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An Optimization Approach for Approximate Nash Equilibria

  • Haralampos Tsaknakis
  • Paul G. Spirakis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4858)

Abstract

In this paper we propose a new methodology for determining approximate Nash equilibria of non-cooperative bimatrix games and, based on that, we provide an efficient algorithm that computes 0.3393-approximate equilibria, the best approximation till now. The methodology is based on the formulation of an appropriate function of pairs of mixed strategies reflecting the maximum deviation of the players’ payoffs from the best payoff each player could achieve given the strategy chosen by the other. We then seek to minimize such a function using descent procedures. As it is unlikely to be able to find global minima in polynomial time, given the recently proven intractability of the problem, we concentrate on the computation of stationary points and prove that they can be approximated arbitrarily close in polynomial time and that they have the above mentioned approximation property. Our result provides the best ε till now for polynomially computable ε-approximate Nash equilibria of bimatrix games. Furthermore, our methodology for computing approximate Nash equilibria has not been used by others.

Keywords

Nash Equilibrium Polynomial Time Stationary Point Descent Direction Feasible Direction 
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

  • Haralampos Tsaknakis
    • 1
  • Paul G. Spirakis
    • 1
    • 2
  1. 1.Research Academic Computer Technology Institute (RACTI)Greece
  2. 2.Dept. of Computer Eng. and Informatics, Patras University, PatrasGreece

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