A polynomial-time Nash equilibrium algorithm for repeated games

  • Authors:
  • Michael L. Littman;Peter Stone

  • Affiliations:
  • Department of Computer Science, Rutgers University, Piscataway, NJ 08854-8019, USA;Department of Computer Sciences, The University of Texas at Austin, Austin, TX 78712-0233, USA

  • Venue:
  • Decision Support Systems - Special issue: The fourth ACM conference on electronic commerce
  • Year:
  • 2005

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Abstract

With the increasing reliance on game theory as a foundation for auctions and electronic commerce, efficient algorithms for computing equilibria in multiplayer general-sum games are of great theoretical and practical interest. The computational complexity of finding a Nash equilibrium for a one-shot bimatrix game is a well-known open problem. This paper treats a related but distinct problem-that of finding a Nash equilibrium for an average-payoff repeated bimatrix game, and presents a polynomial-time algorithm. Our approach draws on the well-known ''folk theorem'' from game theory and shows how finite-state equilibrium strategies can be found efficiently and expressed succinctly.