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An Axiomatization of the Shapley Value Using a Fairness Property

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  • Brink, J.R. van den

    (Tilburg University, Center for Economic Research)

Abstract

In this paper we provide an axiomatization of the Shapley value for TU- games using a fairness property. This property states that if to a game we add another game in which two players are symmetric then their payo s change by the same amount. We show that the Shapley value is characterized by this fairness property, efficiency and the null player property. These three axioms also characterize the Shapley value on important subclasses of games, such as the class of simple games or the class of apex games.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 1999-120.

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Date of creation: 1999
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Handle: RePEc:dgr:kubcen:1999120

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Web page: http://center.uvt.nl

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Keywords: TU-game; Shapley value; fairness; simple games;

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References

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  1. RenÊ van den Brink, 1997. "An Axiomatization of the Disjunctive Permission Value for Games with a Permission Structure," International Journal of Game Theory, Springer, vol. 26(1), pages 27-43.
  2. Chang Chih & Kan Ching-Yu, 1994. "A Study on Decomposable Convex Games," Games and Economic Behavior, Elsevier, vol. 7(1), pages 35-38, July.
  3. (*), Gerard van der Laan & RenÊ van den Brink, 1998. "Axiomatizations of the normalized Banzhaf value and the Shapley value," Social Choice and Welfare, Springer, vol. 15(4), pages 567-582.
  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. Gerard van der Laan & René van den Brink, 1998. "Axiomatization of a class of share functions for n-person games," Theory and Decision, Springer, vol. 44(2), pages 117-148, April.
  6. Roger B. Myerson, 1976. "Graphs and Cooperation in Games," Discussion Papers 246, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Roger B. Myerson, 1978. "Conference Structures and Fair Allocation Rules," Discussion Papers 363, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  9. Haller, Hans, 1994. "Collusion Properties of Values," International Journal of Game Theory, Springer, vol. 23(3), pages 261-81.
  10. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer, vol. 17(2), pages 89-99.
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Citations

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Cited by:
  1. Harald Wiese, 2012. "Values with exogenous payments," Theory and Decision, Springer, vol. 72(4), pages 485-508, April.
  2. Yucel, Eray & Tokel, Emre, 2010. "Fibonacci Hierarchies for Decision Making," MPRA Paper 20973, University Library of Munich, Germany.
  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. René van den Brink & Frank Steffen, 2008. "Axiomatizations of a Positional Power Score and Measure for Hierarchies," Tinbergen Institute Discussion Papers 08-115/1, Tinbergen Institute.
  5. Judit Markus & Anna Radvanyi & Miklos Pinter, 2012. "The Shapley Value for Airport and Irrigation Games," IEHAS Discussion Papers 1207, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
  6. László Á. Kóczy & Miklós Pintér, 2011. "The men who weren't even there: Legislative voting with absentees," Working Paper Series 1104, Óbuda University, Keleti Faculty of Business and Management.
  7. André Casajus, 2011. "Differential marginality, van den Brink fairness, and the Shapley value," Theory and Decision, Springer, vol. 71(2), pages 163-174, August.
  8. René Brink & Youngsub Chun, 2012. "Balanced consistency and balanced cost reduction for sequencing problems," Social Choice and Welfare, Springer, vol. 38(3), pages 519-529, March.
  9. Pierre Dehez, 2011. "Allocation of fixed costs: characterization of the (dual) weighted Shapley value," Working Papers of BETA 2011-03, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
  10. René Brink & Yukihiko Funaki, 2009. "Axiomatizations of a Class of Equal Surplus Sharing Solutions for TU-Games," Theory and Decision, Springer, vol. 67(3), pages 303-340, September.
  11. René van den Brink & Gerard van der Laan & Valeri Vasil'ev, 2003. "Harsanyi Solutions in Line-graph Games," Tinbergen Institute Discussion Papers 03-076/1, Tinbergen Institute.
  12. Paolo Di Giannatale, Francesco Passarelli, 2011. "Voting Chances Instead of Voting Weights," ISLA Working Papers 40, ISLA, Centre for research on Latin American Studies and Transition Economies, Universita' Bocconi, Milano, Italy.
  13. René van den Brink & Yukihiko Funaki, 2004. "Axiomatizations of a Class of Equal Surplus Sharing Solutions for Cooperative Games with Transferable Utility," Tinbergen Institute Discussion Papers 04-136/1, Tinbergen Institute.
  14. André Casajus, 2011. "Marginality, differential marginality, and the Banzhaf value," Theory and Decision, Springer, vol. 71(3), pages 365-372, September.

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