CLOSED-LOOP CONVERGENCE FOR MEAN FIELD GAMES WITH COMMON NOISE

• 成果类型: Article
• 署名作者: Lacker, Daniel; Le Flem, Luc
• 署名单位: Columbia University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1876
• 发表日期: 2023
• 页码: 2681-2733
• 关键词: nash equilibria; finite-state; limit theory; EXISTENCE

摘要

This paper studies the convergence problem for mean field games with common noise. We define a suitable notion of weak mean field equilibria, which we prove captures all subsequential limit points, as n & RARR; & INFIN;, of closed -loop approximate equilibria from the corresponding n-player games. This ex-tends to the common noise setting a recent result of the first author, while also simplifying a key step in the proof and allowing unbounded coefficients and non-i.i.d. initial conditions. Conversely, we show that every weak mean field equilibrium arises as the limit of some sequence of approximate equilibria for the n-player games, as long as the latter are formulated over a broader class of closed-loop strategies which may depend on an additional common signal.