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

Author

Listed:
  • Sylvain Béal

    (CRESE EA3190, Univ. Bourgogne Franche-Comté)

  • Eric Rémila

    (Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne)

  • Philippe Solal

    (Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne)

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 2015-07, CRESE.
    • Handle: RePEc:crb:wpaper:2015-07
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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. 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.
    4. Herings, P. Jean Jacques & van der Laan, Gerard & Talman, Dolf, 2008. "The average tree solution for cycle-free graph games," Games and Economic Behavior, Elsevier, vol. 62(1), pages 77-92, January.
    5. 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.
    6. 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.
    7. Haller, Hans, 1994. "Collusion Properties of Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(3), pages 261-281.
    8. Aadland, David & Kolpin, Van, 1998. "Shared irrigation costs: An empirical and axiomatic analysis," Mathematical Social Sciences, Elsevier, vol. 35(2), pages 203-218, March.
    9. van den Brink, René & van der Laan, Gerard & Moes, Nigel, 2013. "A strategic implementation of the Average Tree solution for cycle-free graph games," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2737-2748.
    10. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    11. Ju, Yuan, 2012. "Reject and renegotiate: The Shapley value in multilateral bargaining," Journal of Mathematical Economics, Elsevier, vol. 48(6), pages 431-436.
    12. Perez-Castrillo, David & Wettstein, David, 2005. "Forming efficient networks," Economics Letters, Elsevier, vol. 87(1), pages 83-87, April.
    13. 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.
    14. 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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    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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