Overview of Constrained Mean Field Games and New Perspectives
When
3:30 – 4:30 p.m., Jan. 27, 2025
Where
Math Room 402
Abstract:
In this talk, I will present an overview of mean field games with state constraints, a topic of growing interest due to its relevance in applications such as pedestrian dynamics and macroeconomic models. State constraints are naturally encountered in these settings, representing boundaries within which agents operate. However, incorporating constraints significantly complicates the analysis, as traditional equilibrium concepts and solutions based on classical PDE systems are no longer applicable.
To address these challenges, I adopt a relaxed formulation of the problem, that allows for the use of set-valued fixed-point arguments to establish the existence of equilibria. By studying the regularity and spatial sensitivity of the relaxed solutions, I show how they can satisfy the Mean Field Games system in a rigorous pointwise sense. This approach not only resolves theoretical difficulties, but also extends the applicability of constrained mean field games to more complex and realistic scenarios.
In addition to providing a comprehensive overview of the field, I will discuss new perspectives and emerging directions, including potential extensions. This talk aims to highlight how mathematical innovation in the study of constrained systems can provide new insights and drive progress across multiple disciplines.
Colloquium Tea Refreshments will be served in the Math Commons Room at 3pm