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Comparing the best-reply strategy and mean-field games: The stationary case

Part of: Miscellaneous topics in calculus of variations and optimal control Elliptic equations and systems Game theory Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  20 November 2020

MATT BARKER ,
PIERRE DEGOND Open the ORCID record for PIERRE DEGOND [Opens in a new window]  and
MARIE-THERESE WOLFRAM
MATT BARKER
Affiliation:
Department of Mathematics Imperial College London, London, SW7 2AZ, UK Grantham Institute, Imperial College London, London, SW7 2AZ, UK emails: m.barker17@imperial.ac.uk; p.degond@imperial.ac.uk
PIERRE DEGOND
Affiliation:
Department of Mathematics Imperial College London, London, SW7 2AZ, UK
MARIE-THERESE WOLFRAM
Affiliation:
University of Warwick, Mathematics Institute, Gibbet Hill Road, CV47AL Coventry, UK Radon Institute for Computational and Applied Mathematics, Altenbergerstr. 69, 4040 Linz, Austria email: m.wolfram@warwick.ac.uk
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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.

Keywords

Fokker–Planck equationsPDEs in connection with game theoryeconomicssocial and behavioural sciencesdifferential games and control

MSC classification

Primary: 35Q84: Fokker-Planck equations 35Q91: PDEs in connection with game theory, economics, social and behavioral sciences 49N70: Differential games
Secondary: 35J15: Second-order elliptic equations 35J57: Boundary value problems for second-order elliptic systems 91A23: Differential games
Type
Papers
Information
European Journal of Applied Mathematics , Volume 33 , Issue 1 , February 2022 , pp. 79 - 110
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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