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Article Dans Une Revue Journal of the European Mathematical Society Année : 2023

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

Résumé

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, shortens 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.
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Dates et versions

hal-02454135 , version 1 (24-01-2020)

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Pierre Cardaliaguet, Marco Cirant, Alessio Porretta. Splitting methods and short time existence for the master equations in mean field games. Journal of the European Mathematical Society, 2023, 25 (5), pp.1823-1918. ⟨10.4171/JEMS/1227⟩. ⟨hal-02454135⟩
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