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A Lagrangian approach for aggregative mean field games of controls with mixed and final constraints

Abstract : The objective of this paper is to analyze the existence of equilibria for a class of deterministic mean field games of controls. The interaction between players is due to both a congestion term and a price function which depends on the distributions of the optimal strategies. Moreover, final state and mixed state-control constraints are considered, the dynamics being nonlinear and affine with respect to the control. The existence of equilibria is obtained by Kakutani's theorem, applied to a fixed point formulation of the problem. Finally, uniqueness results are shown under monotonicity assumptions.
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Preprints, Working Papers, ...
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https://hal.inria.fr/hal-03174167
Contributor : Justina Gianatti <>
Submitted on : Thursday, March 18, 2021 - 11:54:33 PM
Last modification on : Tuesday, March 23, 2021 - 11:57:49 AM

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Bonnans-Gianatti-Pfeiffer.pdf
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  • HAL Id : hal-03174167, version 1
  • ARXIV : 2103.10743

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Joseph Frédéric Bonnans, Justina Gianatti, Laurent Pfeiffer. A Lagrangian approach for aggregative mean field games of controls with mixed and final constraints. 2021. ⟨hal-03174167⟩

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