LQG mean-field games with ergodic cost

Abstract : We consider stochastic differential games with N players, linear-Gaussian dynamics in arbitrary state-space dimension, and long-time-average cost with quadratic running cost. Admissible controls are feedbacks for which the system is ergodic. We first study the existence of affine Nash equilibria by means of an associated system of N Hamilton-Jacobi-Bellman and N Kolmogorov-Fokker-Planck partial differential equations. We give necessary and sufficient conditions for the existence and uniqueness of quadratic-Gaussian solutions in terms of the solvability of suitable algebraic Riccati and Sylvester equations. Under a symmetry condition on the running costs and for nearly identical players we study the large population limit, N tending to infinity, and find a unique quadratic-Gaussian solution of the pair of Mean Field Game HJB-KFP equations. This extends some of the classical results on Mean Field Games by Huang, Caines, and Malhame and by Lasry and Lions, and the more recent paper by one of the authors in the 1-dimensional case.
Type de document :
Communication dans un congrès
52nd IEEE Control and Decision Conference (CDC), 2013, Florence, Italy. pp.2493 - 2498, 2013, Proceedings of the IEEE 52nd Annual Conference on Decision and Control (CDC). 〈10.1109/CDC.2013.6760255〉
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https://hal.inria.fr/hal-01067480
Contributeur : Estelle Bouzat <>
Soumis le : mardi 23 septembre 2014 - 14:55:48
Dernière modification le : lundi 12 février 2018 - 14:24:05

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Martino Bardi, Fabio S. Priuli. LQG mean-field games with ergodic cost. 52nd IEEE Control and Decision Conference (CDC), 2013, Florence, Italy. pp.2493 - 2498, 2013, Proceedings of the IEEE 52nd Annual Conference on Decision and Control (CDC). 〈10.1109/CDC.2013.6760255〉. 〈hal-01067480〉

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