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First Order Mean Field Games with Density Constraints: Pressure Equals Price

Cardaliaguet, Pierre; Mészáros, Alpár R.; Santambrogio, Filippo

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Authors

Pierre Cardaliaguet

Filippo Santambrogio



Abstract

In this paper we study mean field game systems under density constraints as optimality conditions of two optimization problems in duality. A weak solution of the system contains an extra term, an additional price imposed on the saturated zones. We show that this price corresponds to the pressure field from the models of incompressible Euler equations à la Brenier. By this observation we manage to obtain a minimal regularity, which allows us to write optimality conditions at the level of single-agent trajectories and to define a weak notion of Nash equilibrium for our model.

Citation

Cardaliaguet, P., Mészáros, A. R., & Santambrogio, F. (2016). First Order Mean Field Games with Density Constraints: Pressure Equals Price. SIAM Journal on Control and Optimization, 54(5), 2672-2709. https://doi.org/10.1137/15m1029849

Journal Article Type Article
Acceptance Date Jul 20, 2016
Online Publication Date Oct 11, 2016
Publication Date 2016
Deposit Date Oct 1, 2019
Publicly Available Date Mar 28, 2024
Journal SIAM Journal on Control and Optimization
Print ISSN 0363-0129
Electronic ISSN 1095-7138
Publisher Society for Industrial and Applied Mathematics
Peer Reviewed Peer Reviewed
Volume 54
Issue 5
Pages 2672-2709
DOI https://doi.org/10.1137/15m1029849
Related Public URLs https://arxiv.org/abs/1507.02019

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Copyright Statement
© 2016, Society for Industrial and Applied Mathematics.





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