Estimation of the Shapley Value of a Peer-to-peer Energy Sharing Game Using Multi-Step Coalitional Stratified Sampling

Liyang Han*, Thomas Morstyn, Malcolm McCulloch

*Corresponding author for this work

    Research output: Contribution to journalJournal articleResearchpeer-review


    One of the main objectives of a peer-to-peer energy market is to efficiently manage distributed energy resources while creating additional financial benefits for the participants. Cooperative game theory offers such a framework, and the Shapley value, a cooperative game payoff allocation based on the participants’ marginal contributions made to the local energy coalition, is shown to be fair and efficient. However, its high computational complexity limits the size of the game. In order to improve this peer-to-peer cooperative scheme’s scalability, this paper investigates and adapts a stratified sampling method for the Shapley value estimation. It then proposes a multi-step sampling strategy to further reduce the computation time by dividing the samples into incremental parts and terminating the sampling process once a certain level of estimation performance is achieved. Finally, selected case studies demonstrate the effectiveness of the proposed method, which is able to scale up the game from 20 players to 100 players.

    Original languageEnglish
    JournalInternational Journal of Control, Automation and Systems
    Issue number5
    Pages (from-to)1863-1872
    Publication statusPublished - 2021

    Bibliographical note

    Funding Information:
    Recommended by Associate Editor Soohee Han under the direction of Editor-in-Chief Keum-Shik Hong. This work was supported in part by the Engineering and Physical Sciences Research Council under Grants EP/N03466X/1, EP/S000887/1, and EP/S031901/1, and in part by the Oxford Martin Programme on Integrating Renewable Energy.

    Publisher Copyright:
    © 2021, ICROS, KIEE and Springer.


    • Cooperative game theory
    • Energy management
    • Energy storage
    • P2P energy sharing
    • Shapley value


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