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Backward Induction Foundations of the Shapley Value

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  • Ben McQuillin
  • Robert Sugden

Abstract

We present a noncooperative game model of coalitional bargaining, closely based on that of Gul (1989) but solvable by backward induction. In this game, Gul's condition of “value additivity” does not suffice to ensure the existence of a subgame perfect Nash equilibrium that supports the Shapley value, but a related condition—“no positive value‐externalities”—does. Multiple equilibria can arise only in the event of ties, and with a mild restriction on tie‐break rules these equilibria all support the Shapley value.

Suggested Citation

  • Ben McQuillin & Robert Sugden, 2016. "Backward Induction Foundations of the Shapley Value," Econometrica, Econometric Society, vol. 84, pages 2265-2280, November.
    • Handle: RePEc:wly:emetrp:v:84:y:2016:i::p:2265-2280
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    Cited by:

    1. Andrea Caggese & Ander Pérez-Orive, 2017. "Capital Misallocation and Secular Stagnation," Finance and Economics Discussion Series 2017-009, Board of Governors of the Federal Reserve System (U.S.).
    2. Roberto Serrano, 2020. "Sixty-Seven Years of the Nash Program: Time for Retirement?," Working Papers 2020-20, Brown University, Department of Economics.
    3. Andr'e Casajus & Yukihiko Funaki & Frank Huettner, 2024. "Random partitions, potential of the Shapley value, and games with externalities," Papers 2402.00394, arXiv.org.
    4. Alfredo Valencia-Toledo & Juan Vidal-Puga, 2020. "A sequential bargaining protocol for land rental arrangements," Review of Economic Design, Springer;Society for Economic Design, vol. 24(1), pages 65-99, June.
    5. Surajit Borkotokey & Loyimee Gogoi & Dhrubajit Choudhury & Rajnish Kumar, 2022. "Solidarity induced by group contributions: the MI $$^k$$ k -value for transferable utility games," Operational Research, Springer, vol. 22(2), pages 1267-1290, April.
    6. Inés Macho-Stadler & David Pérez-Castrillo & David Wettstein, 2017. "Extensions of the Shapley value for Environments with Externalities," Working Papers 1002, Barcelona School of Economics.
    7. Roberto Serrano, 2021. "Sixty-seven years of the Nash program: time for retirement?," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(1), pages 35-48, March.
    8. McQuillin, Ben & Sugden, Robert, 2018. "Balanced externalities and the Shapley value," Games and Economic Behavior, Elsevier, vol. 108(C), pages 81-92.
    9. Takaaki Abe & Satoshi Nakada, 2023. "Core stability of the Shapley value for cooperative games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(4), pages 523-543, May.
    10. Christian Basteck & Frank Huettner, 2023. "Coalitional Manipulations and Immunity of the Shapley Value," Papers 2310.20415, arXiv.org.

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