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Subgame-Perfect Equilibria for Stochastic Games

School of Statistics, University of Minnesota, Minneapolis, Minnesota 55455
School of Statistics, University of Minnesota, Minneapolis, Minnesota 55455
maitr001{at}umn.edu
bill{at}stat.umn.edu

For an n-person stochastic game with Borel state space S and compact metric action sets A¹, A²,..., Aⁿ, sufficient conditions are given for the existence of subgame-perfect equilibria. One result is that such equilibria exist if the law of motion q(| s, a) is, for fixed s, continuous in a = (a¹,a²,...,aⁿ) for the total variation norm and the payoff functions f¹, f²,...,fⁿ are bounded, Borel measurable functions of the sequence of states (s₁, s₂,...) S and, in addition, are continuous when S is given the product of discrete topologies on S.

Key Words: stochastic games; subgame-perfect equilibria; Borel sets; finitary functions
History: Received: April 1, 2006; revision received: September 1, 2006;