Mean field games equations with quadratic Hamiltonian: a specific\n approach

2011/06/16 by Olivier Guéant, Guéant, Olivier · 5 citations
Economics, Econometrics and Finance · Mathematics · #Analysis of PDEs (math.AP) #Economic theories and models #FOS: Mathematics #Numerical Analysis (math.NA) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1106.3269

openalex publication_date 2011/06/16 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

Mean field games models describing the limit of a large class of stochastic\ndifferential games, as the number of players goes to +\∞, have been\nintroduced by J.-M. Lasry and P.-L. Lions. We use a change of variables to\ntransform the mean field games (MFG) equations into a system of simpler coupled\npartial differential equations, in the case of a quadratic Hamiltonian. This\nsystem is then used to exhibit a monotonic scheme to build solutions of the MFG\nequations. Effective numerical methods based on this constructive scheme are\npresented and numerical experiments are carried out.\n

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