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Weak solutions for potential mean field games of controls

Abstract : We analyze a system of partial differential equations that model a potential mean field game of controls, briefly MFGC. Such a game describes the interaction of infinitely many negligible players competing to optimize a personal value function that depends in aggregate on the state and, most notably, control choice of all other players. A solution of the system corresponds to a Nash Equilibrium, a group optimal strategy for which no one player can improve by altering only their own action. We investigate the second order, possibly degenerate, case with non-strictly elliptic diffusion operator and local coupling function. The main result exploits potentiality to employ variational techniques to provide a unique weak solution to the system, with additional space and time regularity results under additional assumptions. New analytical subtleties occur in obtaining a priori estimates with the introduction of an additional coupling that depends on the state distribution as well as feedback.
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https://hal.inria.fr/hal-03058249
Contributor : Laurent Pfeiffer Connect in order to contact the contributor
Submitted on : Friday, December 11, 2020 - 4:29:58 PM
Last modification on : Friday, January 21, 2022 - 3:11:35 AM
Long-term archiving on: : Friday, March 12, 2021 - 8:06:16 PM

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Jameson Graber, Alan Mullenix, Laurent Pfeiffer. Weak solutions for potential mean field games of controls. Nonlinear Differential Equations and Applications, Springer Verlag, 2021, 28 (5), Paper No 50, 34 p. ⟨10.1007/s00030-021-00712-9⟩. ⟨hal-03058249⟩

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