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Axiomatic characterizations of the weighted solidarity values

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  • Calvo, Emilio
  • Gutiérrez-López, Esther

Abstract

We define and characterize the class of all weighted solidarity values. Our first characterization employs the classical axioms determining the solidarity value (except symmetry), that is, efficiency, additivity and the A-null player axiom, and two new axioms called proportionality and strong individual rationality. In our second axiomatization, the additivity and the A-null player axioms are replaced by a new axiom called average marginality.

Suggested Citation

  • Calvo, Emilio & Gutiérrez-López, Esther, 2014. "Axiomatic characterizations of the weighted solidarity values," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 6-11.
    • Handle: RePEc:eee:matsoc:v:71:y:2014:i:c:p:6-11
    DOI: 10.1016/j.mathsocsci.2014.03.005
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    References listed on IDEAS

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    1. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    2. Emilio Calvo, 2008. "Random marginal and random removal values," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(4), pages 533-563, December.
    3. Sprumont, Yves, 1990. "Population monotonic allocation schemes for cooperative games with transferable utility," Games and Economic Behavior, Elsevier, vol. 2(4), pages 378-394, December.
    4. Radzik, Tadeusz, 2012. "A new look at the role of players’ weights in the weighted Shapley value," European Journal of Operational Research, Elsevier, vol. 223(2), pages 407-416.
    5. Nowak, Andrzej S & Radzik, Tadeusz, 1994. "A Solidarity Value for n-Person Transferable Utility Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(1), pages 43-48.
    6. Nowak, A.S. & Radzik, T., 1995. "On axiomatizations of the weighted Shapley values," Games and Economic Behavior, Elsevier, vol. 8(2), pages 389-405.
    7. Radzik, Tadeusz, 2013. "Is the solidarity value close to the equal split value?," Mathematical Social Sciences, Elsevier, vol. 65(3), pages 195-202.
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    Cited by:

    1. Bourheneddine Ben Dhaou & Abderrahmane Ziad, 2015. "The Free Solidarity Value," Economics Working Paper Archive (University of Rennes & University of Caen) 201508, Center for Research in Economics and Management (CREM), University of Rennes, University of Caen and CNRS.
    2. Zhengxing Zou & René van den Brink & Yukihiko Funaki, 2024. "On weighted-egalitarian values for cooperative games," Tinbergen Institute Discussion Papers 24-021/II, Tinbergen Institute.
    3. Emilio Calvo & Esther Gutiérrez-López, 2017. "Asymmetric players in the Solidarity and Shapley values," Discussion Papers in Economic Behaviour 0217, University of Valencia, ERI-CES.
    4. Gutiérrez-López, Esther, 2020. "Axiomatic characterizations of the egalitarian solidarity values," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 109-115.

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