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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)

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 \(6.2\%\).

Keywords

Facility location Group partition Coalitional stability Approximate equilibrium 

Notes

Acknowledgments

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

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Copyright information

© Springer Nature Switzerland AG 2019

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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