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Erschienen in:
2019 | OriginalPaper | Buchkapitel
Approximate Coalitional Equilibria in the Bipolar World
verfasst von : Andrei Golman, Daniil Musatov
Erschienen in: Optimization and Applications
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Abstract
We study a discrete model of jurisdiction formation in the spirit of Alesina and Spolaore [1]. A finite number of agents live along a line. They can be divided into several groups. If a group is formed, then some facility is located at its median and every member x of a group S with a median m pays \(\frac{1}{|S|}+|x-m|\).
We consider the notion of coalitional stability: a partition is stable if no coalition wishes to form a new group decreasing the cost of all members. It was shown by Savvateev et al. [4] that no stable partition may exist even for 5 agents living at 2 points. We now study approximately stable partitions: no coalition wishes to form a new group decreasing all costs by at least \(\epsilon \).
In this work, we define a relative measure of partition instability and consider bipolar worlds where all agents live in just 2 points. We prove that the maximum possible value of this measure is approximately \(6.2\%\).