“人大数学时间I”第五十三期：郭新
为促进学科交流融合、拓宽师生学术视野、释放科研创新活力，助力人大数学学科走向一流，91黑料 设立“人大数学时间”，以专题研讨、高端学术论坛为载体，搭建数学思想充分碰撞、优秀人才不断涌流、创造活力竞相迸发的舞台。“人大数学时间”将持之以恒，久久为功，立志通过交流与创新、提出重大问题，引领数学学科及相关领域的创新与发展，成为对我国数学发展有贡献意义的平台。以下为“人大数学时间I”第五十三期信息：
议程：
6月11日（星期四）17:00
郭新教授报告及前沿问题探讨
地点：立德楼701
线上：腾讯会议：935-133-908
题目：An alpha-potential game framework for dynamic N-player games
主讲专家：郭新，美国加利福尼亚大学伯克利分校教授
摘要：
Game theory has a long history and the min-max game has been well studied ever since Von Neumann and Nash. The leap from min-max (zero-sum) games to general-sum games is a fundamental escalation in computational and conceptual complexity. Over the past decade, mean field game theory has emerged as a pivotal framework, offering profound theoretical insights and computational advances for the analysis of large-scale, non-zero-sum stochastic games. However, mean field games require homogeneity and weak interaction among players and focus on the limiting behavior when N goes to infinity.
In this talk we will present a new paradigm for dynamic N-player non-cooperative games called alpha-potential games, where the change of a player's value function upon unilateral deviation from her strategy is equal to the change of an alpha-potential function up to an error alpha. This game framework is shown to reduce the challenging task of finding alpha-Nash equilibria for a dynamic game to minimize the associated alpha-potential function. The latter is then shown to be a conditional McKean--Vlasov control problem. In such games, analysis of alpha reveals critical game characteristics, including choices of admissible strategies, the intensity of interactions, and the level of heterogeneity among players. We will discuss through simple examples some recent theoretical developments, their connections with mean-field games, along with a few open problems for this new game framework.
报告人简介：
郭新教授现任美国加州大学伯克利分校Coleman Fung讲席教授，并担任该校工业工程与运筹学系系主任。此前，她曾先后在康奈尔大学（2003–2006年）和IBM研究院（1999–2003年）任职。她是一位享有盛誉、颇具影响力的学者，研究领域涵盖随机过程、控制与博弈、机器学习以及金融数学。她曾担任多家顶级期刊的编委，包括Operations Research、Mathematics of Operations Research、SIAM Journal on Control and Optimization以及Mathematical Finance。她的工作将严谨的数学方法与金融、数据科学、生物学和医疗健康等领域的重要应用紧密结合。值得关注的是，她的研究成果已被业界采纳，实现了数亿美元的成本节约。此外，她还为一些已获美国食品药品监督管理局（FDA）批准的早期癌症检测方法奠定了数学基础。
