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An introductory note to mean field games. Theory and some applications ; Una nota introductoria a los juegos de campo medio. Teoría y algunas aplicaciones

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  • Additional Information
    • Publication Information:
      Universidad Externado de Colombia
    • Publication Date:
      2023
    • Collection:
      Revistas Universidad Externado de Colombia
    • 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. ; Se presentan de forma simple los conceptos fundamentales de la teoría de juegos de campo medio, mostrando que esta se puede ver como un ingenioso acople entre ecuaciones de Hamilton-Jacobi-Bellman y Fokker-Planck-Kolmogorov para el tratamiento de sistemas complejos con un número de agentes muy grande. Se presenta también el concepto de equilibrio para este tipo de juegos y algunas aplicaciones de esta teoría en diferentes campos.
    • File Description:
      application/pdf; text/html
    • Relation:
      https://revistas.uexternado.edu.co/index.php/odeon/article/view/8877/14892; https://revistas.uexternado.edu.co/index.php/odeon/article/view/8877/14893; 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.; https://revistas.uexternado.edu.co/index.php/odeon/article/view/8877
    • Online Access:
      https://revistas.uexternado.edu.co/index.php/odeon/article/view/8877
    • Rights:
      Derechos de autor 2023 John Freddy Moreno Trujillo ; http://creativecommons.org/licenses/by-nc-sa/4.0
    • Accession Number:
      edsbas.81F814CD