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A Generalization of Peleg's Representation Theorem on Constant-Sum Weighted Majority Games

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  • Takayuki Oishi

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 α-nucleolus in which α is a profile of distortion rates of satisfaction of all the coalitions. We apply the α-nucleolus to constant-sum weighted majority games. We show that under assumptions of distortions of satisfaction of winning coalitions the 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, 2019. "A Generalization of Peleg's Representation Theorem on Constant-Sum Weighted Majority Games," Discussion Papers 43, Meisei University, School of Economics.
    • Handle: RePEc:mei:wpaper:43
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    Keywords

    Constant-sum weighted majority games; Homogeneous representation; 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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