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Graphon mean field games and the GMFG equations

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Post-edited
Authors : Caines, Peter E. (Author of the conference)
CIRM (Publisher )

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

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

Additional resources :
https://crowds2019.sciencesconf.org/data/pages/Crowds_book.pdf
https://www.cirm-math.fr/RepOrga/1927/Slides/Caines.pdf
    Information on the Video

    Film maker : Recanzone, Luca
    Language : English
    Available date : 25/06/2019
    Conference Date : 05/06/2019
    Subseries : Research talks
    arXiv category : Optimization and Control
    Mathematical Area(s) : Combinatorics ; Control Theory & Optimization ; PDE ; Probability & Statistics
    Format : MP4 (.mp4) - HD
    Video Time : 00:33:33
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2019-06-05_Caines.mp4
Information on the Event

Event Title : Foules : modèles et commande / Crowds: Models and Control
Event Organizers : Giua, Alessandro ; Morancey, Morgan ; Piccoli, Benedetto ; Rossi, Francesco ; Wolfram, Marie-Thérèse
Dates : 03/06/2019 - 07/06/2019
Event Year : 2019
Event URL : 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

See Also

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