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- W2951948908 abstract "We consider stationary viscous Mean-Field Games systems in the case of local, decreasing and unbounded coupling. These systems arise in ergodic mean-field game theory, and describe Nash equilibria of games with a large number of agents aiming at aggregation. We show how the dimension of the state space, the behavior of the coupling and the Hamiltonian at infinity affect the existence and non-existence of regular solutions. Our approach relies on the study of Sobolev regularity of the invariant measure and a blow-up procedure which is calibrated on the scaling properties of the system. In very special cases we observe uniqueness of solutions. Finally, we apply our methods to obtain new existence results for MFG systems with competition, namely when the coupling is local and increasing." @default.
- W2951948908 created "2019-06-27" @default.
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- W2951948908 date "2016-02-12" @default.
- W2951948908 modified "2023-09-27" @default.
- W2951948908 title "Stationary focusing Mean Field Games" @default.
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