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Article Dans Une Revue SIAM Journal on Control and Optimization Année : 2016

First order Mean Field Games with density constraints: Pressure equals Price

Résumé

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's equations à la Brenier. By this observation we manage to obtain a minimal regularity, which allows to write optimality conditions at the level of single agent trajectories and to define a weak notion of Nash equilibrium for our model.
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Dates et versions

hal-01173947 , version 1 (07-07-2015)
hal-01173947 , version 2 (06-12-2016)

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Pierre Cardaliaguet, Alpár Richárd Mészáros, Filippo Santambrogio. First order Mean Field Games with density constraints: Pressure equals Price. SIAM Journal on Control and Optimization, 2016, 54 (5), pp.2672-2709. ⟨hal-01173947v2⟩
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