Journal ArticleDOI
Jeux à champ moyen. I – Le cas stationnaire
TLDR
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.About:
This article is published in Comptes Rendus Mathematique.The article was published on 2006-11-01. It has received 802 citations till now.read more
Citations
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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.
Journal ArticleDOI
Jeux à champ moyen. II – Horizon fini et contrôle optimal
TL;DR: 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.
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inspired by the work of Jean-Michel Lasry, and the course was based upon the articles of the three authors and upon unpublished materials they developed.
Proceedings ArticleDOI
Decentralized charging control for large populations of plug-in electric vehicles
TL;DR: The paper shows that under certain mild conditions, there exists a unique Nash equilibrium that almost satisfies the control objective to minimize electricity generation costs by establishing a PEV charging schedule that fills the overnight demand valley.
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
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.
Journal ArticleDOI
Ergodic Bellman systems for stochastic games in arbitrary dimension
Alain Bensoussan,Jens Frehse +1 more
TL;DR: In this paper, the authors studied the convergence of stochastic games with cost functions to the ergodic Bellman equation and showed that the average cost converges with respect to the discount ρ → 0.
Journal ArticleDOI
Towards a self-consistent theory of volatility
TL;DR: In this paper, a theory nouvelle on the formation of the volatilite is proposed, which prend en compte l'influence de la couverture d'options sur la dynamique du prix du sous-jacent.