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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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Contributor : Laurent Pfeiffer <>
Submitted on : Friday, December 11, 2020 - 4:29:58 PM
Last modification on : Saturday, December 12, 2020 - 3:59:04 AM


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  • HAL Id : hal-03058249, version 1



Jameson Graber, Alan Mullenix, Laurent Pfeiffer. Weak solutions for potential mean field games of controls. 2020. ⟨hal-03058249⟩



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