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Alternative Axiomatic Characterizations of the Shapley and Banzhaf Values

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  • Feltkamp, Vincent

Abstract

In a paper in 1975, Dubey characterized the Shapley-Shubik index axiomatically on the class of monotonic simple games. In 1979, Dubey and Shapley characterized the Banzhaf index in a similar way. This paper extends these characterizations to axiomatic characterizations of the Shapley and Banzhaf values on the class of control games, on the class of simple games and on the class of all transferable utility games. In particular, it is shown that the additivity axiom which is usually used to characterize these values on the class of all transferable utility games can be weakened without changing the result.

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Bibliographic Info

Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 24 (1995)
Issue (Month): 2 ()
Pages: 179-86

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Handle: RePEc:spr:jogath:v:24:y:1995:i:2:p:179-86

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Cited by:
  1. Carreras, Francesc & Giménez, José Miguel, 2010. "Semivalues: power,potential and multilinear extensions," MPRA Paper 27620, University Library of Munich, Germany.
  2. Amer, Rafael & Gimenez, Jose Miguel, 2006. "An axiomatic characterization for regular semivalues," Mathematical Social Sciences, Elsevier, vol. 51(2), pages 217-226, March.
  3. René van den Brink, 2004. "Null or Zero Players: The Difference between the Shapley Value and the Egalitarian Solution," Tinbergen Institute Discussion Papers 04-127/1, Tinbergen Institute.
  4. Carreras, Francesc & Giménez, José Miguel, 2011. "Power and potential maps induced by any semivalue: Some algebraic properties and computation by multilinear extensions," European Journal of Operational Research, Elsevier, vol. 211(1), pages 148-159, May.
  5. Federico Valenciano & Annick Laruelle, 2000. "- Shapley-Shubik And Banzhaf Indices Revisited," Working Papers. Serie AD 2000-02, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  6. Dragan, Irinel, 1996. "New mathematical properties of the Banzhaf value," European Journal of Operational Research, Elsevier, vol. 95(2), pages 451-463, December.
  7. Kamijo, Yoshio & Kongo, Takumi, 2012. "Whose deletion does not affect your payoff? The difference between the Shapley value, the egalitarian value, the solidarity value, and the Banzhaf value," European Journal of Operational Research, Elsevier, vol. 216(3), pages 638-646.
  8. Lorenzo-Freire, S. & Alonso-Meijide, J.M. & Casas-Mendez, B. & Fiestras-Janeiro, M.G., 2007. "Characterizations of the Deegan-Packel and Johnston power indices," European Journal of Operational Research, Elsevier, vol. 177(1), pages 431-444, February.
  9. Sanchez-Soriano, Joaquin, 2003. "The pairwise egalitarian solution," European Journal of Operational Research, Elsevier, vol. 150(1), pages 220-231, October.
  10. André Casajus, 2011. "Marginality, differential marginality, and the Banzhaf value," Theory and Decision, Springer, vol. 71(3), pages 365-372, September.
  11. Carreras, Francesc, 2005. "A decisiveness index for simple games," European Journal of Operational Research, Elsevier, vol. 163(2), pages 370-387, June.
  12. André Casajus, 2014. "Collusion, quarrel, and the Banzhaf value," International Journal of Game Theory, Springer, vol. 43(1), pages 1-11, February.
  13. Amer, Rafael & Carreras, Francese & Gimenez, Jose Miguel, 2002. "The modified Banzhaf value for games with coalition structure: an axiomatic characterization," Mathematical Social Sciences, Elsevier, vol. 43(1), pages 45-54, January.
  14. Federico Valenciano & Annick Laruelle, 2003. "Potential, Value And Probability," Working Papers. Serie AD 2003-01, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  15. Carreras, Francesc & Freixas, Josep & Puente, Maria Albina, 2003. "Semivalues as power indices," European Journal of Operational Research, Elsevier, vol. 149(3), pages 676-687, September.

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