This paper solves a mean-field type hierarchical optimal control problem in electricity market.The authors consider n-1 prosumers and one producer.The ith prosumer,for 1 ＜ i ＜ n,is a leader of the (i-1)th prosumer and is a follower of the (i + 1)th prosumer.The first player (agent)is the follower at the bottom whereas the nth is the leader at the top.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 square of the conditional expectation of the controls of the agents.The authors provide a semi-explicit solution of the corresponding mean-field-type hierarchical control problem with common noise.Finally,the authors illustrate the obtained result via a numerical example with two different scenarios.

FRIHI Zahrate El Oula;CHOUTRI Salah Eddine;BARREIRO-GOMEZ Julian;TEMBINE Hamidou

Laboratory of Probability and Statistics (LaPS),Department of Mathematics,Badji-Mokhtar University,B.P.12,Annaba 23000,Algeria;Research Institute,New York University Abu Dhabi,PO Box 129188,Abu Dhabi,UAE;Learning &Game Theory Laboratory,New York University Abu Dhabi,Saadiyat Campus PO Box 129188,UAE

系统科学与复杂性学报（英文版）

[1]FRIHI Zahrate El Oula;CHOUTRI Salah Eddine;BARREIRO-GOMEZ Julian;TEMBINE Hamidou-.Hierarchical Mean-Field Type Control of Price Dynamics for Electricity in Smart Grid)[J].系统科学与复杂性学报（英文版）,2022(01):1-17

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