Abstract

With the increasing reliance on game theory as a foundation for auctions and electronic commerce, ecient algorithms for computing equilibria in multiplayer general-sum games are of great theoretical and practical interest. The computational complexity of nding 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 nding a Nash equilibrium for an average-payo repeated bimatrix game, and presents a polynomial-time algorithm. Our approach draws on the well known \folk theorem" from game theory and shows how nite-state equilibrium strategies can be found eciently and expressed succinctly.

Citations