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New Algorithms for Approximate Nash Equilibria in Bimatrix Games

  • Hartwig Bosse
  • Jaroslaw Byrka
  • Evangelos Markakis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4858)

Abstract

We consider the problem of computing additively approximate Nash equilibria in non-cooperative two-player games. We provide a new polynomial time algorithm that achieves an approximation guarantee of 0.36392. Our work improves the previously best known (0.38197 + ε)-approximation algorithm of Daskalakis, Mehta and Papadimitriou [6].

First, we provide a simpler algorithm, which also achieves 0.38197. This algorithm is then tuned, improving the approximation error to 0.36392. Our method is relatively fast, as it requires solving only one linear program and it is based on using the solution of an auxiliary zero-sum game as a starting point.

Keywords

Nash Equilibrium Mixed Strategy Pure Strategy Polynomial Time Algorithm Optimal Response 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Hartwig Bosse
    • 1
  • Jaroslaw Byrka
    • 1
  • Evangelos Markakis
    • 1
  1. 1.CWI (Center for Math and Computer Science), AmsterdamThe Netherlands

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