Vertexons and Embedded Graphon Mean Field Games
4Peter Caines (McGill University)
https://simons.berkeley.edu/node/22609
Graph Limits, Nonparametric Models, and Estimation
An embedded vertexon sequence is the sequence of vertex sets of a sequence of graphs in a connected compact set $M$ in $R^{m}$ together with an asymptotically dense partition hierarchy of $M$. Vertexon sequences and the associated graph sequences have subsequential limit measures in $M$ and $M^2$ respectively, independent of the partition hierarchy within a large class. The differentiation of functions on vertexon limits with open support in $M,$ and certain directional derivatives in the support of the associated graphon measure in $M^2,$ may be defined. Consequently, subject to conditions, one may seek stationary node dependent Nash values for Embedded Graphon Mean Field Games (EGMFGs). An example will be given in the case of a class of Linear Quadratic Gaussian EGMFGs.\
Work with Rinel Foguen-Tschuendom, Shuang Gao, Minyi Huang