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Graphon mean field games and the GMFG equations

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Post-edited
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 : Researchers
    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

Données de citation

DOI : 10.24350/CIRM.V.19534403
Citer cette vidéo: 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

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