Abstract
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 , of closed-loop approximate equilibria from the corresponding n-player games. This extends 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.
Funding Statement
This work was partially supported by the Air Force Office of Scientific Research Grant FA9550-19-1-0291.
Citation
Daniel Lacker. Luc Le Flem. "Closed-loop convergence for mean field games with common noise." Ann. Appl. Probab. 33 (4) 2681 - 2733, August 2023. https://doi.org/10.1214/22-AAP1876
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