The DOI matches its Crossref record; 10 of the 10 references it cites were found in a registry or an index.
Mean field games
Open accessAbstract
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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Cites
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The Master equation in mean field theory
Bensoussan, A., Frehse, J., & Yam, S. C. P. (2015) · Journal de Mathématiques Pures et Appliquées · doi:10.1016/j.matpur.2014.11.005 · Cited by 138
Mean-field models in swarm robotics: a survey
Elamvazhuthi, K., & Berman, S. (2019) · Bioinspiration & Biomimetics · doi:10.1088/1748-3190/ab49a4 · Cited by 110
On the interpretation of the Master Equation
Bensoussan, A., Frehse, J., & Yam, S. C. P. (2017) · Stochastic Processes and their Applications · doi:10.1016/j.spa.2016.10.004 · Cited by 76
Wireless Network Intelligence at the Edge
Park, J., Samarakoon, S., Bennis, M., & Debbah, M. (2019) · Proceedings of the IEEE · doi:10.1109/jproc.2019.2941458 · Cited by 92
Distributed control design for balancing the grid using flexible loads
Chen, Y., Hashmi, M. U., Mathias, J., Bušić, A., & Meyn, S. (2018) · The IMA Volumes in Mathematics and its Applications · doi:10.1007/978-1-4939-7822-9_16 · Cited by 51
Metadata
- Authors
- Lasry, J.-M., & Lions, P.-L.
- Venue
- Japanese Journal of Mathematics
- Published
- 2007-03
- Volume
- 2
- Issue
- 1
- Pages
- 229-260
- ISSN
- 0075-3432 (ISSN-L)
- 0289-2316
- 1861-3624
- OpenAlex
- W2038686546
- Cited by
- 2,635
- References
- 10
- FWCI
- 33.07
- Type
- journal article
- Language
- en
- Open access
- diamond
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
