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The Shapley value without efficiency and additivity

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  • Casajus, André

Abstract

We provide a new characterization of the Shapley value neither using the efficiency axiom nor the additivity axiom. In this characterization, efficiency is replaced by the gain-loss axiom (Einy and Haimanko, 2011, Game Econ Behav 73: 615-621), i.e., whenever the total worth generated does not change, a player can only gain at the expense of another one. Additivity and the equal treatment axiom are substituted by fairness (van den Brink, 2001, Int J Game Theory 30: 309-319) or differential marginality (Casajus, 2011, Theor Decis 71: 163-174), where the latter requires equal productivity differentials of two players to translate into equal payoff differentials. The third axiom of our characterization is the standard dummy player axiom.

Suggested Citation

  • Casajus, André, 2012. "The Shapley value without efficiency and additivity," Working Papers 114, University of Leipzig, Faculty of Economics and Management Science.
    • Handle: RePEc:zbw:leiwps:114
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    References listed on IDEAS

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    1. Grossmann, Volker & Steger, Thomas M. & Trimborn, Timo, 2013. "The macroeconomics of TANSTAAFL," Journal of Macroeconomics, Elsevier, vol. 38(PA), pages 76-85.
    2. Schäfer, Andreas & Schneider, Maik T., 2015. "Endogenous Enforcement Of Intellectual Property, North–South Trade, And Growth," Macroeconomic Dynamics, Cambridge University Press, vol. 19(5), pages 1074-1115, July.
    3. McKinnon, Ronald & Schnabl, Gunther, 2008. "China's exchange rate impasse and the weak U.S. dollar," Working Papers 73, University of Leipzig, Faculty of Economics and Management Science.
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    Cited by:

    1. Ritu Dutta & Souvik Roy & Surajit Borkotokey, 2023. "The Generalized Shapley Value of Cooperative Games as a Social Preference Function," Group Decision and Negotiation, Springer, vol. 32(2), pages 277-300, April.

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    More about this item

    Keywords

    shapley value; gain-loss axiom; differential marginality; efficiency; additivity;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D60 - Microeconomics - - Welfare Economics - - - General

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