Mean field games systems of first order

Pierre Cardaliaguet 1 Philip Jameson Graber 2, 3
3 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées
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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https://hal.archives-ouvertes.fr/hal-00925905
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Submitted on : Wednesday, January 8, 2014 - 6:24:03 PM
Last modification on : Wednesday, March 27, 2019 - 4:08:29 PM
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  • HAL Id : hal-00925905, version 1
  • ARXIV : 1401.1789

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Pierre Cardaliaguet, Philip Jameson Graber. Mean field games systems of first order. ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2015, 21 (3), pp.690-722. ⟨hal-00925905⟩

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