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A probabilistic weak formulation of mean field games and applications

Author(s): Carmona, Rene; Lacker, D

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dc.contributor.authorCarmona, Rene-
dc.contributor.authorLacker, D-
dc.identifier.citationCarmona, R, Lacker, D. (2015). A probabilistic weak formulation of mean field games and applications. Annals of Applied Probability, 25 (3), 1189 - 1231. doi:10.1214/14-AAP1020en_US
dc.description.abstract© Institute of Mathematical Statistics, 2015. Mean field games are studied by means of the weak formulation of stochastic optimal control. This approach allows the mean field interactions to enter through both state and control processes and take a form which is general enough to include rank and nearest-neighbor effects. Moreover, the data may depend discontinuously on the state variable, and more generally its entire history. Existence and uniqueness results are proven, along with a procedure for identifying and constructing distributed strategies which provide approximate Nash equlibria for finite-player games. Our results are applied to a new class of multi-agent price impact models and a class of flocking models for which we prove existence of equilibria.en_US
dc.format.extent1189 - 1231en_US
dc.relation.ispartofAnnals of Applied Probabilityen_US
dc.rightsAuthor's manuscripten_US
dc.titleA probabilistic weak formulation of mean field games and applicationsen_US
dc.typeJournal Articleen_US

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