The essential coalitions index in games with restricted cooperation

Martí Jané Ballarín ()
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Martí Jané Ballarín: Universitat de Barcelona
Authors registered in the RePEc Author Service: Martí Jané Ballarín

No 2023/449, UB School of Economics Working Papers from University of Barcelona School of Economics

Abstract: We propose a new power index, which we call the essential coalitions index. Within the field of power indices, the new measure extends the Deegan-Packel power index to situations with restricted cooperation. In general, the class of games we study are not simple; with this in mind, we will introduce the essential coalitions as an analogue to the minimal winning coalitions of a simple game, since they generalize some relevant properties. We will first define the new index in terms of three reasonable assumptions, with a similar flavor to those used for the Deegan-Packel index; then, we will formally characterize the index. Finally, through numeric examples, we compare the essential coalitions index to the probabilistic Deegan-Packel index. We see that, in the latter's domain, the two indices only differ by a constant factor. Moreover, the new index is fit to analyze power in the formation of stable coalitions to run a government or a company board.

Keywords: Cooperative games; simple games; cooperation index; power indices. (search for similar items in EconPapers)
JEL-codes: C71 D71 D72 (search for similar items in EconPapers)
Pages: 21 pages
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:ewp:wpaper:449web

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