Abstract:This paper studies the vanishing viscosity approximation to mean field games (MFGs) in $\mathbb{R}^d$ with a nonlocal and possibly non-separable Hamiltonian. We prove that the value function converges at a rate of $\mathcal{O}(\beta)$, where $\beta^2$ is the diffusivity constant, which matches the classical convergence rate of vanishing viscosity for Hamilton-Jacobi (HJ) equations. The same rate is also obtained for the approximation of the distribution of players as well as for the gradient of the value function. The proof is a combination of probabilistic and analytical arguments by first analyzing the forward-backward stochastic differential equation associated with the MFG, and then applying a general stability result for HJ equations. Applications of our result to $N$-player games, mean field control, and policy iteration for solving MFGs are also presented.
From: Winston Yu [view email]
[v1]
Sat, 24 May 2025 05:47:23 UTC (589 KB)
[v2]
Thu, 11 Sep 2025 16:29:23 UTC (605 KB)
[v3]
Tue, 28 Jul 2026 03:10:35 UTC (593 KB)
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