Quantitative Convergence for Displacement Monotone Mean Field Games with Controlled Volatility

• 成果类型: Article
• 署名作者: Jackson, Joe; Tangpib, Ludovic
• 署名单位: University of Chicago; Princeton University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2023.0106
• 发表日期: 2024
• 页码: 2527-2564
• 关键词: master equation; BEHAVIOR

摘要

We study the convergence problem for mean field games with common noise and controlled volatility. We adopt the strategy recently put forth by Laurie re and the second author, using the maximum principle to recast the convergence problem as a question of forward-backward propagation of chaos (i.e., (conditional) propagation of chaos for systems of particles evolving forward and backward in time). Our main results show that displacement monotonicity can be used to obtain this propagation of chaos, which leads to quantitative convergence results for open-loop Nash equilibria for a class of mean field games. Our results seem to be the first (quantitative or qualitative) that apply to games in which the common noise is controlled. The proofs are relatively simple and rely on a wellknown technique for proving wellposedness of forward-backward stochastic differential equations, which is combined with displacement monotonicity in a novel way. To demonstrate the flexibility of the approach, we also use the same arguments to obtain convergence results for a class of infinite horizon discounted mean field games.