An introductory note to mean field games. Theory and some applications

Una nota introductoria a los juegos de campo medio. Teoría y algunas aplicaciones

Main Article Content

Abstract

The fundamental concepts of mean field game theory are presented in a sim­ple way, showing that this can be seen as an ingenious coupling between the Hamilton-Jacobi-Bellman and Fokker-Planck-Kolmogorov equations for the treatment of complex systems with a number of very large agents. The concept of equilibrium for this type of games and some applications of this theory in different fields are also presented.

Downloads

Download data is not yet available.

Article Details

References (SEE)

Almgren, R., y Chriss, N. (2001). Optimal execution of portfolio transactions. Journal of Risk, 3, 5-40.

Carmona, R. (2020). Applications of mean field games in financial engineering and economic theory. arXiv preprint arXiv:2012.05237.

Carmona, R., Delarue, F., y Lacker, D. (2017). Mean field games of timing and models for bank runs. Applied Mathematics & Optimization, 76, 217-260.

Carmona, R., Fouque, J.-P., y Sun, L.-H. (2013). Mean field games and systemic risk. arXiv preprint arXiv:1308.2172.

Chan, P., y Sircar, R. (2017). Fracking, renewables, and mean field games. SIAM Review, 59(3), 588-615.

Delarue, F. (2017). Mean field games: A toy model on an erd¨os-renyi graph. ESAIM: Proceedings and Surveys, 60, 1-26.

Lasry, J.-M., y Lions, P.-L. (2006). Jeux `a champ moyen. i–le cas stationnaire. Comptes Rendus Math´ematique, 343(9), 619-625.

Nourian, M., Caines, P. E., Malhame, R. P., y Huang, M. (2012). Nash, social and centralized solutions to consensus problems via mean field control theory. IEEE Transactions on Automatic Control, 58(3), 639-653.

Citado por