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.

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Decision Support Systems, Vol. 39 (2005), pp. 55-66.

@article{DSS04, title={A Polynomial-time Nash Equilibrium Algorithm for Repeated Games}, author={Michael L. Littman and Peter Stone}, volume={39}, journal={Decision Support Systems}, pages={55-66}, url="http://www.cs.utexas.edu/users/ai-lab?DSS04", year={2005} }