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On axiomatizations of the weighted Shapley values


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  • Nowak, A.S.
  • Radzik, T.


The family of weighted Shapley values for cooperative n-person transferable utility games is studied. We assume first that the weights of the players are given exogenously and provide two axiomatic characterizations of the corresponding weighted Shapley value. Our first characterization is based on the classical axioms determining the Shapley value with the symmetry axiom replaced by a new postulate called the [omega]-mutual dependence. In our second axiomatization we use among other things the strong monotonicity property of Young (1985, Int. J. Game Theory 14, 65-72). Finally, we give a new axiomatic characterization of the family of all weighted Shapley values. Journal of Economic Literature Classification Number: C71, D46.

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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 8 (1995)
Issue (Month): 2 ()
Pages: 389-405

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Handle: RePEc:eee:gamebe:v:8:y:1995:i:2:p:389-405

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  1. Monderer, Dov & Samet, Dov & Shapley, Lloyd S, 1992. "Weighted Values and the Core," International Journal of Game Theory, Springer, vol. 21(1), pages 27-39.
  2. Chun, Youngsub, 1991. "On the Symmetric and Weighted Shapley Values," International Journal of Game Theory, Springer, vol. 20(2), pages 183-90.
  3. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
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Cited by:
  1. Kranich, Laurence, 1997. "Cooperative Games with Hedonic Coalitions," Games and Economic Behavior, Elsevier, vol. 18(1), pages 83-97, January.
  2. 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.
  3. Tadeusz Radzik & Andrzej Nowak & Theo Driessen, 1997. "Weighted Banzhaf values," Computational Statistics, Springer, vol. 45(1), pages 109-118, February.
  4. Marcin Malawski, 2002. "Equal treatment, symmetry and Banzhaf value axiomatizations," International Journal of Game Theory, Springer, vol. 31(1), pages 47-67.
  5. David Housman, 2002. "Linear and symmetric allocation methods for partially defined cooperative games," International Journal of Game Theory, Springer, vol. 30(3), pages 377-404.
  6. Guillaume Haeringer, 1998. "A new weight scheme for the Shapley value," Game Theory and Information 9807001, EconWPA.
  7. Conklin, Michael & Powaga, Ken & Lipovetsky, Stan, 2004. "Customer satisfaction analysis: Identification of key drivers," European Journal of Operational Research, Elsevier, vol. 154(3), pages 819-827, May.


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