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Potential, Value And Probability

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Author Info

  • 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.

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File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-2003-01.pdf
File Function: Fisrt version / Primera version, 2003
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Bibliographic Info

Paper provided by Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) in its series Working Papers. Serie AD with number 2003-01.

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Length: 27 pages
Date of creation: Jan 2003
Date of revision:
Publication status: Published by Ivie
Handle: RePEc:ivi:wpasad:2003-01

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Related research

Keywords: Coalition games; value; potential;

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References

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  1. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  2. Feltkamp, V., 1993. "Alternative Axiomatic Characterizations of the Shapley and Banzhaf Values," Papers 9353, Tilburg - Center for Economic Research.
  3. 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).
  4. Roth, Alvin E, 1977. "The Shapley Value as a von Neumann-Morgenstern Utility," Econometrica, Econometric Society, vol. 45(3), pages 657-64, April.
  5. Robert J. Weber, 1979. "Subjectivity in the Valuation of Games," Cowles Foundation Discussion Papers 515, Cowles Foundation for Research in Economics, Yale University.
  6. Roth, Alvin E., 1977. "Utility functions for simple games," Journal of Economic Theory, Elsevier, vol. 16(2), pages 481-489, December.
  7. E. Calvo & Juan Carlos Santos, 2000. "Weighted weak semivalues," International Journal of Game Theory, Springer, vol. 29(1), pages 1-9.
  8. Calvo, Emilio & Santos, Juan Carlos, 1997. "Potentials in cooperative TU-games," Mathematical Social Sciences, Elsevier, vol. 34(2), pages 175-190, October.
  9. 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.
  10. Pradeep Dubey & Robert J. Weber, 1977. "Probabilistic Values for Games," Cowles Foundation Discussion Papers 471, Cowles Foundation for Research in Economics, Yale University.
  11. Ehud Kalai & Dov Samet, 1983. "On Weighted Shapley Values," Discussion Papers 602, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  12. 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).
  13. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
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