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Characterizations of weighted and equal division values

Author

Listed:
  • Sylvain Béal

    (Université Bourgogne Franche-Comté)

  • André Casajus

    (LSI Leipziger Spieltheoretisches Institut
    HHL Leipzig Graduate School of Management)

  • Frank Huettner

    (LSI Leipziger Spieltheoretisches Institut
    HHL Leipzig Graduate School of Management)

  • Eric Rémila

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

  • Philippe Solal

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

Abstract

New and recent axioms for cooperative games with transferable utilities are introduced. The non-negative player axiom requires to assign a non-negative payoff to a player that belongs to coalitions with non-negative worth only. The axiom of addition invariance on bi-partitions requires that the payoff vector recommended by a value should not be affected by an identical change in worth of both a coalition and the complementary coalition. The nullified solidarity axiom requires that if a player who becomes null weakly loses (gains) from such a change, then every other player should weakly lose (gain) too. We study the consequence of imposing some of these axioms in addition to some classical axioms. It turns out that the resulting values or set of values have all in common to split efficiently the worth achieved by the grand coalition according to an exogenously given weight vector. As a result, we also obtain new characterizations of the equal division value.

Suggested Citation

  • 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.
    • Handle: RePEc:kap:theord:v:80:y:2016:i:4:d:10.1007_s11238-015-9519-7
    DOI: 10.1007/s11238-015-9519-7
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    Cited by:

    1. Zhengxing Zou & Rene van den Brink, 2020. "Sharing the Surplus and Proportional Values," Tinbergen Institute Discussion Papers 20-014/II, Tinbergen Institute.
    2. Sylvain Béal & Eric Rémila & Philippe Solal, 2015. "Discounted Tree Solutions," Working Papers hal-01377923, HAL.
    3. Lina Mallozzi & Juan Vidal-Puga, 2021. "Uncertainty in cooperative interval games: how Hurwicz criterion compatibility leads to egalitarianism," Annals of Operations Research, Springer, vol. 301(1), pages 143-159, June.
    4. Donald Nganmegni Njoya & Issofa Moyouwou & Nicolas Gabriel Andjiga, 2021. "The equal-surplus Shapley value for chance-constrained games on finite sample spaces," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 463-499, June.
    5. Sylvain Béal & Florian Navarro, 2020. "Necessary versus equal players in axiomatic studies," Working Papers 2020-01, CRESE.
    6. Zhengxing Zou & René Brink & Yukihiko Funaki, 2022. "Sharing the surplus and proportional values," Theory and Decision, Springer, vol. 93(1), pages 185-217, July.
    7. David Lowing & Kevin Techer, 2022. "Marginalism, egalitarianism and efficiency in multi-choice games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(4), pages 815-861, November.
    8. Zhengxing Zou & René Brink & Youngsub Chun & Yukihiko Funaki, 2021. "Axiomatizations of the proportional division value," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(1), pages 35-62, July.
    9. Sylvain Béal & Eric Rémila & Philippe Solal, 2019. "Coalitional desirability and the equal division value," Theory and Decision, Springer, vol. 86(1), pages 95-106, February.
    10. David Lowing & Kevin Techer, 2021. "Marginalism, Egalitarianism and E ciency in Multi-Choice Games," Working Papers halshs-03334056, HAL.
    11. Calleja, Pere & Llerena Garrés, Francesc, 2016. "Consistency distinguishes the (weighted) Shapley value, the (weighted) surplus division value and the prenucleolus," Working Papers 2072/266577, Universitat Rovira i Virgili, Department of Economics.
    12. Béal, Sylvain & Ferrières, Sylvain & Rémila, Eric & Solal, Philippe, 2016. "Axiomatic characterizations under players nullification," Mathematical Social Sciences, Elsevier, vol. 80(C), pages 47-57.
    13. Sylvain Ferrières, 2016. "Smoothness, nullified equal loss property and equal division values," Working Papers 2016-01, CRESE.
    14. André Casajus & Koji Yokote, 2019. "Weakly differentially monotonic solutions for cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(3), pages 979-997, September.
    15. Takaaki Abe & Satoshi Nakada, 2019. "The weighted-egalitarian Shapley values," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(2), pages 197-213, February.

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