Weak solutions for first order mean field games with local coupling
Cardaliaguet, Pierre (2015), Weak solutions for first order mean field games with local coupling, in Piernicola Bettiol, Piermarco Cannarsa, Giovanni Colombo, Monica Motta, Franco Rampazzo, Analysis and Geometry in Control Theory and its Applications, Springer : Berlin Heidelberg, p. 111-158. 10.1007/978-3-319-06917-3_5
External document linkhttps://arxiv.org/abs/1305.7015v1
Book titleAnalysis and Geometry in Control Theory and its Applications
Book authorPiernicola Bettiol, Piermarco Cannarsa, Giovanni Colombo, Monica Motta, Franco Rampazzo
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Abstract (EN)Existence and uniqueness of a weak solution for first order mean field game systems with local coupling are obtained by variational methods. This solution can be used to devise $\epsilon-$Nash equilibria for deterministic differential games with a finite (but large) number of players. For smooth data, the first component of the weak solution of the MFG system is proved to satisfy (in a viscosity sense) a time-space degenerate elliptic differential equation.
Subjects / Keywordsgame theory; variational methods; field game systems; Nash equilibrium
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Cardaliaguet, Pierre; Graber, Philip Jameson; Porretta, Alessio; Tonon, Daniela (2015) Article accepté pour publication ou publié