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Comptes Rendus. Mathématique

Jeux à champ moyen, Équations aux dérivées partielles
Strategic advantages in mean field games with a major player
[Avantages stratégiques dans des jeux à champ moyen avec un agent majoritaire]
Comptes Rendus. Mathématique, Tome 358 (2020) no. 2, pp. 113-118.

Cette note porte sur une problématique de modélisation issue de la théorie des jeux à champ moyen. On montre comment il est possible de modéliser des jeux à champ moyen avec un agent majoritaire qui a un avantage stratégique, tout en restant dans un cas où on ne considère que des stratégies markoviennes en boucles fermées pour tous les joueurs. Nous illustrons ce fait autour de trois exemples.

This note is concerned with a modeling question arising from the mean field games theory. We show how to model mean field games involving a major player which has a strategic advantage, while only allowing closed loop markovian strategies for all the players. We illustrate this property through three examples.

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DOI : https://doi.org/10.5802/crmath.1
@article{CRMATH_2020__358_2_113_0,
     author = {Charles Bertucci and Jean-Michel Lasry and Pierre-Louis Lions},
     title = {Strategic advantages in mean field games with a major player},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {113--118},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {2},
     year = {2020},
     doi = {10.5802/crmath.1},
     language = {en},
}
Charles Bertucci; Jean-Michel Lasry; Pierre-Louis Lions. Strategic advantages in mean field games with a major player. Comptes Rendus. Mathématique, Tome 358 (2020) no. 2, pp. 113-118. doi : 10.5802/crmath.1. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.1/

[1] Alain Bensoussan; Man H. M. Chau; Sheung C. P. Yam Mean field games with a dominating player, Appl. Math. Optim., Volume 74 (2016) no. 1, pp. 91-128 | Article | MR 3518868 | Zbl 1348.49031

[2] Charles Bertucci Fokker-planck equations of jumping particles and mean field games of impulse control (2018) (https://arxiv.org/abs/1803.06126) | Zbl 1406.35448

[3] Charles Bertucci Optimal stopping in mean field games, an obstacle problem approach, J. Math. Pures Appl., Volume 120 (2018), pp. 165-194 | Article | MR 3906158 | Zbl 1406.35448

[4] Charles Bertucci; Jean-Michel Lasry; Pierre-Louis Lions Some remarks on mean field games, Commun. Partial Differ. Equations, Volume 44 (2019) no. 3, pp. 205-227 | Article | MR 3941633 | Zbl 1411.91100

[5] Pierre Cardaliaguet; Marco Cirant; Alessio Porretta Remarks on Nash equilibria in mean field game models with a major player (2018) (https://arxiv.org/abs/1811.02811)

[6] René Carmona; François Delarue Probabilistic Theory of Mean Field Games with Applications I-II, Probability Theory and Stochastic Modelling, Volume 83-84, Springer, 2018 | Zbl 1422.91014

[7] Minyi Huang; Roland P Malhamé; Peter E. Caines Large population stochastic dynamic games: closed-loop McKean–Vlasov systems and the Nash certainty equivalence principle, Commun. Inf. Syst., Volume 6 (2006) no. 3, pp. 221-252 | MR 2346927 | Zbl 1136.91349

[8] Per Krusell; Anthony A. Smith Jr Income and wealth heterogeneity in the macroeconomy, J. Polit. Econ., Volume 106 (1998) no. 5, pp. 867-896 | Article

[9] Jean-Michel Lasry; Pierre-Louis Lions Mean field games, Jap. J. Math., Volume 2 (2007) no. 1, pp. 229-260 | Article | MR 2295621 | Zbl 1156.91321

[10] Jean-Michel Lasry; Pierre-Louis Lions Mean-field games with a major player, C. R. Math. Acad. Sci. Paris, Volume 356 (2018) no. 8, pp. 886-890 | Article | MR 3851543 | Zbl 1410.91048

[11] Pierre-Louis Lions Cours au Collège de France, 2007 (https://www.college-de-france.fr/site/pierre-louis-lions/_course.htm)