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Potential, Value And Probability

Author

Listed:
  • Federico Valenciano

    (Universidad del País Vasco)

  • Annick Laruelle

    (Universidad de Alicante)

Abstract

This paper focuses on the probabilistic point of view and proposes a extremely simple probabilistic model that provides a single and simple story to account for several extensions of the Shapley value, as weighted Shapley values, semivalues, and weak (weighted or not) semivalues, and the Shapley value itself. Moreover, some of the most interesting conditions or notions that have been introduced in the search of alternatives to Shapley's seminal characterization, as 'balanced contributions' and the 'potential', are reinterpreted from this same point of view. In this new light these notions and some results lose their 'mystery' and acquire a clear and simple meaning. These illuminating reinterpretations strongly vindicate the complementariness of the probabilistic and the axiomatic approaches, and shed serious doubts about the achievements of the axiomatic approach since Nash's and Shapley's seminal papers in connection with the genuine notion of value.

Suggested Citation

  • Federico Valenciano & Annick Laruelle, 2003. "Potential, Value And Probability," Working Papers. Serie AD 2003-01, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    • Handle: RePEc:ivi:wpasad:2003-01
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    File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-2003-01.pdf
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    References listed on IDEAS

    as
    1. Pradeep Dubey & Abraham Neyman & Robert J. Weber, 1979. "Value Theory without Efficiency," Cowles Foundation Discussion Papers 513, Cowles Foundation for Research in Economics, Yale University.
    2. Federico Valenciano & Annick Laruelle, 2002. "Assessment Of Voting Situations: The Probabilistic Foundations," Working Papers. Serie AD 2002-22, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    3. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    4. Ehud Kalai & Dov Samet, 1983. "On Weighted Shapley Values," Discussion Papers 602, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. Roth, Alvin, 2012. "The Shapley Value as a von Neumann-Morgenstern Utility," Ekonomicheskaya Politika / Economic Policy, Russian Presidential Academy of National Economy and Public Administration, vol. 6, pages 1-9.
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    7. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
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    10. Robert J. Weber, 1977. "Probabilistic Values for Games," Cowles Foundation Discussion Papers 471R, Cowles Foundation for Research in Economics, Yale University.
    11. Federico Valenciano & Annick Laruelle, 2000. "- Power Indices And The Veil Of Ignorance," Working Papers. Serie AD 2000-13, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    12. Robert J. Weber, 1979. "Subjectivity in the Valuation of Games," Cowles Foundation Discussion Papers 515, Cowles Foundation for Research in Economics, Yale University.
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    More about this item

    Keywords

    Coalition games; value; potential;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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