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Consistency of the Equal Split-Off Set

Author

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  • Dietzenbacher, Bas

    (Tilburg University, Center For Economic Research)

  • Yanovskaya, E.

Abstract

This paper axiomatically studies the equal split-o set [Branzei, Dimitrov, Tijs 2006) as a solution for cooperative games with transferable utility. This solution extends the well-known [Dutta Ray 1989] solution for convex games to arbitrary games. By deriving several characterizations, we explore the relation of the equal split-o set with various consistency notions.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Dietzenbacher, Bas & Yanovskaya, E., 2019. "Consistency of the Equal Split-Off Set," Discussion Paper 2019-023, Tilburg University, Center for Economic Research.
    • Handle: RePEc:tiu:tiucen:2846ead5-71b5-4d0c-bf0b-59445287cfd1
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    References listed on IDEAS

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    1. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-635, May.
    2. Moulin, Herve, 1985. "The separability axiom and equal-sharing methods," Journal of Economic Theory, Elsevier, vol. 36(1), pages 120-148, June.
    3. Llerena, Francesc & Mauri, Llúcia, 2017. "On the existence of the Dutta–Ray’s egalitarian solution," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 92-99.
    4. Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2004. "The Equal Split-Off Set for Cooperative Games," Other publications TiSEM d83ae0df-8e70-4427-a46a-2, Tilburg University, School of Economics and Management.
    5. Jens Leth Hougaard & Lars Thorlund-Petersen & Bezalel Peleg, 2001. "On the set of Lorenz-maximal imputations in the core of a balanced game," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 147-165.
    6. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer;Game Theory Society, vol. 15(3), pages 187-200.
    7. William Thomson, 2011. "Consistency and its converse: an introduction," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 257-291, December.
    8. Dutta, B, 1990. "The Egalitarian Solution and Reduced Game Properties in Convex Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(2), pages 153-169.
    9. Francesc Llerena & Llúcia Mauri, 2016. "Reduced games and egalitarian solutions," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 1053-1069, November.
    10. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    11. Tadenuma, K, 1992. "Reduced Games, Consistency, and the Core," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(4), pages 325-334.
    12. Klijn, Flip & Slikker, Marco & Tijs, Stef & Zarzuelo, Jose, 2000. "The egalitarian solution for convex games: some characterizations," Mathematical Social Sciences, Elsevier, vol. 40(1), pages 111-121, July.
    13. Javier Arin & Jeroen Kuipers & Dries Vermeulen, 2008. "An axiomatic approach to egalitarianism in TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(4), pages 565-580, December.
    14. Derks, J J M, 1992. "A Short Proof of the Inclusion of the Core in the Weber Set," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(2), pages 149-150.
    15. Morton Davis & Michael Maschler, 1965. "The kernel of a cooperative game," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 12(3), pages 223-259, September.
    16. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October.
    17. Javier Arin & Elena Inarra, 2001. "Egalitarian solutions in the core," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 187-193.
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    Citations

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    Cited by:

    1. Dietzenbacher, Bas & Yanovskaya, Elena, 2023. "The equal split-off set for NTU-games," Mathematical Social Sciences, Elsevier, vol. 121(C), pages 61-67.
    2. Dietzenbacher, Bas & Yanovskaya, Elena, 2021. "Self-antidual extensions and subsolutions," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 105-109.
    3. Dietzenbacher, Bas & Yanovskaya, Elena, 2020. "Antiduality in exact partition games," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 116-121.

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    More about this item

    Keywords

    transferable utility games; egalitrianism; equal split-off set; consistency;
    All these keywords.

    JEL classification:

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

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