Mean field games systems of first order

2014/01/08 by Cardaliaguet, Pierre, Graber, Philip Jameson · 4 citations
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1401.1789

Abstract

We consider a system of mean field games with local coupling in the deterministic limit. Under general structure conditions on the Hamiltonian and coupling, we prove existence and uniqueness of the weak solution, characterizing this solution as the minimizer of some optimal control of Hamilton-Jacobi and continuity equations. We also prove that this solution converges in the long time average to the solution of the associated ergodic problem.

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• Solving Mean-Field Games with Monotonicity Methods in Banach Spaces
• Beyond separability: convergence rate of vanishing viscosity approximations to mean field games via FBSDE stability

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