Communications in Mathematical Sciences

Volume 15 (2017)

Number 5

Mean-field games and model predictive control

Pages: 1403 – 1422



Pierre Degond (Department of Mathematics, Imperial College London, United Kingdom)

Michael Herty (Department of Mathematics, RWTH Aachen University, Aachen, Germany)

Jian-Guo Liu (Department of Physics and Department of Mathematics, Duke University, Durham, North Carolina, U.S.A.)


Mean-Field Games are games with a continuum of players that incorporate the timedimension 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.


mean-field games, multi-agent systems

2010 Mathematics Subject Classification

35L65, 90B30

Received 10 April 2016

Published 26 June 2017