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Null or Zero Players: The Difference between the Shapley Value and the Egalitarian Solution

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Author Info
René van den Brink () (Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam)

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Abstract

A situation in which a finite set of players can generate certain payoffs by cooperation can be described by a cooperative game with transferable utility. A solution for TU-games assigns to every TU-game a distribution of the payoffs that can be earned over the individual players. Two well-known solutions for TU-games are the Shapley value and the egalitarian solution. The Shapley value is characterized in various ways. Most characterizations use some axiom related to null players, i.e. players who contribute nothing to any coalition. We show that in these characterizations, replacing null players by zero players characterizes the egalitarian solution, where a player is a zero player if every coalition containing this player earns zero worth. We illustrate this difference between these two solutions by applying them to auction games.

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Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 04-127/1.

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Date of creation: 19 Nov 2004
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Handle: RePEc:dgr:uvatin:20040127

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Web page: http://www.tinbergen.nl/

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Related research
Keywords: Null players; zero players; Shapley value; egalitarian solution; strong monotonicity; coalitional monotonicity; auction games;

Find related papers by JEL classification:
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
D44 - Microeconomics - - Market Structure and Pricing - - - Auctions

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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. Rothschild, R., 2001. "On the use of a modified Shapley value to determine the optimal size of a cartel," Journal of Economic Behavior & Organization, Elsevier, vol. 45(1), pages 37-47, May. [Downloadable!] (restricted)
  2. Sergiu Hart, 2006. "Shapley Value," Discussion Paper Series dp421, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem. [Downloadable!]
  3. Graham, Daniel A & Marshall, Robert C & Richard, Jean-Francois, 1990. "Differential Payments within a Bidder Coalition and the Shapley Value," American Economic Review, American Economic Association, vol. 80(3), pages 493-510, June. [Downloadable!] (restricted)
  4. Maniquet, Francois, 2003. "A characterization of the Shapley value in queueing problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 90-103, March. [Downloadable!] (restricted)
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  5. Brink, R. van den, 1999. "An axiomatization of the shapley value using a fairness property," Discussion Paper 120, Tilburg University, Center for Economic Research. [Downloadable!]
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  6. Branzei, R. & Fragnelli, V. & Tijs, S., 2000. "Tree-connected peer group situations and peer group games," Discussion Paper 117, Tilburg University, Center for Economic Research. [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. Chun, Youngsub, 1989. "A new axiomatization of the shapley value," Games and Economic Behavior, Elsevier, vol. 1(2), pages 119-130, June. [Downloadable!] (restricted)
  9. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October. [Downloadable!] (restricted)
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  10. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May. [Downloadable!] (restricted)
  11. Algaba, E. & Bilbao, J.M. & Brink, R. van den, 2000. "Cooperative games on antimatroids," Discussion Paper 124, Tilburg University, Center for Economic Research. [Downloadable!]
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Cited by:
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  1. 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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