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Article Dans Une Revue SIAM Journal on Control and Optimization Année : 2023

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

Résumé

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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Dates et versions

hal-03174167 , version 1 (18-03-2021)
hal-03174167 , version 2 (17-01-2022)

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J. Frédéric Bonnans, Justina Gianatti, Laurent Pfeiffer. A Lagrangian approach for aggregative mean field games of controls with mixed and final constraints. SIAM Journal on Control and Optimization, 2023, 61 (1), pp.105-134. ⟨10.1137/21M1407720⟩. ⟨hal-03174167v2⟩
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