【摘要】In this talk we introduce a probability criterion into two-person zero-sum discrete-time non-stationary Markov games, and show a mild condition, under which we establish a comparison theorem and derive a sequence of Shapley equations for the probability criterion. Using the comparison theorem and the Shapley equations, we not only prove the existences of the value of the game and a Nash equilibrium, but also provide a value iteration algorithm for computing  (at least approximating) the value of the game and Nash equilibria. Finally, an inventory-production example is presented to illustrate the applications of our results.

【报告人简介】郭先平，教授，博士生导师，国家杰出青年科学基金获得者（2009年），1996年于中南大学获博士学位，2002于中山大学晋升为教授，2003年入选教育部优秀青年教师资助计划，2004年入选教育部新世纪优秀人才支持计划，2010年被评为珠江学者特聘教授。担（曾）任国际（SCI）杂志 Advances in Applied Probability，Journal of Applied Probability，Science China Mathematics，Journal of Dynamics and Games，及国内期刊《中国科学：数学》、《应用数学学报》、《应用概率统计》、《运筹学学报》等杂志编委。研究兴趣为马氏决策过程、随机博弈、风险控制、排队优化等。