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An axiomatization of the Shapley value using a fairness property

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Author Info
René van den Brink () (Department of Econometrics, Free University, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands Revised August 2001)

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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 payoffs 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 the class of simple games.

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

Volume (Year): 30 (2002)
Issue (Month): 3 ()
Pages: 309-319
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Handle: RePEc:spr:jogath:v:30:y:2002:i:3:p:309-319

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Related research
Keywords: TU-game · Shapley value · fairness · simple games.;

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer, vol. 17(2), pages 89-99.
  2. Haller, Hans, 1994. "Collusion Properties of Values," International Journal of Game Theory, Springer, vol. 23(3), pages 261-81.
  3. 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.
  4. (*), 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. [Downloadable!] (restricted)
  5. Chang Chih & Kan Ching-Yu, 1994. "A Study on Decomposable Convex Games," Games and Economic Behavior, Elsevier, vol. 7(1), pages 35-38, July. [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. Roger B. Myerson, 1978. "Conference Structures and Fair Allocation Rules," Discussion Papers 363, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  8. Roger B. Myerson, 1976. "Graphs and Cooperation in Games," Discussion Papers 246, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  9. 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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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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. [Downloadable!]
  2. 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. [Downloadable!]
  3. 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. [Downloadable!]
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