On Lipschitz solutions of mean field games master equations - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2023

On Lipschitz solutions of mean field games master equations

Résumé

We develop a theory of existence and uniqueness of solutions of MFG master equations when the initial condition is Lipschitz continuous. Namely, we show that as long as the solution of the master equation is Lipschitz continuous in space, it is uniquely defined. Because we do not impose any structural assumptions, such as monotonicity for instance, there is a maximal time of existence for the notion of solution we provide. We analyze three cases: the case of a finite state space, the case of master equation set on a Hilbert space, and finally on the set of probability measures, all in cases involving common noises. In the last case, the Lipschitz continuity we refer to is on the gradient of the value function with respect to the state variable of the player.
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Dates et versions

hal-03980892 , version 1 (09-02-2023)

Identifiants

  • HAL Id : hal-03980892 , version 1

Citer

Charles Bertucci, Jean-Michel Lasry, Pierre-Louis Lions. On Lipschitz solutions of mean field games master equations. 2023. ⟨hal-03980892⟩
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