Rates of convergence for the policy iteration method for Mean Field Games systems

Camilli, Fabio; Tang, Qing

doi:10.1016/j.jmaa.2022.126138

Cited by 9 publications

(1 citation statement)

References 21 publications

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“…To design implicit finite difference schemes, iterative methods are needed to reduce the problem to a sequence of linear systems. Iterative methods employed in solving MFGs include Newton's method [6,7,9,28], fixed point iteration, fictitious play, policy iteration [15,29], smoothed policy iteration [34], etc. In particular, numerical solution of MFGs with non-separable Hamiltonian have been discussed in, e.g., [6,7,23,28,29].…”

Section: Introductionmentioning

confidence: 99%

On the Quadratic Convergence of Newton’s Method for Mean Field Games with Non-separable Hamiltonian

Camilli,

Tang

2024

Dyn Games Appl

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We analyze asymptotic convergence properties of Newton’s method for a class of evolutive Mean Field Games systems with non-separable Hamiltonian arising in mean field type models with congestion. We prove the well posedness of the Mean Field Game system with non-separable Hamiltonian and of the linear system giving the Newton iterations. Then, by forward induction and assuming that the initial guess is sufficiently close to the solution of problem, we show a quadratic rate of convergence for the approximation of the Mean Field Game system by Newton’s method. We also consider the case of a nonlocal coupling, but with separable Hamiltonian, and we show a similar rate of convergence.

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