economics
  • Year:
  • 2006

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Abstract

We focus on the problem of computing an ε-Nash equilibrium of a bimatrix game, when ε is an absolute constant. We present a simple algorithm for computing a $\frac{3}{4}$-Nash equilibrium for any bimatrix game in strongly polynomial time and we next show how to extend this algorithm so as to obtain a (potentially stronger) parameterized approximation. Namely, we present an algorithm that computes a $\frac{2+\lambda}{4}$-Nash equilibrium, where λ is the minimum, among all Nash equilibria, expected payoff of either player. The suggested algorithm runs in time polynomial in the number of strategies available to the players.