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

Author

Listed:
  • Sylvain Béal

    (CRESE - Centre de REcherches sur les Stratégies Economiques (UR 3190) - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE])

  • Eric Rémila

    (GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - ENS de Lyon - École normale supérieure de Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique)

  • Philippe Solal

    (GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - ENS de Lyon - École normale supérieure de Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique)

Abstract

We provide a strategic implementation of the sequential equal surplus division rule (Béal et al., 2014). 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 (2001), but takes into account the direction of the edges connecting any two players in the rood tree, which reflects some dominance relation between them.

Suggested Citation

  • Sylvain Béal & Eric Rémila & Philippe Solal, 2015. "A strategic implementation of the sequential equal surplus division rule for digraph cooperative games," Working Papers hal-01376910, HAL.
    • Handle: RePEc:hal:wpaper:hal-01376910
    Note: View the original document on HAL open archive server: https://hal.science/hal-01376910
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    References listed on IDEAS

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    1. Juan Vidal-Puga, 2005. "Implementation of the Levels Structure Value," Annals of Operations Research, Springer, vol. 137(1), pages 191-209, July.
    2. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(2), pages 89-99.
    3. Sylvain Béal & Amandine Ghintran & Eric Rémila & Philippe Solal, 2015. "The sequential equal surplus division for rooted forest games and an application to sharing a river with bifurcations," Theory and Decision, Springer, vol. 79(2), pages 251-283, September.
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    9. 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.
    10. Slikker, Marco, 2007. "Bidding for surplus in network allocation problems," Journal of Economic Theory, Elsevier, vol. 137(1), pages 493-511, November.
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    12. Yuan Ju & David Wettstein, 2009. "Implementing cooperative solution concepts: a generalized bidding approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(2), pages 307-330, May.
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    15. 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.
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    Cited by:

    1. 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.
    2. 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.
    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; 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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