Splitting methods and short time existence for the master equations in mean field games

  • Pierre Cardaliaguet

    Université Paris-Dauphine; PSL Research University, Paris, France
  • Marco Cirant

    Università di Padova, Italy
  • Alessio Porretta

    Università di Roma Tor Vergata, Italy
Splitting methods and short time existence for the master equations in mean field games cover
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Abstract

We develop a splitting method to prove the well-posedness, in short time, of solutions for two master equations in mean field game (MFG) theory: the second order master equation, describing MFGs with a common noise, and the system of master equations associated with MFGs with a major player. Both problems are infinite-dimensional equations stated in the space of probability measures. Our new approach simplifies and generalizes previous existence results for second order master equations and provides the first existence result for systems associated with MFG problems with a major player.

Cite this article

Pierre Cardaliaguet, Marco Cirant, Alessio Porretta, Splitting methods and short time existence for the master equations in mean field games. J. Eur. Math. Soc. 25 (2023), no. 5, pp. 1823–1918

DOI 10.4171/JEMS/1227