Mean field games
 JeanMichel Lasry,
 PierreLouis Lions
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We survey here some recent studies concerning what we call meanfield models by analogy with Statistical Mechanics and Physics. More precisely, we present three examples of our meanfield 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 meanfield 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 wellposed 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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 Title
 Mean field games
 Journal

Japanese Journal of Mathematics
Volume 2, Issue 1 , pp 229260
 Cover Date
 20070301
 DOI
 10.1007/s1153700706578
 Print ISSN
 02892316
 Online ISSN
 18613624
 Publisher
 SpringerVerlag
 Additional Links
 Authors

 JeanMichel Lasry ^{(1)}
 PierreLouis Lions ^{(2)} ^{(3)}
 Author Affiliations

 1. Institut de Finance, Université ParisDauphine, Place du Maréchal de Lattre de Tassigny, 75775, Paris Cedex 16, France
 2. Collège de France, 3 rue d’Ulm, 75005, Paris, France
 3. CeremadeUMR CNRS 7549, Université ParisDauphine, Place du Maréchal de Lattre de Tassigny, 75775, Paris Cedex 16, France