Meanfield games and model predictive control
File(s)Degond_Herty_Liu_revised_new.pdf (402.11 KB)
Accepted version
Author(s)
Degond, PAA
Herty, M
Liu, JG
Type
Journal Article
Abstract
Mean-Field Games are games with a continuum of players that incorporate the time-
dimension through a control-theoretic approach. Recently, simpler approaches relying on the Best
Reply Strategy have been proposed. They assume that the agents navigate their strategies towards
their goal by taking the direction of steepest descent of their cost function (i.e. the opposite of the
utility function). In this paper, we explore the link between Mean-Field Games and the Best Reply
Strategy approach. This is done by introducing a Model Predictive Control framework, which consists
of setting the Mean-Field Game over a short time interval which recedes as time moves on. We show
that the Model Predictive Control offers a compromise between a possibly unrealistic Mean-Field Game
approach and the sub-optimal Best Reply Strategy.
dimension through a control-theoretic approach. Recently, simpler approaches relying on the Best
Reply Strategy have been proposed. They assume that the agents navigate their strategies towards
their goal by taking the direction of steepest descent of their cost function (i.e. the opposite of the
utility function). In this paper, we explore the link between Mean-Field Games and the Best Reply
Strategy approach. This is done by introducing a Model Predictive Control framework, which consists
of setting the Mean-Field Game over a short time interval which recedes as time moves on. We show
that the Model Predictive Control offers a compromise between a possibly unrealistic Mean-Field Game
approach and the sub-optimal Best Reply Strategy.
Date Issued
2017-01-01
Date Acceptance
2017-02-11
Citation
Communications in Mathematical Sciences, 15 (5), pp.1403-1422
ISSN
1945-0796
Publisher
International Press
Start Page
1403
End Page
1422
Journal / Book Title
Communications in Mathematical Sciences
Volume
15
Issue
5
Copyright Statement
© by International Press of Boston, Inc. All rights reserved.
Sponsor
The Royal Society
Grant Number
WM130048
Subjects
0101 Pure Mathematics
0102 Applied Mathematics
1502 Banking, Finance And Investment
Publication Status
Published