Journal ArticleDOI
Jeux à champ moyen. II – Horizon fini et contrôle optimal
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Lasry et al. as mentioned in this paper considered the case of Nash equilibria for stochastic control type problems in finite horizon and presented general existence and uniqueness results for the partial differential equations systems that they introduced.About:
This article is published in Comptes Rendus Mathematique.The article was published on 2006-11-15. It has received 776 citations till now.read more
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Journal ArticleDOI
Mean Field Games
TL;DR: In this paper, the authors present three examples of the mean-field approach to modelling in economics and finance (or other related subjects) and show that these nonlinear problems are essentially well-posed problems with unique solutions.
Book
Optimal Transport for Applied Mathematicians : Calculus of Variations, PDEs, and Modeling
TL;DR: In this paper, the primal and dual problems of one-dimensional problems are considered. But they do not consider the dual problems in L^1 and L^infinity theory.
Posted Content
Mean Field Games and Applications
TL;DR: This text is inspired from a “Cours Bachelier” held in January 2009 and taught by Jean-Michel Lasry, based upon the articles of the three authors and upon unpublished materials they developed.
Book ChapterDOI
Mean Field Games and Applications
TL;DR: The Course Bachelier 2009 as discussed by the authors was inspired from a course inspired by the work of Jean-Michel Lasry, and the course was based upon the articles of the three authors and upon unpublished materials they developed.
Journal ArticleDOI
Mean Field Games: Numerical Methods
TL;DR: Numerical methods for the approximation of the stationary and evolutive versions of stochastic differential game models are proposed here and existence and uniqueness properties as well as bounds for the solutions of the discrete schemes are investigated.
References
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Journal ArticleDOI
Markets with a continuum of traders
TL;DR: In this paper, it is shown that the core of a market coincides with the set of its equilibrium allocations, i.e., allocations which constitute a competitive equilibrium when combined with an appropriate price structure.
Journal ArticleDOI
Jeux à champ moyen. I – Le cas stationnaire
TL;DR: Lasry et al. as mentioned in this paper introduce an approche generale for modeliser des jeux avec un tres grand nombre of joueurs, and consider des equilibres de Nash a N joues for des problemes stochastiques en temps long and deduisons rigoureusement les equations de type « champ moyen » quand N tend vers l'infini.
Journal ArticleDOI
Large Deviations Asymptotics for Spherical Integrals
Alice Guionnet,Ofer Zeitouni +1 more
TL;DR: In this paper, the authors prove the existence of the limit I(β)N(DN, EN) = √ log n−2 log I(α, β), where α is the Haar measure on the orthogonal group ON when β = 1 and β = 2 and EN is the diagonal real matrices whose spectral measures converge to μD, μE.
Journal ArticleDOI
Nonlinear elliptic systems in stochastic game theory.
Alain Bensoussan,Jens Frehse +1 more
TL;DR: On etudie des systemes d'equations aux derivees partielles non lineaires provenant de la theorie des jeux differentiels stochastiques au sens de Nash as discussed by the authors.