The policy iteration method is a classical algorithm for solving optimal control problems. In this paper, we introduce a policy iteration method for Mean Field Games systems, and we study the convergence of this procedure to a solution of the problem. We also introduce suitable discretizations to numerically solve both stationary and evolutive problems. We show the convergence of the policy iteration method for the discrete problem and we study the performance of the proposed algorithm on some examples in dimension one and two.
A policy iteration method for mean field games / Cacace S.; Camilli F.; Goffi A.. - In: ESAIM. COCV. - ISSN 1292-8119. - STAMPA. - 27:(2021), pp. 85.1-85.19. [10.1051/cocv/2021081]
A policy iteration method for mean field games
Goffi A.
2021
Abstract
The policy iteration method is a classical algorithm for solving optimal control problems. In this paper, we introduce a policy iteration method for Mean Field Games systems, and we study the convergence of this procedure to a solution of the problem. We also introduce suitable discretizations to numerically solve both stationary and evolutive problems. We show the convergence of the policy iteration method for the discrete problem and we study the performance of the proposed algorithm on some examples in dimension one and two.
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