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A new weight scheme for the Shapley value

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  • Haeringer, Guillaume

Abstract

It is well known since Owen (Management Science, 1968) that the weights in the weighted Shapley value cannot be interpreted as a measure of power (i.e. of the ability to bargain) of the players. This paper proposes a new weight scheme for the Shapley value. Weights in this framework have to be interpreted as a measure of bargaining power. Two different axiomatic characterization of this new value are proposed: one including the weights in the axioms and one without.

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File URL: http://www.sciencedirect.com/science/article/B6V88-4JW11Y8-2/2/b23d7798d4f6f6262784a3a55ba87a5e
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Bibliographic Info

Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 52 (2006)
Issue (Month): 1 (July)
Pages: 88-98

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Handle: RePEc:eee:matsoc:v:52:y:2006:i:1:p:88-98

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Web page: http://www.elsevier.com/locate/inca/505565

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References

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  1. Ehud Kalai & Dov Samet, 1983. "On Weighted Shapley Values," Discussion Papers 602, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Nowak, A.S. & Radzik, T., 1995. "On axiomatizations of the weighted Shapley values," Games and Economic Behavior, Elsevier, vol. 8(2), pages 389-405.
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Cited by:
  1. Vidal-Puga, Juan, 2012. "The Harsanyi paradox and the “right to talk” in bargaining among coalitions," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 214-224.
  2. Inés Macho-Stadler & David Pérez-Castrillo & David Wettstein, 2010. "Dividends and weighted values in games with externalities," International Journal of Game Theory, Springer, vol. 39(1), pages 177-184, March.
  3. Radzik, Tadeusz, 2012. "A new look at the role of players’ weights in the weighted Shapley value," European Journal of Operational Research, Elsevier, vol. 223(2), pages 407-416.
  4. Jean-François Caulier & Michel Grabisch & Agnieszka Rusinowska, 2013. "An allocation rule for dynamic random network formation processes," Documents de travail du Centre d'Economie de la Sorbonne 13063, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  5. Amandine Ghintran, 2010. "A weighted position value," Working Paper Series 1008, Óbuda University, Keleti Faculty of Business and Management.
  6. Gómez-Rúa, María & Vidal-Puga, Juan, 2008. "The axiomatic approach to three values in games with coalition structure," MPRA Paper 8904, University Library of Munich, Germany.
  7. van den Nouweland, Anne & Slikker, Marco, 2012. "An axiomatic characterization of the position value for network situations," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 266-271.
  8. Dinko Dimitrov & Claus-Jochen Haake, 2006. "An axiomatic approach to composite solutions," Working Papers 385, Bielefeld University, Center for Mathematical Economics.
  9. Ghintran, Amandine, 2013. "Weighted position values," Mathematical Social Sciences, Elsevier, vol. 65(3), pages 157-163.

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