Subgame-Perfect Equilibria for Stochastic Games

  • Authors:

  • Ashok P. Maitra;William D. Sudderth

  • Affiliations:

  • School of Statistics, University of Minnesota, Minneapolis, Minnesota 55455;School of Statistics, University of Minnesota, Minneapolis, Minnesota 55455

  • Venue:
  • Mathematics of Operations Research
  • Year:
  • 2007

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Abstract

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,...) ∈ SN and, in addition, are continuous when SN is given the product of discrete topologies on S.