A class of infinite horizon mean field games on networks.

Authors
  • ACHDOU Yves
  • DAO Manh khang
  • LEY Olivier
  • TCHOU Nicoletta
Publication date
2019
Publication type
Journal Article
Summary 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.
Publisher
American Institute of Mathematical Sciences (AIMS)
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