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On axiomatizations of the weighted Shapley values

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  • Nowak, A.S.
  • Radzik, T.

Abstract

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.

Suggested Citation

  • Nowak, A.S. & Radzik, T., 1995. "On axiomatizations of the weighted Shapley values," Games and Economic Behavior, Elsevier, vol. 8(2), pages 389-405.
    • Handle: RePEc:eee:gamebe:v:8:y:1995:i:2:p:389-405
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    References listed on IDEAS

    as
    1. Monderer, Dov & Samet, Dov & Shapley, Lloyd S, 1992. "Weighted Values and the Core," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(1), pages 27-39.
    2. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    3. Chun, Youngsub, 1991. "On the Symmetric and Weighted Shapley Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(2), pages 183-190.
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    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D46 - Microeconomics - - Market Structure, Pricing, and Design - - - Value Theory

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