Comparing the best reply strategy and mean field games: the stationary case
File(s)
Accepted version
Author(s)
Barker, Matt
Degond, Pierre
Wolfram, Marie-Therese
Type
Journal Article
Abstract
Mean-field games (MFGs) and the best-reply strategy (BRS) are two methods of describing competitive optimisation of systems of interacting agents. The latter can be interpreted as an approximation of the respective MFG system. In this paper, we present an analysis and comparison of the two approaches in the stationary case. We provide novel existence and uniqueness results for the stationary boundary value problems related to the MFG and BRS formulations, and we present an analytical and numerical comparison of the two paradigms in some specific modelling situations.
Date Issued
2022-02-01
Date Acceptance
2020-10-16
Citation
European Journal of Applied Mathematics, 2022, 33 (1), pp.79-110
ISSN
0956-7925
Publisher
Cambridge University Press
Start Page
79
End Page
110
Journal / Book Title
European Journal of Applied Mathematics
Volume
33
Issue
1
Copyright Statement
© The Author(s), 2020. Published by Cambridge University Press. This paper has been accepted for publication and will appear in a revised form, subsequent to peer-review and/or editorial input by Cambridge University Press.
Sponsor
The Royal Society
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Grant Number
WM130048
EP/M006883/1
EP/N014529/1
Subjects
math.OC
math.OC
math.AP
0102 Applied Mathematics
Applied Mathematics
Publication Status
Published
Date Publish Online
2020-11-20