On the Graphon Mean Field Game Equations: Individual Agent Affine Dynamics and Mean Field Dependent Performance Functions

2020/09/25 by Caines, Peter E., HO, Daniel W. C., Huang, Minyi +2
#35M30 #60J60 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR)

paper · doi:10.48550/arxiv.2009.12144

Abstract

This paper establishes unique solvability of a class of Graphon Mean Field Game equations. The special case of a constant graphon yields the result for the Mean Field Game equations.

Related

• Graphon Mean Field Games with a Representative Player: Analysis and Learning Algorithm
• LQG Graphon Mean Field Games: Analysis via Graphon Invariant Subspaces
• Learning Graphon Mean Field Games and Approximate Nash Equilibria
• Probabilistic Analysis of Graphon Mean Field Control
• Master equation of discrete time graphon mean field games and teams