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Coalitional desirability and the equal division value

Author

Listed:
  • Sylvain Béal

    () (Université de Bourgogne Franche-Comté, CRESE)

  • Eric Rémila

    () (Université de Saint-Etienne, Gate)

  • Phillippe Solal

    () (Université de Saint-Etienne, Gate)

Abstract

We introduce three natural collective variants of the well-known axiom of Desirability (Maschler and Peleg, 1966), which require that if the (per capita) contributions of a rst coalition are at least as large as the (per capita) contributions of a second coalition, then the (average) payo in the rst coalition should be as large as the (average) payo in the second coalition. These axioms are called Coalitional desirability and Average coalitional desirability. The third variant, called Uniform coalitional desirability applies only to coalitions with the same size. We show that Coalitional desirability is very strong: no value satis es simultaneously this axiom and Eciency. To the contrary, the combination of either Average coalitional desirability or Uniform coalitional desirability with Eciency and Additivity characterizes the Equal Division value.

Suggested Citation

  • Sylvain Béal & Eric Rémila & Phillippe Solal, 2017. "Coalitional desirability and the equal division value," Working Papers 2017-08, CRESE.
  • Handle: RePEc:crb:wpaper:2017-08
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    File URL: http://crese.univ-fcomte.fr/WP-2017-08.pdf
    File Function: First version, 2017
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    References listed on IDEAS

    as
    1. Sylvain Béal & Eric Rémila & Philippe Solal, 2015. "Axioms of invariance for TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 891-902, November.
    2. Einy, Ezra & Neyman, Abraham, 1989. "Large symmetric games are characterized by completeness of the desirability relation," Journal of Economic Theory, Elsevier, vol. 48(2), pages 369-385, August.
    3. Sébastien Courtin & Bertrand Tchantcho, 2015. "A note on the ordinal equivalence of power indices in games with coalition structure," Theory and Decision, Springer, vol. 78(4), pages 617-628, April.
    4. Pierre Dehez & Daniela Tellone, 2013. "Data Games: Sharing Public Goods with Exclusion," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 15(4), pages 654-673, August.
    5. 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.
    6. Pierre Dehez & Daniela Tellone, 2013. "Data Games: Sharing Public Goods with Exclusion," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 15(4), pages 654-673, August.
    7. René Brink & Yukihiko Funaki, 2009. "Axiomatizations of a Class of Equal Surplus Sharing Solutions for TU-Games," Theory and Decision, Springer, vol. 67(3), pages 303-340, September.
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    9. Sylvain Béal & André Casajus & Frank Huettner & Eric Rémila & Philippe Solal, 2016. "Characterizations of weighted and equal division values," Theory and Decision, Springer, vol. 80(4), pages 649-667, April.
    10. Casajus, André & Huettner, Frank, 2013. "Null players, solidarity, and the egalitarian Shapley values," Journal of Mathematical Economics, Elsevier, vol. 49(1), pages 58-61.
    11. René Brink & Youngsub Chun & Yukihiko Funaki & Boram Park, 2016. "Consistency, population solidarity, and egalitarian solutions for TU-games," Theory and Decision, Springer, vol. 81(3), pages 427-447, September.
    12. 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.
    13. Einy, Ezra & Lehrer, Ehud, 1989. "Regular Simple Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(2), pages 195-207.
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    15. Einy, Ezra, 1985. "The desirability relation of simple games," Mathematical Social Sciences, Elsevier, vol. 10(2), pages 155-168, October.
    16. Molinero, Xavier & Riquelme, Fabián & Serna, Maria, 2015. "Forms of representation for simple games: Sizes, conversions and equivalences," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 87-102.
    17. Peleg, Bezalel, 1980. "A theory of coalition formation in committees," Journal of Mathematical Economics, Elsevier, vol. 7(2), pages 115-134, July.
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    More about this item

    Keywords

    Desirability; Coalitional desirability; Average coalitional desirability; Uniform coalitional desirability; Equal Division value; Shapley value.;

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