Скачать или смотреть Peter Caines: Vertexon-Graphons and Embedded GMFG Systems

Atelier/Workshop: Jeux à champ moyen/Mean Field Games
11 Avril/April 11: http://www.crm.umontreal.ca/2022/Game...
Peter Caines: A vertexon in a connected compact set $M$ in $R^{m}$ is defined to be the vertex set of a graph together with an asymptotically dense partition hierarchy of $M$. It is shown that sequences of vertexons have subsequential vertexon limits in $M$ independent of the particular hierarchy employed. Consequently, the differentiation of functions on vertexon limits with open support is well defined. Further, along any convergent vertexon sequence, the associated sequence of graphs has subsequential graph edge limits termed (embedded) graphons; the resulting vertexon-graphon limit pair permits the definition of critical nodes and other features involving differentiation with respect to node location in embedded Graphon Mean Field Game (GMFG) systems, that is to say, GMFG systems with nodes lying in a limiting vertexon in $M \subset R^{m}$. A further feature of vertexon limits is that they provide a form of node population density which extends the local agent population aspect of GMFG systems.