Mean field games

By Jean-Michel Lasry, Pierre-Louis Lions. 2007

3,220 citations recorded by the source corpus.

Abstract.We survey here some recent studies concerning what we call mean-field models by analogy with Statistical Mechanics and Physics. More precisely, we present three examples of our mean-field approach to modelling in Economics and Finance (or other related subjects...). Roughly speaking, we are concerned with situations that involve a very large number of “rational players” with a limited information (or visibility) on the “game”. Each player chooses his optimal strategy in view of the global (or macroscopic) informations that are available to him and that result from the actions of all players. In the three examples we mention here, we derive a mean-field problem which consists in nonlinear differential equations. These equations are of a new type and our main goal here is to study them and establish their links with various fields of Analysis. We show in particular that these nonlinear problems are essentially well-posed problems i.e., have unique solutions. In addition, we give various limiting cases, examples and possible extensions. And we mention many open problems.

Subfields: Economics and Econometrics, Finance

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Citations in the corpus

Wireless Network Intelligence at the Edge (2018, methodology): “In this game, both computational complexity and the number of communication rounds across devices increase exponentially with N , which can be remedied at using the MFG theory [160].”
A Maximum Principle for SDEs of Mean-Field Type (2011, background): “A more general form of this control problem has been studied in [1], and to some extent in [ 12 ], using an extended version of the dynamic programming principle.”
$N$-player games and mean-field games with absorption (2016, methodology): “For simplicity, we only consider a setting analogous to that of Lasry and Lions [33], where the dynamics are of calculus-of-variation-type with additive noise and the running costs split into two parts, one depending on the control, the other on the measure variable.”
On the connection between symmetric $N$-player games and mean field games (2014, methodology): “To this end, we employ a local martingale problem in the spirit of Stroock and Varadhan (1979). The use of martingale problems, together with weak convergence methods, has a long tradition in the analysis of McKean–Vlasov limits for uncontrolled weakly interacting systems [for instance, Funaki (1984”
Distribution dependent SDEs driven by additive fractional Brownian motion (2021, background): “For this reason, DDSDEs have found applications in numerous fields, see the review [27] and the references therein; let us also mention their connection to mean-field games [31].”
Mean Field Games of Timing and Models for Bank Runs (2016, positive): “Our models are closely related to the mean field games introduced independently by Lasry and Lions [29] and Caines et al.”
From the master equation to mean field game limit theory: a central limit theorem (2018, methodology): “The original formulation of Lasry and Lions [35] is a forward-backward PDE system, which is essentially equivalent to this fixed point procedure, when σ0 = 0.”
Finite Mean Field Games: Fictitious play and convergence to a first order continuous mean field game (2018, background): “1 Introduction Mean Field Games (MFGs) were introduced by Lasry and Lions in [21, 22, 23] and, independently, by Huang, Caines and Malhamé in [20].”