Extended mean-field games

  • Pierre-Louis Lions

    Collège de France and Université de Paris-Dauphine, Paris, France
  • Panagiotis E. Souganidis

    The University of Chicago, USA
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We introduce a new class of coupled forward-backward in time systems consisting of a forward Hamilton–Jacobi and a backward quasilinear transport equation, which we call extended mean-field games system. This new class of equations strictly contains the classical mean-field games system with no common noise and its homogenization limit, and optimal transportation-type control problems. We also identify a new and meaningful ‘‘monotonicity’’-type condition that yields well-posedeness. The same condition yields uniqueness in the Hilbertian setting for the master equation without common noise as well as the hyperbolic system describing finite-state mean-field games.

Cite this article

Pierre-Louis Lions, Panagiotis E. Souganidis, Extended mean-field games. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 31 (2020), no. 3, pp. 611–625

DOI 10.4171/RLM/907