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

Takayuki Oishi ()
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Takayuki Oishi: Meisei University

Economic Theory Bulletin, 2020, vol. 8, issue 1, No 10, 113-123

Abstract: 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.

Keywords: Constant-sum weighted majority games; Homogeneous representation; $$\alpha $$ α -Nucleolus; Distorted satisfaction; Peleg’s representation theorem (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s40505-019-00171-7

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