Geodesic
Some estimates for stationary extended mean field games
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (2013), pp. 24-31.

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Mean field games theory is a recent area of study introduced by Lions and Lasry in a series of seminal papers in 2006. Mean field games model situations of competition between large number of rational agents that play noncooperative dynamic games under certain symmetry assumptions. In this paper we consider quasivariational mean field games system with additional dependence on a velocity field of the players. We obtain certain estimates for the solutions to this system. In a forthcoming paper we intend to obtain an existence result using this kind of estimates and continuation method.
Keywords: mean field games, velocity field dependence, stationary.
Mots-clés : quasivariational 
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V. K. Voskanyan; D. Gomes. Some estimates for stationary extended mean field games. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (2013), pp. 24-31. http://geodesic.mathdoc.fr/item/UZERU_2013_1_a4/

[1] M. Huang, P.E. Caines, R.P. Malhamè, “Large-Population Cost-Coupled LQG Problems with Nonuniform Agents: Individual-Mass Behavior and Decentralized $\varepsilon$-Nash Equilibria”, Trans. Automat. Control, 52:9 (2007), 1560–1571 | DOI | MR

[2] M. Huang, R.P. Malhamè, P.E. Caines, “Large-Population Stochastic Dynamic Games: ClosedLoop McKean-Vlasov Systems and the Nash Certainty Equivalence Principle”, Commun. Inf. Syst., 6:3 (2006), 221–251 | MR

[3] J.- M. Lasry, P.- L. Lions, “Jeux à Champ Moyen. I. Le Cas Stationnaire”, C. R. Math. Acad. Sci., 343:9 (2006), 619–625 | DOI | MR | Zbl

[4] J.- M. Lasry, P.- L. Lions, “Jeux à Champ Moyen. II. Horizon Fini et Contrôle Optimal”, C. R. Math. Acad. Sci., 343:10 (2006), 679–684 | DOI | MR | Zbl

[5] J.- M. Lasry, P.- L. Lions, “Jeux Mean Field Games”, Jpn. J. Math., 2:1 (2007), 229–260 | DOI | MR | Zbl

[6] J.- M. Lasry, P.- L. Lions, Jeux Mean Field Games, Cahiers de la Chaire Finance et Développement Durable, 2007 | MR

[7] J.- M. Lasry, P.- L. Lions, O. Gueant, “Mean Field Games and Applications”, Paris-Princeton Lectures on Mathematical Finance, 2010 | MR

[8] J.- M. Lasry, P.- L. Lions, O. Gueant, Application of Mean Field Games to Growth Theory, Preprint, 2010

[9] A. Lachapelle, J. Salomon, G. Turinici, “Computation of Mean Field Equilibria in Economics”, Mathematical Models and Methods in Applied Sciences, 20:4 (2010), 567–588 | DOI | MR | Zbl

[10] Y. Achdou, I.C. Dolcetta, Mean Field Games: Numerical Methods, Preprint, 2010 | MR

[11] F. Camilli, Y. Achdou, I.C. Dolcetta, Mean Field Games: Numerical Methods for the Planning Problem, Preprint, 2010

[12] D. Gomes, J. Mohr, R.R. Souza, “Discrete Time, Finite State Space Mean Field Games”, Journal de Mathematiques Pures et Appliquées, 93:2 (2010) | MR | Zbl

[13] D. Gomes, J. Mohr, R.R. Souza, Continuous Time Finite State Mean Field Games, Preprint, 2011

[14] D. Gomes, “A Stochastic Analogue of Aubry-Mather Theory”, Nonlinearity, 15:3 (2002), 581–603 | DOI | MR | Zbl

[15] O. Gueant, Mean Field Games and Applications to Economics, Ph.D. Thesis, Université Paris Dauphine, Paris, 2009

[16] P. Cardaliaguet, J.- M. Lasry, P.- L. Lions, A. Porretta, “Long Time Average of Mean Field Games”, Networks and Heterogeneous Media, 7:2 (2012), 279–301 | DOI | MR | Zbl

[17] D. Gomes, H. Sanchez-Morgado, On the Stochastic Evans-Aronsson Problem, Preprint, 2011

[18] D. Gomes, G. Pires, H. Sanchez-Morgado, A-Priori Estimates for Stationary Mean-Field Games, Preprint, 2012 | MR