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Chapitres

Graphon mean field games and the GMFG equations

De Peter E. Caines

Apparaît dans la collection : Foules : modèles et commande / Crowds: Models and Control

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.

Informations sur la vidéo

Date de captation 05/06/2019
Date de publication 25/06/2019
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Réalisateur(s) Luca Recanzone
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19534403
Citer cette vidéo Caines, Peter E. (05/06/2019). Graphon mean field games and the GMFG equations. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19534403
URL https://dx.doi.org/10.24350/CIRM.V.19534403

Domaine(s)

Optimisation et contrôle

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

Codes MSC

Document(s)

https://www.cirm-math.fr/RepOrga/1927/Slides/Caines.pdf

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