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Cohesive efficiency in TU-games: Two extensions of the Shapley value

Author

Listed:
  • Sylvain Béal

    (Université de Bourgogne Franche-Comté, CRESE)

  • André Casajus

    (HHL Leipzig Graduate School of Management, Dr. Hops Craft Beer Bar, Leipzig, Germany)

  • Eric Rémila

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

  • Philippe Solal

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

Abstract

We relax the assumption that the grand coalition must form by imposing the axiom of Cohesive efficiency: the total payoffs that the players can share is equal to the maximal total worth generated by a coalition structure. We determine how the three main axiomatic characterizations of the Shapley value are affected when the classical axiom of Efficiency is replaced by Cohesive efficiency. We introduce and characterize two variants of the Shapley value that are compatible with Cohesive efficiency. We show that our approach is not limited to variants of the Shapley value.

Suggested Citation

  • Sylvain Béal & André Casajus & Eric Rémila & Philippe Solal, 2019. "Cohesive efficiency in TU-games: Two extensions of the Shapley value," Working Papers 2019-03, CRESE.
    • Handle: RePEc:crb:wpaper:2019-03
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    References listed on IDEAS

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    1. Vito Fragnelli & Ignacio García-Jurado & Luciano Méndez-Naya, 2000. "On shortest path games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(2), pages 251-264, November.
    2. 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.
    3. van den Brink, René & Khmelnitskaya, Anna & van der Laan, Gerard, 2012. "An efficient and fair solution for communication graph games," Economics Letters, Elsevier, vol. 117(3), pages 786-789.
    4. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2015. "Preserving or removing special players: What keeps your payoff unchanged in TU-games?," Mathematical Social Sciences, Elsevier, vol. 73(C), pages 23-31.
    5. René Brink & Ilya Katsev & Gerard Laan, 2011. "Axiomatizations of two types of Shapley values for games on union closed systems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(1), pages 175-188, May.
    6. Moulin, Herve, 1985. "The separability axiom and equal-sharing methods," Journal of Economic Theory, Elsevier, vol. 36(1), pages 120-148, June.
    7. Yuan Ju & Peter Borm & Pieter Ruys, 2007. "The consensus value: a new solution concept for cooperative games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(4), pages 685-703, June.
    8. Bezalel Peleg, 1989. "An Axiomatization of the Core of Market Games," Mathematics of Operations Research, INFORMS, vol. 14(3), pages 448-456, August.
    9. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
    10. Sylvain Béal & Marc Deschamps & Philippe Solal, 2016. "Comparable Axiomatizations of Two Allocation Rules for Cooperative Games with Transferable Utility and Their Subclass of Data Games," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 18(6), pages 992-1004, December.
    11. Martin Shubik, 1962. "Incentives, Decentralized Control, the Assignment of Joint Costs and Internal Pricing," Management Science, INFORMS, vol. 8(3), pages 325-343, April.
    12. Moulin, Herve, 1992. "An Application of the Shapley Value to Fair Division with Money," Econometrica, Econometric Society, vol. 60(6), pages 1331-1349, November.
    13. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    14. Tadenuma, K, 1992. "Reduced Games, Consistency, and the Core," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(4), pages 325-334.
    15. Casajus, André & Huettner, Frank, 2013. "Null players, solidarity, and the egalitarian Shapley values," Journal of Mathematical Economics, Elsevier, vol. 49(1), pages 58-61.
    16. Arnold, Tone & Schwalbe, Ulrich, 2002. "Dynamic coalition formation and the core," Journal of Economic Behavior & Organization, Elsevier, vol. 49(3), pages 363-380, November.
    17. Rene van den Brink & Ilya Katsev & Gerard van der Laan, 2011. "Games on Union Closed Systems," Tinbergen Institute Discussion Papers 11-036/1, Tinbergen Institute.
    18. AUMANN, Robert J. & DREZE, Jacques H., 1974. "Cooperative games with coalition structures," LIDAM Reprints CORE 217, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    19. Voorneveld, Mark & van den Nouweland, Anne, 1998. "A new axiomatization of the core of games with transferable utility," Economics Letters, Elsevier, vol. 60(2), pages 151-155, August.
    20. Peter Sudhölter & Yan-An Hwang, 2001. "Axiomatizations of the core on the universal domain and other natural domains," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(4), pages 597-623.
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