Mean Field Games
Lions, Pierre-Louis; Lasry, Jean-Michel (2007), Mean Field Games, Japanese Journal of Mathematics, 2, 1, p. 229-260. http://dx.doi.org/10.1007/s11537-007-0657-8
TypeArticle accepté pour publication ou publié
Nom de la revueJapanese Journal of Mathematics
MétadonnéesAfficher la notice complète
Résumé (EN)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.
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