活动时间：2024-12-26 13:30
活动地点：2号学院楼2432
主讲人：郭先平
主讲人中文简介：
郭先平，中山大学数学学院教授、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。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。
活动内容摘要：
This talk is on the existence and computation of a Nash equilibrium for the zero-sum stochastic games with the risk-sensitive average criterion. For the games with finite states and actions, we first establish the existence of the value and a Nash equilibrium under a new communication condition, which is slightly weaker than the irreducibility condition in the existing literature. Then, by introducing a so-called irreducible coefficient and showing its equivalence to the irreducibility condition, we design a value-iteration algorithm, and prove that it can be used to obtain any $\varepsilon$-approximation of the value in a finite number of iterations. Furthermore, basing on the $\varepsilon$-approximation of the value and the irreducible coefficient, we further provide an approximation-algorithm, and also prove that any $\varepsilon$-Nash equilibrium can be obtained by the approximation-algorithm in a finite number of iterations. Finally, an numerical example of energy management in smart grids is presented to illustrate our results.
主持人：闫理坦、张振中