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H 2 Graphon mean field games and the GMFG equations

Auteurs : Caines, Peter E. (Auteur de la Conférence)
CIRM (Editeur )

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introduction to graphons graphon control sytems graphon mean field games LQG-GMFG example

Résumé : Very large networks linking dynamical agents are now ubiquitous and there is significant interest in their analysis, design and control. The emergence of the graphon theory of large networks and their infinite limits has recently enabled the formulation of a theory of the centralized control of dynamical systems distributed on asymptotically infinite networks [Gao and Caines, IEEE CDC 2017, 2018]. Furthermore, the study of the decentralized control of such systems has been initiated in [Caines and Huang, IEEE CDC 2018] where Graphon Mean Field Games (GMFG) and the GMFG equations are formulated for the analysis of non-cooperative dynamical games on unbounded networks. In this talk the GMFG framework will be first be presented followed by the basic existence and uniqueness results for the GMFG equations, together with an epsilon-Nash theorem relating the infinite population equilibria on infinite networks to that of finite population equilibria on finite networks.

Keywords : mean field games; stochastic control; graphons

Codes MSC :
93E20 - Optimal stochastic control
93E35 - Stochastic learning and adaptive control
49N70 - Differential games in calculus of variations
91A13 - Games with infinitely many players

Ressources complémentaires :
https://crowds2019.sciencesconf.org/data/pages/Crowds_book.pdf
https://www.cirm-math.fr/RepOrga/1927/Slides/Caines.pdf

    Informations sur la Vidéo

    Langue : Anglais
    Date de publication : 25/06/2019
    Date de captation : 05/06/2019
    Sous collection : Research talks
    arXiv category : Optimization and Control
    Domaine : Combinatorics ; Control Theory & Optimization ; PDE ; Probability & Statistics
    Format : MP4 (.mp4) - HD
    Durée : 00:33:33
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2019-06-05_Caines.mp4

Informations sur la rencontre

Nom de la rencontre : Foules : modèles et commande / Crowds: Models and Control
Organisateurs de la rencontre : Giua, Alessandro ; Morancey, Morgan ; Piccoli, Benedetto ; Rossi, Francesco ; Wolfram, Marie-Thérèse
Dates : 03/06/2019 - 07/06/2019
Année de la rencontre : 2019
URL Congrès : https://conferences.cirm-math.fr/1927.html

Citation Data

DOI : 10.24350/CIRM.V.19534403
Cite this video as: Caines, Peter E. (2019). Graphon mean field games and the GMFG equations. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19534403
URI : http://dx.doi.org/10.24350/CIRM.V.19534403

Voir aussi

Bibliographie

  • PAULI, Wolfgang et ENZ, Charles P. Thermodynamics and the kinetic theory of gases. Courier Corporation, 2000. -

  • HERRON, Isom H. et FOSTER, Michael R. Partial differential equations in fluid dynamics. Cambridge University Press, 2008. -

  • DOOB, J. L. Stochastic processes. Wiley, 1953. -

  • KARATZAS, Ioannis, SHREVE, Steven. Brownian motion and stochastic calculus. Springer Science & Business Media, vol. 113, 2012. - https://doi.org/10.1007/978-1-4612-0949-2

  • GUÉANT, Olivier. Existence and uniqueness result for mean field games with congestion effect on graphs. Applied Mathematics & Optimization, 2015, vol. 72, no 2, p. 291-303. - https://doi.org/10.1007/s00245-014-9280-2

  • DELARUE, François. Mean field games: A toy model on an Erdös-Renyi graph. ESAIM: Proceedings and Surveys, 2017, vol. 60, p. 1-26. - https://hal.archives-ouvertes.fr/hal-01457409/document

  • LOVÁSZ, László. Large networks and graph limits. American Mathematical Soc., Colloquium Publications, vol. 60, 2012. -

  • LOVÁSZ, László et SZEGEDY, Balázs. Limits of dense graph sequences. Journal of Combinatorial Theory, Series B, 2006, vol. 96, no 6, p. 933-957. - https://doi.org/10.1016/j.jctb.2006.05.002

  • BORGS, Christian, CHAYES, Jennifer, LOVÁSZ, László, et al. Graph limits and parameter testing. In : Proceedings of the thirty-eighth annual ACM symposium on Theory of computing. ACM, 2006. p. 261-270. -

  • BORGS, Christian, CHAYES, Jennifer T., LOVÁSZ, László, et al. Convergent sequences of dense graphs I: Subgraph frequencies, metric properties and testing. Advances in Mathematics, 2008, vol. 219, no 6, p. 1801-1851. - https://arxiv.org/abs/math/0702004

  • BORGS, Christian, CHAYES, Jennifer T., LOVÁSZ, László, et al. Convergent sequences of dense graphs II. Multiway cuts and statistical physics. Annals of Mathematics, 2012, vol. 176, no 1, p. 151-219. - https://doi.org/10.4007/annals.2012.176.1.2

  • GAO, S., CAINES, P. E. Controlling complex networks of linear systems via graphon limits. The Symposium of Controlling Complex Networks of NetSci17, June 2017. -

  • GAO, S. Minimum energy control of arbitrary size networks of linear systems via graphon limits. The SIAM Workshop on Network Science, July 2017. -

  • GAO, S. The control of arbitrary size networks of linear systems via graphon limits: An initial investigation. Proceedings of the 56th IEEE Conference on Decision and Control (CDC), pp. 1052-1057, Dec. 2017. - http://www.cim.mcgill.ca/~sgao/paper/CDC17GraphonMMControl.pdf

  • PARISE, Francesca et OZDAGLAR, Asuman. Graphon games. arXiv preprint arXiv:1802.00080, 2018. - https://arxiv.org/abs/1802.00080

  • GAO, Shuang et CAINES, Peter E. The control of arbitrary size networks of linear systems via graphon limits: An initial investigation. In : 2017 IEEE 56th Annual Conference on Decision and Control (CDC). IEEE, 2017. p. 1052-1057. - https://doi.org/10.1109/CDC.2017.8263796

  • HUANG, Minyi, CAINES, Peter E., et MALHAMÉ, Roland P. The NCE (mean field) principle with locality dependent cost interactions. IEEE Transactions on Automatic Control, 2010, vol. 55, no 12, p. 2799-2805. - https://doi.org/10.1109/TAC.2010.2069410

  • CAINES, Peter E. Mean field games. Encyclopedia of Systems and Control, 2015, p. 706-712. - https://link.springer.com/content/pdf/10.1007/978-1-4471-5102-9_30-1.pdf

  • CAINES, P.E., HUANG, M., MALHAME, R.P. Mean Field Games. In: Basar T., Zaccour G. (eds) Handbook of Dynamic Game Theory. Springer, p. 1-28, 2017. - https://doi.org/10.1007/978-3-319-27335-8_7-1

  • HUANG, Minyi, MALHAMÉ, Roland P., CAINES, Peter E., et al. Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle. Communications in Information & Systems, 2006, vol. 6, no 3, p. 221-252. - http://www.ims.cuhk.edu.hk/~cis/2006.3/05.pdf

  • SZNITMAN, Alain-Sol. Topics in propagation of chaos. In : Ecole d'été de probabilités de Saint-Flour XIX—1989. Springer, Berlin, Heidelberg, 1991. p. 165-251. - https://doi.org/10.1007/BFb0085169

  • FLEMING, Wendell H. et RISHEL, Raymond W. Deterministic and stochastic optimal control. Springer Science & Business Media, 2012. - https://doi.org/10.1007/978-1-4612-6380-7

  • LADYZHENSKAIA, Olga Aleksandrovna, SOLONNIKOV, Vsevolod Alekseevich, et URAL'CEVA, Nina N. Linear and quasi-linear equations of parabolic type. American Mathematical Soc., 1968. -

  • ŞEN, Nevroz et CAINES, Peter E. Mean field game theory with a partially observed major agent. SIAM Journal on Control and Optimization, 2016, vol. 54, no 6, p. 3174-3224. - https://doi.org/10.1137/16M1063010



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