New Directions in Mean Field Games: MFG Subpopulation Behaviours and Graphon MFG Systems
Abstract
The proposed program of research concerns two new directions in the Mean Field Game (MFG) area which we shall term respectively MFG Subpopulation Behaviours, and Graphon Mean Field Game systems. Each of these topics has its distinct set of fundamental research problems, solution strategies and domains of application, but they are linked by their common foundation in MFG theory. First, the central problem concerning subpopulations of a society of agents within MFG systems theory is to understand the behaviour of finite groups of major agents and finite groups of internally competing or cooperating assemblies of large populations of minor agents. A feature of the newly expanded MFG framework is that agents will also be able to individually or collectively change their dynamical behaviour, that is to say they will be individually modelled by hybrid control systems. This in turn leads to the analysis of coalitions of minor and major agents, including solutions to the heretofore intractable problems of the formation, performance and stability of coalitions. Second, the principal objective of Graphon Mean Field Game (GMFG) theory is to give an overarching theory for the behaviour of populations of agents interacting via MFG dynamics when the agents are distributed over asymptotically infinite networks. This work is based upon the recently developed and profoundly influential graphon theory of large networks and their infinite limits. Centralized control problems have already been formulated by the proposer within the framework of dynamical systems on graphons. The current work greatly extends that analysis to populations of competing dynamical agents for which the game theoretic equilibria are expressed in terms of the newly defined GMFG equations, these being a sweeping generalization of the classical MFG PDEs.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jan 14, 2022
- Source ID
- FA95501910138
Entities
People
- Peter E. Caines
Organizations
- Air Force Office of Scientific Research
- McGill University
- United States Air Force