Entropic optimal planning for path-dependent mean field games - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year : 2022

Entropic optimal planning for path-dependent mean field games

Abstract

In the context of mean field games, with possible control of the diffusion coefficient, we consider a path-dependent version of the planning problem introduced by P.L. Lions: given a pair of marginal distributions $(\mu_0, \mu_1)$, find a specification of the game problem starting from the initial distribution $\mu_0$, and inducing the target distribution $\mu_1$ at the mean field game equilibrium. Our main result reduces the path-dependent planning problem into an embedding problem, that is, constructing a McKean-Vlasov dynamics with given marginals $(\mu_0,\mu_1)$. Some sufficient conditions on $(\mu_0,\mu_1)$ are provided to guarantee the existence of solutions. We also characterize, up to integrability, the minimum entropy solution of the planning problem. In particular, as uniqueness does not hold anymore in our path-dependent setting, one can naturally introduce an optimal planning problem which would be reduced to an optimal transport problem along with controlled McKean-Vlasov dynamics.
Fichier principal
Vignette du fichier
MFG_Planning_2022_10_23_Resubmit.pdf (369.26 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03903130 , version 1 (16-12-2022)

Identifiers

Cite

Zhenjie Ren, Xiaolu Tan, Nizar Touzi, Junjian Yang. Entropic optimal planning for path-dependent mean field games. 2022. ⟨hal-03903130⟩
62 View
41 Download

Altmetric

Share

Gmail Facebook X LinkedIn More