| Issue |
ESAIM: COCV
Volume 28, 2022
|
|
|---|---|---|
| Article Number | 24 | |
| Number of page(s) | 24 | |
| DOI | https://doi.org/10.1051/cocv/2022020 | |
| Published online | 25 May 2022 | |
On the Graphon Mean Field Game equations: Individual agent affine dynamics and mean field dependent performance functions*
1
Department of Electrical and Computer Engineering, McGill University, Montreal, Canada
2
Department of Mathematics, City University of Hong Kong, Hong Kong
3
School of Mathematics and Statistics, Carleton University, Ottawa, ON, Canada
4
Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, USA
** Corresponding author: qsong@wpi.edu
Received:
31
January
2021
Accepted:
1
March
2022
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.
Mathematics Subject Classification: 35M30 / 60J60
Key words: Mean Field Games / Graphon / Hamilton-Jacobi-Bellman equation
The research of P.E. Caines, D. Ho, and Q. Song were supported in part by the RGC of Hong Kong CityU (11201518). The work of P. E. Caines was partially supported by AFOSR grant FA9550-19-1-0138. The research work of M. Huang was supported by NSERC. We acknowledge the valuable comments from anonymous reviewers.
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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