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Extragradient methods for mean field games of controls an...
[Submitted on 16 Feb 2026 (v1), last revised 18 Jun 2026 (this v · 2026-06-19 · via math updates on arXiv.org

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Abstract:In this paper we present a numerical scheme to solve coupled mean field forward-backward stochastic differential equations driven by monotone vector fields. This is based on an adaptation of so called extragradient methods by characterizing solutions as zeros of monotone variational inequalities in a Hilbert space. We first introduce the procedure in the context of mean field games of controls and highlight its connection to the fictitious play. Under sufficiently strong monotonicity assumptions, we demonstrate that the sequence of approximate solutions converges exponentially fast. Then we extend the method and main results to general forward backward systems of stochastic differential equations that do not necessarily stem from optimal control.

Submission history

From: charles meynard [view email] [via CCSD proxy]
[v1] Mon, 16 Feb 2026 10:25:39 UTC (211 KB)
[v2] Mon, 16 Mar 2026 13:35:19 UTC (202 KB)
[v3] Thu, 18 Jun 2026 14:19:48 UTC (443 KB)