A Note on Approximate Nash Equilibria

  • Constantinos Daskalakis
  • Aranyak Mehta
  • Christos Papadimitriou
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4286)

Abstract

In view of the intractability of finding a Nash equilibrium, it is important to understand the limits of approximation in this context. A subexponential approximation scheme is known [LMM03], and no approximation better than \(1\over 4\) is possible by any algorithm that examines equilibria involving fewer than logn strategies [Alt94]. We give a simple, linear-time algorithm examining just two strategies per player and resulting in a \(1\over 2\)-approximate Nash equilibrium in any 2-player game. For the more demanding notion of well-supported approximate equilibrium due to [DGP06] no nontrivial bound is known; we show that the problem can be reduced to the case of win-lose games (games with all utilities 0–1), and that an approximation of \(5\over 6\) is possible contingent upon a graph-theoretic conjecture.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Constantinos Daskalakis
    • 1
  • Aranyak Mehta
    • 2
  • Christos Papadimitriou
    • 1
  1. 1.University of CaliforniaBerkeleyUSA
  2. 2.IBM Almaden Research CenterSan JoseUSA

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