报告人：Prof. Jiacheng Zhang ( The Chinese University of Hong Kong)

时间：2026年6月5日（星期五）上午10:00-12:00

地点：清华大学双清综合楼304

摘要：This talk establishes a primal-dual formulation for continuous-time mean field games (MFGs) and provides a complete analytical characterization of the set of all Nash equilibria (NEs). We first show that for any given mean field flow, the representative player’s control problem with measurable coefficients is equivalent to a linear program over the space of occupation measures. We then establish the dual formulation of this linear program as a maximization problem over smooth sub-solutions of the associated Hamilton-Jacobi-Bellman (HJB) equation, which plays a fundamental role in characterizing NEs of MFGs. Finally, a complete characterization of all NEs for MFGs is established by the strong duality between the linear program and its dual problem. This strong duality is obtained by studying the solvability of the dual problem, and in particular through analyzing the regularity of the associated HJB equation.  Compared with existing approaches for MFGs, the primal-dual formulation and its NE characterization require neither the convexity of the associated Hamiltonian nor the uniqueness of its optimizer, and remain applicable when the HJB equation lacks classical or even continuous solutions.

This is a joint work with Xin Guo, Anran Hu and Yufei Zhang.

报告人简介: Jiacheng Zhang is an Assistant Professor at Department of Statistic, The Chinese University of Hong Kong. Previously, he was a postdoctoral researcher in Industrial Engineering & Operations Research Department at Univeristy of California, Berkeley.  He obtained his Ph. D. in the Department of Operations Research and Financial Engineering at Princeton University in 2021. Prior to these, he received his bachelor's degree in pure and applied Mathematics from Tsinghua University in 2016. His research focus lies in the theory of probability and stochastic optimization. He has worked on stochastic partial differential equations, especially, Mckean-Vlasov type equation, partial differential equations, mathematical finance like stochastic portfolio theory and stochastic volatility modeling in the past few years.

邀请人：梁宗霞