Embedded Graphon Mean Field Game Systems

Group Research Seminar at Berkeley

Speaker: Peter Caines

Zoom link
Meeting ID: 983 8143 0081
Passcode: 070166
 

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 enabled the formulation of theories of centralized control of large population dynamical systems distributed on asymptotically infinite networks [S. Gao and PEC, IEEECDC 2017, IEEE TAC 2020] and of Graphon Mean Field Games on such networks [PEC and M. Huang, IEEE CDC 2018, SICON 2021]. In this talk we present the basic existence and uniqueness results for the GMFG equations, and then the epsilon-Nash results relating infinite population equilibria on infinite networks to those of finite population equilibria on finite networks.

Further, for networks whose vertices are embedded in a compact subset M ⊂R^m, convergent subsequences of vertex sets and edge sets exist in M and M^2 respectively. Subject to simple conditions, the differentiation of functions on graphon limits is then defined and this permits, in particular, the location of maximal and minimal Nash value nodes for Embedded GMFG systems.

Work with Rinel Foguen-Tcheundom, Shuang Gao, and Minyi Huang.