讲座题目：Continuous Behavioural Function Equilibria and Approximation Schemes

          in Bayesian Games with Non-Finite Type and Action Spaces

主 讲 人：大连理工大学张立卫教授

时     间：2018年12月10日（周一）15：15-16：15

地     点：6号学院楼402会议室

主办单位：002cc白菜资讯

摘     要：

Meirowitz (2003) showed existence of continuous behavioural function equilibria for Bayesian games with non-finite type and action spaces. A key condition for the proof of the existence result is equi-continuity of behavioural functions which, according to Meirowitz (2003), is likely to fail or difficult to verify. In this paper, we advance the research by presenting some verifiable conditions for the required equi-continuity, namely some growth conditions of the expected utility functions of each player at equilibria. In the case when the growth is of second order, we demonstrate that the condition is guaranteed by strong concavity of the utility function. Moreover, by using recent research on polynomial decision rules and optimal discretization approaches in stochastic and robust optimization, we propose some approximation schemes for the Bayesian equilibrium problem: first, by restricting the behavioural functions to polynomial functions of certain order over the space of types, we demonstrate that solving a Bayesian polynomial behavioural function equilibrium is down to solving a finite dimensional stochastic equilibrium problem; second, we apply the optimal quantization method due to Pflug and Pichler (2011) to develop an effective discretization scheme for solving the latter. Error bounds are derived for the respective approximation schemes under moderate conditions and both academic examples and numerical results are presented to explain the Bayesian equilibrium problem and their approximation schemes.  (This is a joint work with Dr. Shaoyan Guo and  Prof. Huifu Xu).

主讲人简介：

 张立卫，大连理工大学数学科学学院教授，运筹学与控制论业博士生指导教师，金融数学与保险精算专业博士生指导教师。

   他于1989年，1992年，1998年分别在大连理工大学获得理学学士，硕士，博士学位，1999-2001在中科院计算数学所从事博士后工作。目前的研究兴趣是“矩阵优化”，“随机规划”与“PDE约束控制与优化”。他完成和主持自然科学基金面上基金5项，重点基金子课题两项。发表SCI检索论文100多篇，包括在国际顶级期刊Mathematical Programming, Operations Research, SIAM J. Optimization, Mathematics of Operations Research 和Mathematics of Computation 发表论文10多篇。

张立卫现任中国运筹学会常务理事，中国运筹学会数学规划分会副理事长，中国运筹学会金融工程与金融风险管理分会常务理事。

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