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A new weight scheme for the Shapley value

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  • Guillaume Haeringer

    (Universite Louis Pasteur)

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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Bibliographic Info

Paper provided by EconWPA in its series Game Theory and Information with number 9807001.

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Length: 11 pages
Date of creation: 15 Jul 1998
Date of revision:
Handle: RePEc:wpa:wuwpga:9807001

Note: Type of Document - PostScript; prepared on IBM PC - PC-TEX; to print on PostScript - A4; pages: 11 . 11 pages, postscript, prepared from dvips
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Keywords: Shapley value; weights; monotonicity;

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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. Inés Macho-Stadler & David Pérez-Castrillo & David Wettstein, 2008. "Dividends and Weighted Values in Games with Externalities," Working Papers 366, Barcelona Graduate School of Economics.
  2. 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.
  3. 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.
  4. Ghintran, Amandine, 2013. "Weighted position values," Mathematical Social Sciences, Elsevier, vol. 65(3), pages 157-163.
  5. Gómez-Rúa, María & Vidal-Puga, Juan, 2010. "The axiomatic approach to three values in games with coalition structure," European Journal of Operational Research, Elsevier, vol. 207(2), pages 795-806, December.
  6. Jean-François Caulier & Michel Grabisch & Agnieszka Rusinowska, 2013. "An allocation rule for dynamic random network formation processes," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00881125, HAL.
  7. Dinko Dimitrov & Claus-Jochen Haake, 2006. "An axiomatic approach to composite solutions," Working Papers 385, Bielefeld University, Center for Mathematical Economics.
  8. 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.
  9. Amandine Ghintran, 2009. "A weighted position value," Working Papers hal-00420430, HAL.

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