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A generalization of Peleg’s representation theorem on constant-sum weighted majority games

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  • Takayuki Oishi

    (Meisei University)

Abstract

We propose a variant of the nucleolus associated with distorted satisfaction of each coalition in TU games. This solution is referred to as the $$\alpha $$α-nucleolus in which $$\alpha $$α is a profile of distortion rates of satisfaction of all the coalitions. We apply the $$\alpha $$α-nucleolus to constant-sum weighted majority games. We show that under assumptions of distortions of satisfaction of winning coalitions the $$\alpha $$α-nucleolus is the unique normalized homogeneous representation of constant-sum weighted majority games which assigns a zero to each null player. As corollary of this result, we derive the well-known Peleg’s representation theorem.

Suggested Citation

  • Takayuki Oishi, 2020. "A generalization of Peleg’s representation theorem on constant-sum weighted majority games," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 113-123, April.
    • Handle: RePEc:spr:etbull:v:8:y:2020:i:1:d:10.1007_s40505-019-00171-7
    DOI: 10.1007/s40505-019-00171-7
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    References listed on IDEAS

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    1. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
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    5. Maschler, Michael, 1992. "The bargaining set, kernel, and nucleolus," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 18, pages 591-667, Elsevier.
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    More about this item

    Keywords

    Constant-sum weighted majority games; Homogeneous representation; $$alpha $$ α -Nucleolus; Distorted satisfaction; Peleg’s representation theorem;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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