We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham Research Online
You are in:

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.


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
Full text:(VoR) Version of Record
Download PDF
Publisher Web site:
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

Save or Share this output

Look up in GoogleScholar