Rate of Convergence for First-Order Singular Perturbation Problems: Hamilton–Jacobi–Isaacs Equations and Mean Field Games of Acceleration

This work focuses on the rate of convergence for singular perturbation problems for first-order Hamilton–Jacobi equations. We use the nonlinear adjoint method to analyze how the Hamiltonian’s regularizing effect on the initial data influences the convergence rate. As an application we derive the rate of convergence for singularly perturbed two-players zero-sum deterministic differential games (i.e., leading to Hamilton–Jacobi–Isaacs equations) and, subsequently, in case of singularly perturbed mean field games of acceleration. Namely, we show that in both the models the rate of convergence is \(\varepsilon \) $\epsilon$ .