Speaker: Prof. 曹志刚 (Zhigang Cao)

Title: Beyond Global Maximizers: Unveiling the Full Potential of Potential Games

Schedule: April 3, Wed 1:30-3:00 PM

Location: 诚明楼（Chengming Hall） RM315

Introduction: 曹志刚，北京交通大学经济管理学院“卓越百人计划”教授，毕业于中科院数学与系统科学研究院。长期从事合作博弈、交通博弈、网络博弈和算法博弈等方面的研究，在包括 Operations Research、Mathematics of Operations Research、Games and Economic Behavior、Journal of Mathematical Economics、Social Choice and Welfare 等国际顶级期刊发表多篇论文。相关成果曾获中国信息经济学理论贡献奖、系统科学与系统工程青年科技奖、中国决策科学青年科技奖和关肇直青年研究奖等荣誉。先后主持国家自然科学基金委的青年、面上和优青项目。兼任中国“双法”研究会智能决策与博弈分会副理事长、中国运筹学会博弈论分会副理事长、中国系统工程学会副秘书长、中国信息经济学会常务理事、管理科学与工程学会理事和中国运筹学会理事等职务。

Abstract: The potential function method is a powerful tool to study the existence, uniqueness, and refinement of Nash equilibrium (Slade, 1994; Monderer and Shapley, 1996). Global maximizers of a potential function are Nash equilibria of the corresponding strategic game, but not necessarily vice versa. Neither do local maximizers nor stationary points correspond precisely to Nash equilibria. Which type of points of a potential function corresponds precisely to Nash equilibria? The absence of a concise answer may cause at least expositional inconveniences. We point out that they are block coordinate-wise maximizers, a class of points already studied in optimization. Motivated by Tseng (2001), we generalize a result of Neyman (1997) on uniqueness of Nash equilibrium. We also argue that selecting Nash equilibrium via the global maximizers of potentials has certain limitations, and raise the issue of potential selection.