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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)

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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
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Publisher 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
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Publication status: Published by Ivie
Handle: RePEc:ivi:wpasad:2003-01

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Related research
Keywords: Coalition games; value; potential;

Find related papers by JEL classification:
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

References listed on IDEAS
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  1. Roth, Alvin E, 1977. "The Shapley Value as a von Neumann-Morgenstern Utility," Econometrica, Econometric Society, vol. 45(3), pages 657-64, April. [Downloadable!] (restricted)
  2. Pradeep Dubey & Abraham Neyman & Robert J. Weber, 1979. "Value Theory without Efficiency," Cowles Foundation Discussion Papers 513, Cowles Foundation, Yale University. [Downloadable!]
  3. Robert J. Weber, 1977. "Probabilistic Values for Games," Cowles Foundation Discussion Papers 471R, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  4. Roth, Alvin E., 1977. "Utility functions for simple games," Journal of Economic Theory, Elsevier, vol. 16(2), pages 481-489, December. [Downloadable!] (restricted)
  5. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April. [Downloadable!] (restricted)
  6. Ehud Kalai & Dov Samet, 1983. "On Weighted Shapley Values," Discussion Papers 602, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  7. Feltkamp, Vincent, 1995. "Alternative Axiomatic Characterizations of the Shapley and Banzhaf Values," International Journal of Game Theory, Springer, vol. 24(2), pages 179-86.
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  8. E. Calvo & Juan Carlos Santos, 2000. "Weighted weak semivalues," International Journal of Game Theory, Springer, vol. 29(1), pages 1-9. [Downloadable!] (restricted)
  9. Robert J. Weber, 1979. "Subjectivity in the Valuation of Games," Cowles Foundation Discussion Papers 515, Cowles Foundation, Yale University. [Downloadable!]
  10. Calvo, Emilio & Santos, Juan Carlos, 1997. "Potentials in cooperative TU-games," Mathematical Social Sciences, Elsevier, vol. 34(2), pages 175-190, October. [Downloadable!] (restricted)
  11. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May. [Downloadable!] (restricted)
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