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A strategic implementation of the sequential equal surplus division rule for digraph cooperative games

Author

Listed:
  • Sylvain Béal

    (Univ. Bourgogne Franche-Comté)

  • Eric Rémila

    (Université de Saint-Etienne)

  • Philippe Solal

    (Université de Saint-Etienne)

Abstract

We provide a strategic implementation of the sequential equal surplus division rule (Béal et al. in Theory Decis 79:251–283, 2015). Precisely, we design a non-cooperative mechanism of which the unique subgame perfect equilibrium payoffs correspond to the sequential equal surplus division outcome of a superadditive rooted tree TU-game. This mechanism borrowed from the bidding mechanism designed by Pérez-Castrillo and Wettstein (J Econ Theory 100:274–294, 2001), but takes into account the direction of the edges connecting any two players in the rooted tree, which reflects some dominance relation between them. Our proofs rely on interesting properties that we provide for a general class of bidding mechanisms.

Suggested Citation

  • Sylvain Béal & Eric Rémila & Philippe Solal, 2017. "A strategic implementation of the sequential equal surplus division rule for digraph cooperative games," Annals of Operations Research, Springer, vol. 253(1), pages 43-59, June.
    • Handle: RePEc:spr:annopr:v:253:y:2017:i:1:d:10.1007_s10479-016-2290-5
    DOI: 10.1007/s10479-016-2290-5
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    References listed on IDEAS

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    Cited by:

    1. Béal, Sylvain & Ferrières, Sylvain & Rémila, Eric & Solal, Philippe, 2018. "Axiomatization of an allocation rule for ordered tree TU-games," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 132-140.
    2. Borkotokey, Surajit & Choudhury, Dhrubajit & Kumar, Rajnish & Sarangi, Sudipta, 2020. "Consolidating Marginalism and Egalitarianism: A New Value for Transferable Utility Games," QBS Working Paper Series 2020/12, Queen's University Belfast, Queen's Business School.
    3. Dhrubajit Choudhury & Surajit Borkotokey & Rajnish Kumar & Sudipta Sarangi, 2021. "The Egalitarian Shapley value: a generalization based on coalition sizes," Annals of Operations Research, Springer, vol. 301(1), pages 55-63, June.
    4. Liu, Jia-Cai & Sheu, Jiuh-Biing & Li, Deng-Feng & Dai, Yong-Wu, 2021. "Collaborative profit allocation schemes for logistics enterprise coalitions with incomplete information," Omega, Elsevier, vol. 101(C).

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    More about this item

    Keywords

    Bidding approach; ‘Take-it-or-leave-it’ procedure; Implementation; Rooted tree TU-games; Sequential equal surplus division;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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