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First order mean field games with density constraints : pressure equals price.

Cardaliaguet, Pierre and Mészáros, Alpár R. and Santambrogio, Filippo (2016) 'First order mean field games with density constraints : pressure equals price.', SIAM journal on control and optimization., 54 (5). pp. 2672-2709.

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.

Item Type:Article
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1137/15M1029849
Publisher statement:© 2016, Society for Industrial and Applied Mathematics.
Date accepted:20 July 2016
Date deposited:28 February 2020
Date of first online publication:11 October 2016
Date first made open access:28 February 2020

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