A Mean-Field Game Approach to Price Formation

Embargo End Date
2021-02-17

Type
Article

Authors
Gomes, Diogo A.
Saúde, João

KAUST Department
Applied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Online Publication Date
2020-02-17

Print Publication Date
2021-03

Date
2020-02-17

Abstract
Here, we introduce a price formation model where a large number of small players can store and trade a commodity such as electricity. Our model is a constrained mean-field game (MFG) where the price is a Lagrange multiplier for the supply versus demand balance condition. We establish the existence of a unique solution using a fixed-point argument. In particular, we show that the price is well defined, and it is a Lipschitz function of time. Then, we study linear-quadratic models that can be solved explicitly and compare our model with real data.

Citation
Gomes, D. A., & Saúde, J. (2020). A Mean-Field Game Approach to Price Formation. Dynamic Games and Applications. doi:10.1007/s13235-020-00348-x

Acknowledgements
Diogo A. Gomes was partially supported by KAUST baseline funds and KAUST OSR-CRG2017-3452. João Saúde was partially supported by FCT/Portugal through the CMU-Portugal Program.

Publisher
Springer Nature

Journal
Dynamic Games and Applications

DOI
10.1007/s13235-020-00348-x

arXiv
1807.07088

Additional Links
http://link.springer.com/10.1007/s13235-020-00348-x

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