A Class of Infinite Horizon Mean Field Games on Networks

Abstract : We consider stochastic mean field games for which the state space is a network. In the ergodic case, they are described by a system coupling a Hamilton-Jacobi-Bellman equation and a Fokker-Planck equation, whose unknowns are the invariant measure m, a value function u, and the ergodic constant ρ. The function u is continuous and satisfies general Kirchhoff conditions at the vertices. The invariant measure m satisfies dual transmission conditions: in particular, m is discontinuous across the vertices in general, and the values of m on each side of the vertices satisfy special compatibility conditions. Existence and uniqueness are proven, under suitable assumptions.
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Submitted on : Tuesday, May 29, 2018 - 8:34:50 AM
Last modification on : Wednesday, March 27, 2019 - 1:34:51 AM
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  • HAL Id : hal-01802120, version 1
  • ARXIV : 1805.11290

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Yves Achdou, Manh-Khang Dao, Olivier Ley, Nicoletta Tchou. A Class of Infinite Horizon Mean Field Games on Networks. 2018. ⟨hal-01802120⟩

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