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Graphon Mean Field Games and the GMFG Equations

Banff International Research Station for Mathematical Innovation and Discovery

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.

Mathematics; Probability theory and stochastic processes; Statistics

video/mp4

Author affiliation: McGill University

2021-01-15

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/77101

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/