Finite Horizon Mean Field Games on Networks

Abstract : We consider finite horizon stochastic mean field games in which the state space is a network. They are described by a system coupling a backward in time Hamilton-Jacobi-Bellman equation and a forward in time Fokker-Planck equation. The value function u is continuous and satisfies general Kirchhoff conditions at the vertices. The density m of the distribution of states satisfies dual transmission conditions: in particular, m is generally discontinuous across the vertices, and the values of m on each side of the vertices satisfy special compatibility conditions. The stress is put on the case when the Hamiltonian is Lipschitz continuous. Existence and uniqueness are proven.
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https://hal.archives-ouvertes.fr/hal-02058824
Contributor : Olivier Ley <>
Submitted on : Wednesday, March 6, 2019 - 10:56:27 AM
Last modification on : Wednesday, May 15, 2019 - 3:42:19 AM
Long-term archiving on : Friday, June 7, 2019 - 7:39:10 PM

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  • HAL Id : hal-02058824, version 1
  • ARXIV : 1903.02761

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Yves Achdou, Manh-Khang Dao, Olivier Ley, Nicoletta Tchou. Finite Horizon Mean Field Games on Networks. 2019. ⟨hal-02058824⟩

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