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Weak Solutions for Potential Mean Field Games of Controls by P. Jameson Graber; Alan Mullenix; Laurent Pfeiffer is a Mathematics article available to read on EtoBox.

What is Weak Solutions for Potential Mean Field Games of Controls about?

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 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.

Who reads Weak Solutions for Potential Mean Field Games of Controls?

Author

P. Jameson Graber; Alan Mullenix; Laurent Pfeiffer

Publisher

Springer Science and Business Media LLC

Published

2021

Language

EN

Field

Mathematics (Physical Sciences)