Continuous-time mean field games: a primal-dual characterization

Add to your list(s) Download to your calendar using vCal

• Jiacheng Zhang (Chinese University of Hong Kong)
• Tuesday 11 November 2025, 14:40-15:20
• Seminar Room 1, Newton Institute.

If you have a question about this talk, please contact nobody.

SCLW01 - Bridging Stochastic Control And Reinforcement Learning: Theories and Applications

This paper 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 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. Compared with existing approaches for MFGs, the primal-dual formulation and its NE characterization do not require the convexity of the associated Hamiltonian or the uniqueness of its optimizer, and remain applicable when the HJB equation lacks classical or even continuous solutions.

This talk is part of the Isaac Newton Institute Seminar Series series.

This talk is included in these lists:

• All CMS events
• Featured lists
• INI info aggregator
• Isaac Newton Institute Seminar Series
• School of Physical Sciences
• Seminar Room 1, Newton Institute
• bld31

Note that ex-directory lists are not shown.