Polynomial Algorithms for Approximating Nash Equilibria of Bimatrix Games

  • Spyros C. Kontogiannis
  • Panagiota N. Panagopoulou
  • Paul G. Spirakis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4286)


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.


Nash Equilibrium Mixed Strategy Pure Strategy Absolute Constant Polynomial Algorithm 
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 2006

Authors and Affiliations

  • Spyros C. Kontogiannis
    • 1
    • 3
  • Panagiota N. Panagopoulou
    • 2
    • 3
  • Paul G. Spirakis
    • 2
    • 3
  1. 1.Computer Science DepartmentUniversity of IoanninaIoanninaGreece
  2. 2.Department of Computer Engineering and InformaticsPatras UniversityGreece
  3. 3.Research Academic Computer Technology InstitutePatras UniversityRion, PatrasGreece

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