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Axiomatizations of the proportional Shapley value

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  • Besner, Manfred

Abstract

We provide new axiomatic characterizations of the proportional Shapley value, a weighted value with the worths of the singletons as weights. This value satisfies anonymity and therefore symmetry just as the Shapley value and has characterizations which are proportional counterparts to the famous characterizations of the Shapley value in Shapley (1953b), Myerson (1980) and Young (1985a). If the stand alone worths are plausible weights the proportional Shapley value is a convincing alternative to the Shapley value for example in cost allocation. We introduce two new axioms, called proportionality and player splitting respectively. Each of which gives a main difference between the proportional Shapley value and the Shapley value.

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  • Besner, Manfred, 2017. "Axiomatizations of the proportional Shapley value," MPRA Paper 82990, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:82990
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    References listed on IDEAS

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    5. K. Michael Ortmann, 2000. "The proportional value for positive cooperative games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(2), pages 235-248, April.
    6. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    7. Roth, Ae & Verrecchia, Re, 1979. "Shapley Value As Applied To Cost Allocation - Reinterpretation," Journal of Accounting Research, Wiley Blackwell, vol. 17(1), pages 295-303.
    8. Gangolly, Js, 1981. "On Joint Cost Allocation - Independent Cost Proportional Scheme (Icps) And Its Properties," Journal of Accounting Research, Wiley Blackwell, vol. 19(2), pages 299-312.
    9. Chun, Youngsub, 1989. "A new axiomatization of the shapley value," Games and Economic Behavior, Elsevier, vol. 1(2), pages 119-130, June.
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    11. René Brink & René Levínský & Miroslav Zelený, 2015. "On proper Shapley values for monotone TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 449-471, May.
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    Cited by:

    1. Besner, Manfred, 2018. "Proportional Shapley levels values," MPRA Paper 87120, University Library of Munich, Germany.
    2. Besner, Manfred, 2018. "Player splitting, players merging, the Shapley set value and the Harsanyi set value," MPRA Paper 87125, University Library of Munich, Germany.

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    More about this item

    Keywords

    Cost allocation; Dividends; Proportional Shapley value; (Weighted) Shapley value; Proportionality; Player splitting;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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