Zero-Sum Stochastic Games with Partial Information and Average Payoff

Abstract

Abstract. We consider discrete time partially observable zero-sum stochastic game with average payoff criterion. We study the game using an equivalent completely observable game. We show that the game has a value and also we come up with a pair of optimal strategies for both the players.

A probability criterion for zero-sum stochastic games

“…As is well-known, the criteria commonly used in stochastic games are the average (payoff) criterion [3,8,13,14,15,16,24,22,25] and the (expected) discounted (payoff) criterion [4,5,20,24] and the many references therein. More precisely, for the game models based on discrete-time stochastic processes, Hernández-Lerma and Lasserre [8] studied the two-person zero-sum dynamic stochastic games under the average criterion in Borel spaces with a possibly unbounded payoff function, established the existence of the solution to the Shapley equation and provided some interesting martingale characterizations of optimal policies; Saha [22] extended some of the results in [8] to the case of partial observations; Sennott [24] discussed both the average and discounted criteria with unbounded payoff functions in the nonzerosum case. For the models based on continuous-time stochastic processes, Guo and Hernández-Lerma studied the discounted criterion in [5] for the zero-sum case and 370 XIANGXIANG HUANG, XIANPING GUO AND JIANPING PENG in [4] for the nonzero-sum case.…”