Closed-loop convergence for mean field games with common noise

DOI10.1214/22-AAP1876zbMATH Open1519.49026arXiv2107.03273OpenAlexW3181839803MaRDI QIDQ6109922

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Publication date: 31 July 2023

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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 $noinfty$, 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.

Full work available at URL: https://arxiv.org/abs/2107.03273

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