Mean-field games with a major player

Jean-Michel Lasry; Pierre-Louis Lions

doi:10.1016/j.crma.2018.06.001

Partial differential equations/Game theory

Mean-field games with a major player

Presented by: Pierre-Louis Lions

Jean-Michel Lasry ¹; Pierre-Louis Lions ²

¹ Université Paris-Dauphine–PSL, place du Maréchal-de Lattre-de-Tassigny, 75775 Paris cedex 16, France
² Collège de France–PSL, 3 rue d'Ulm, 75005 Paris, France

Comptes Rendus. Mathématique, Volume 356 (2018) no. 8, pp. 886-890.

Abstract
Résumé

We introduce and study mathematically a new class of mean-field-game systems of equations. This class of equations allows us to model situations involving one major player (or agent) and a “large” group of “small” players.

Nous introduisons et étudions mathématiquement une classe nouvelle de jeux à champ moyen. Les systèmes d'équations que nous présentons permettent de modéliser les situations faisant intervenir un joueur dominant et un « grand » groupe de « petits » joueurs.

Received: 2018-06-06
Accepted: 2018-06-07
Published online: 2018-06-22

DOI: 10.1016/j.crma.2018.06.001

Author's affiliations:

Jean-Michel Lasry ¹; Pierre-Louis Lions ²

¹ Université Paris-Dauphine–PSL, place du Maréchal-de Lattre-de-Tassigny, 75775 Paris cedex 16, France
² Collège de France–PSL, 3 rue d'Ulm, 75005 Paris, France

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     title = {Mean-field games with a major player},
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Jean-Michel Lasry; Pierre-Louis Lions. Mean-field games with a major player. Comptes Rendus. Mathématique, Volume 356 (2018) no. 8, pp. 886-890. doi : 10.1016/j.crma.2018.06.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.06.001/

References
Cited by

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[3] R. Carmona; F. Delarue Probabilistic Theory of Mean Field Games with Applications I–II, Springer, 2018

[4] M. Huang; P.P. Malhamé; P.E. Gaines Large population stochastic dynamics games, Commun. Inf. Syst., Volume 6 (2006), pp. 221-252

[5] P. Krusell; A.D. Sinith Income and wealth heterogeneity in the macroeconomy, J. Polit. Econ., Volume 106 (1998), pp. 867-896

[6] J-M. Lasry; P-L. Lions Jeux à champ moyen I. Le cas stationnaire, C. R. Acad. Sci. Paris, Ser. I, Volume 343 (2006), pp. 619-625

[7] J-M. Lasry; P-L. Lions Jeux à champ moyen II. Horizon fini et contrôle optimal, C. R. Acad. Sci. Paris, Ser. I, Volume 343 (2006), pp. 679-684

[8] J-M. Lasry; P-L. Lions Mean field games, Jpn. J. Math., Volume 2 (2007), pp. 229-260

[9] P-L. Lions, 2007–2012 http://www.college-de-france.fr/site/pierre-louis-lions (Videos and abstracts at)

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