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, 45110 Ioannina, Greece and Research Academic Computer Technology Institute, N. Kazantzaki Street, University of Patra, Rion, 26500 Patra, Greec ...;Research Academic Computer Technology Institute, N. Kazantzaki Street, University of Patra, Rion, 26500 Patra, Greece and Department of Computer Engineering and Informatics, University of Patra, G ...;Research Academic Computer Technology Institute, N. Kazantzaki Street, University of Patra, Rion, 26500 Patra, Greece and Department of Computer Engineering and Informatics, University of Patra, G ...

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2009

Quantified Score

Hi-index 5.29

Visualization

Abstract

We focus on the problem of computing an @e-Nash equilibrium of a bimatrix game, when @e is an absolute constant. We present a simple algorithm for computing a 34-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 2+@l4-Nash equilibrium, where @l 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.