On the existence of classical solutions for stationary extended mean field games

In this paper we consider extended stationary mean-field games, that is mean-field games which depend on the velocity field of the players. We prove various a-priori estimates which generalize the results for quasi-variational mean-field games in Gomes et al. (2012). In addition we use adjoint metho...

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Published inNonlinear analysis Vol. 99; pp. 49 - 79
Main Authors Gomes, Diogo A., Patrizi, Stefania, Voskanyan, Vardan
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.04.2014
Subjects
A-priori estimates
Adjoints
Classical solutions
Continuity
Estimates
Games
Mean field games
Nonlinearity
Players
Regularity
Mean field games
A-priori estimates
Classical solutions
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Summary:In this paper we consider extended stationary mean-field games, that is mean-field games which depend on the velocity field of the players. We prove various a-priori estimates which generalize the results for quasi-variational mean-field games in Gomes et al. (2012). In addition we use adjoint method techniques to obtain higher regularity bounds. Then we establish the existence of smooth solutions under fairly general conditions by applying the continuity method. When applied to standard stationary mean-field games as in Lasry and Lions (2006), Gomes and Sanchez-Morgado (2011) or Gomes et al. (2012) this paper yields various new estimates and regularity properties not available previously. We discuss additionally several examples where the existence of classical solutions can be proved.
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ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2013.12.016