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

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

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 fie...

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Veröffentlicht in:SIAM journal on control and optimization 2016-01, Vol.54 (5), p.2672-2709
Hauptverfasser: Cardaliaguet, Pierre, Mészáros, Alpár R., Santambrogio, Filippo
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Optimization and Control
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container_title SIAM journal on control and optimization
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creator Cardaliaguet, Pierre
Mészáros, Alpár R.
Santambrogio, Filippo
description 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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title First Order Mean Field Games with Density Constraints: Pressure Equals Price
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