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Uncertainty of the Shapley Value

Author

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  • Vladislav Kargin

    (Cornerstone Research)

Abstract

This paper introduces a measure of uncertainty in the determination of the Shapley value, illustrates it with examples, and studies some of its properties. The introduced measure of uncertainty quantifies random variations in a player's marginal contribution during the bargaining process. The measure is symmetric with respect to exchangeable substitutions in the players, equal to zero for dummy player, and convex in the game argument. The measure is illustrated by several examples of abstract games and an example from epidemiology.

Suggested Citation

  • Vladislav Kargin, 2003. "Uncertainty of the Shapley Value," Game Theory and Information 0309003, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpga:0309003
    Note: Type of Document - pdf; prepared on IBM PC ; pages: 12
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/0309/0309003.pdf
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    References listed on IDEAS

    as
    1. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, April.
    2. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-380, March.
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    Cited by:

    1. Stefano Moretti & Fioravante Patrone, 2008. "Transversality of the Shapley value," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 1-41, July.
    2. Del Castillo, Maria Fernanda & Dimitrakopoulos, Roussos, 2016. "A multivariate destination policy for geometallurgical variables in mineral value chains using coalition-formation clustering," Resources Policy, Elsevier, vol. 50(C), pages 322-332.
    3. Karl Michael Ortmann, 2016. "The link between the Shapley value and the beta factor," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 39(2), pages 311-325, November.

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    More about this item

    Keywords

    Shapley Value; game theory;

    JEL classification:

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

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