On a classical solution to the master equation of a first order mean field game

Mean field games;Master equation;Hamilton-Jacobi equations;Fixed-point method;Characteristic equations;Wasserstein gradient

Mayorga Tatarin, Sergio ; Gangbo, Wilfrid Swiech, Andrzej Mathematics Yao, Yao De La Llave, Rafael Cvitanovic, Predrag ; Gangbo, Wilfrid

University:Georgia Institute of Technology

Department:Mathematics

关键词: Mean field games;    Master equation;    Hamilton-Jacobi equations;    Fixed-point method;    Characteristic equations;    Wasserstein gradient;   

Others  :  https://smartech.gatech.edu/bitstream/1853/61760/1/MAYORGATATARIN-DISSERTATION-2019.pdf

美国|英语

来源: SMARTech Repository

【 摘 要 】

For a first order (deterministic) mean-field game with nonlocal couplings, a classical solution is constructed for the associated, so-called master equation, a partial differential equation in infinite- dimensional space with a nonlocal term, assuming the time horizon is sufficiently small and the coefficients are smooth enough, without convexity conditions on the individual Hamiltonian. The couplings, albeit smooth, are not assumed to derive from a potential, which makes the result currently the most general one for short time horizon. The approach to obtain the master equation is inspired by that of Gangbo and Święch [GŚ15] for the problem in which the Hamiltonian is quadratic and the couplings derive from a potential, but we use a non-variational method and require further results of the calculus on the Wasserstein space that has been advanced recently by Gangbo et. al. [GC17; Gan18].