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An axiomatic approach to composite solutions

Author

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  • Dimitrov, Dinko

    (Center for Mathematical Economics, Bielefeld University)

  • Haake, Claus-Jochen

    (Center for Mathematical Economics, Bielefeld University)

Abstract

We investigate a situation in which gains from cooperation are represented by a cooperative TU-game and a solution proposes a division of coalitional worths. In addition, asymmetries among players outside the game are captured by a vector of exogenous weights. If a solution measures players' payoffs inherent in the game, and a coalition has formed, then the question is how to measure players' overall payoffs in that coalition. For this we introduce the notion of a composite solution. We provide an axiomatic characterization of a specific composite solution, in which exogenous weights enter in a proportional fashion.

Suggested Citation

  • Dimitrov, Dinko & Haake, Claus-Jochen, 2011. "An axiomatic approach to composite solutions," Center for Mathematical Economics Working Papers 385, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:385
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    File URL: https://pub.uni-bielefeld.de/download/2315647/2319824
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    References listed on IDEAS

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    1. Haeringer, Guillaume, 2006. "A new weight scheme for the Shapley value," Mathematical Social Sciences, Elsevier, vol. 52(1), pages 88-98, July.
    2. James M. Snyder Jr. & Michael M. Ting & Stephen Ansolabehere, 2005. "Legislative Bargaining under Weighted Voting," American Economic Review, American Economic Association, vol. 95(4), pages 981-1004, September.
    3. Ehud Kalai & Dov Samet, 1983. "On Weighted Shapley Values," Discussion Papers 602, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Dimitrov, Dinko & Haake, Claus-Jochen, 2008. "Stable governments and the semistrict core," Games and Economic Behavior, Elsevier, vol. 62(2), pages 460-475, March.
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    Cited by:

    1. Dimitrov, Dinko & Haake, Claus-Jochen, 2011. "Stable governments and the semistrict core," Center for Mathematical Economics Working Papers 378, Center for Mathematical Economics, Bielefeld University.

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    Keywords

    Composite solution; External weights;

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