Abstract：This paper investigates a two-person zero-sum semi-Markov game with stopping and control under the expected discounted reward criterion, where players can both use controls to influence the evolution of the game and choose to stop the game. Under some mild conditions, we prove the Shapley equation has a solution. Using this solution, we establish the existence of the value, and construct a Nash equilibrium consisting of stopping times and stationary controls. Additionally, we develop an iterative algorithm to to compute ε-Nash equilibria. Finally, an example of an energy management system is given to illustrate the applications of our results.
郭先平，男，博士，博士生导师，国家杰出青年科学基金获得者，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入担(曾)任国际(SCI) 杂志Advances in Applied Probabihty, 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》等杂志编委。研究兴趣为马氏决策过程、随机博弈等。
