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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.

Keywords

Nash Equilibrium Mixed Strategy Pure Strategy Original Game Normal Form Game 
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

  • 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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