On non-uniqueness and uniqueness of solutions in finite-horizon Mean Field Games
ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 44.

This paper presents a class of evolutive Mean Field Games with multiple solutions for all time horizons T and convex but non-smooth Hamiltonian H, as well as for smooth H and T large enough. The phenomenon is analysed in both the PDE and the probabilistic setting. The examples are compared with the current theory about uniqueness of solutions. In particular, a new result on uniqueness for the MFG PDEs with small data, e.g., small T, is proved. Some results are also extended to MFGs with two populations.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2018026
Classification : 49L20, 60H10
Mots-clés : Mean Field Games, finite horizon, non-uniqueness of solutions, uniqueness of solutions, multipopulation MFG
Bardi, Martino 1 ; Fischer, Markus 1

1 
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Bardi, Martino; Fischer, Markus. On non-uniqueness and uniqueness of solutions in finite-horizon Mean Field Games. ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 44. doi : 10.1051/cocv/2018026. https://www.numdam.org/articles/10.1051/cocv/2018026/

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