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Hart–Mas-Colell implementation of the discounted Shapley value

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  • Tomohiko Kawamori

    (Meijo University)

Abstract

We consider an implementation of the discounted Shapley value. We modify the Hart–Mas-Colell model such that each player discounts future payoffs and proposes not only an allocation, but also a coalition. We show that the discounted Shapley value is supported by each stationary subgame perfect equilibrium of the modified game such that in each subgame, the coalition that consists of all active players immediately forms. We also provide conditions for such a stationary subgame perfect equilibrium to exist.

Suggested Citation

  • Tomohiko Kawamori, 2016. "Hart–Mas-Colell implementation of the discounted Shapley value," Theory and Decision, Springer, vol. 81(3), pages 357-369, September.
  • Handle: RePEc:kap:theord:v:81:y:2016:i:3:d:10.1007_s11238-016-9536-1
    DOI: 10.1007/s11238-016-9536-1
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    References listed on IDEAS

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    1. Perez-Castrillo, David & Wettstein, David, 2001. "Bidding for the Surplus : A Non-cooperative Approach to the Shapley Value," Journal of Economic Theory, Elsevier, vol. 100(2), pages 274-294, October.
    2. Okada, Akira, 1996. "A Noncooperative Coalitional Bargaining Game with Random Proposers," Games and Economic Behavior, Elsevier, vol. 16(1), pages 97-108, September.
    3. Emilio Calvo & Esther Gutiérrez-López, 2016. "A strategic approach for the discounted Shapley values," Theory and Decision, Springer, vol. 80(2), pages 271-293, February.
    4. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-380, March.
    5. René Brink & Yukihiko Funaki & Yuan Ju, 2013. "Reconciling marginalism with egalitarianism: consistency, monotonicity, and implementation of egalitarian Shapley values," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 693-714, March.
    6. Moldovanu Benny & Winter Eyal, 1995. "Order Independent Equilibria," Games and Economic Behavior, Elsevier, vol. 9(1), pages 21-34, April.
    7. Rene van den Brink & Yukihiko Funaki, 2010. "Axiomatization and Implementation of Discounted Shapley Values," Tinbergen Institute Discussion Papers 10-065/1, Tinbergen Institute.
    8. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
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    Cited by:

    1. Calvo, Emilio & Gutiérrez-López, Esther, 2021. "Recursive and bargaining values," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 97-106.
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    3. Emilio Calvo & Esther Gutiérrez-López, 2016. "A strategic approach for the discounted Shapley values," Theory and Decision, Springer, vol. 80(2), pages 271-293, February.

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