Geodesic
On the turnpike property for mean field games
Minimax theory and its applications, Tome 3 (2018) no. 2
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Weconsider the behavior of mean field games systems in the long horizon, under the assumption of monotonicity of the coupling term. Assuming that the Hamiltonian is globally Lipschitz and locally uniformly convex, we show that the time dependent solution is exponentially close to the ergodic stationary state in the long intermediate stages. This is evidence of the socalled exponential turnpike property for optimal control problems. Indeed, our proof follows a general approach which relies on the stabilization through the Riccati feedback of the associated linearized system.
Mots-clés : Mean field games, monotonicity, ergodic stationary state, exponential turnpike prop erty, optimal control 
@article{MTA_2018_3_2_a4,
     author = {Alessio Porretta},
     title = {On the turnpike property for mean field games},
     journal = {Minimax theory and its applications},
     year = {2018},
     volume = {3},
     number = {2},
     zbl = {1406.49025},
     url = {http://geodesic.mathdoc.fr/item/MTA_2018_3_2_a4/}
}
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Alessio Porretta. On the turnpike property for mean field games. Minimax theory and its applications, Tome 3 (2018) no. 2. http://geodesic.mathdoc.fr/item/MTA_2018_3_2_a4/