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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/200632
The essential coalitions index in games with restricted cooperation
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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.
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JANÉ BALLARÍN, Martí. The essential coalitions index in games with restricted cooperation. UB Economics – Working Papers. 2023 E23/449. [consulted: 17 of June of 2026]. Available at: https://hdl.handle.net/2445/200632