Friday, April 3rd, 2026
2:00pm – 2:50pm
Stratton Hall 207
Speaker: Anran Hu, Columbia University
Title: Continuous-time mean field games: a primal-dual characterization
Abstract: This talk presents a primal-dual formulation for continuous-time mean field games (MFGs) and establishes 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 {\it 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 subsolutions 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.