Approximate Coalitional Equilibria in the Bipolar World

  • Andrei Golman
  • Daniil MusatovEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 974)


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 \(6.2\%\).


Facility location Group partition Coalitional stability Approximate equilibrium 



We want to thank Alexei Savvateev for his support and advice during the work on this paper.


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Authors and Affiliations

  1. 1.Moscow Institute of Physics and TechnologyDolgoprudnyRussia
  2. 2.Russian Presidential Academy of National Economy and Public AdministrationMoscowRussia
  3. 3.Caucasus Mathematical Center at Adyghe State UniversityMaykopRussia

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