Abstract
In this article, a profit optimization between electricity producers is formulated and solved. The problem is described by a linear jump-diffusion system of conditional mean-field type where the conditioning is with respect to common noise and a quadratic cost functional involving the second moment, the square of the conditional expectation of the control actions of the producers. We provide semi-explicit solution of the corresponding mean-field-type game problem with common noise. The equilibrium strategies are in state-and-conditional mean-field feedback form, where the mean-field term is the conditional price given the realization of the global uncertainty. The methodology is extended to a situation of incomplete information mean-field-type game in which each producer knows its own type but not the types of the other producers. We compute the Bayesian mean-field-type equilibrium in a semi-explicit way and show that it is not ex post resilient.
Original language | English (US) |
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Pages (from-to) | 798-818 |
Number of pages | 21 |
Journal | Dynamic Games and Applications |
Volume | 10 |
Issue number | 4 |
DOIs | |
State | Published - Dec 2020 |
Keywords
- Electricity price dynamics
- Mean-field-type games
- Smart grids
ASJC Scopus subject areas
- Statistics and Probability
- Computer Science Applications
- Computer Graphics and Computer-Aided Design
- Computational Theory and Mathematics
- Computational Mathematics
- Applied Mathematics