Spatial equilibrium in a multidimensional space: An immigration-consistent division into countries centered at barycenter

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

Abstract

It studies the problem of immigration proof partition for communities (countries) in a multidimensional space. This is an existence problem of Tiebout type equilibrium, where migration stability suggests that every inhabitant has no incentives to change current jurisdiction. In particular, an inhabitant at every frontier point has equal costs for all available jurisdictions. It is required that the inter-country border is represented by a continuous curve. The paper presents the solution for the case of the costs described as the sum of the two values: the ratio of total costs on the total weight of the population plus transportation costs to the center presented as a barycenter of the state. In the literature, this setting is considered as a case of especial theoretical interest and difficulty. The existence of equilibrium division is stated via an approximation reducing the problem to the earlier studied case, in which centers of the states never can coincide: to do this an earlier proved a generalization of conic Krasnosel’skii fixed point theorem is applied.

Original languageEnglish
Title of host publicationMathematical Optimization Theory and Operations Research - 18th International Conference, MOTOR 2019, Proceedings
EditorsMichael Khachay, Panos Pardalos, Yury Kochetov
PublisherSpringer-Verlag GmbH and Co. KG
Pages651-672
Number of pages22
ISBN (Print)9783030226282
DOIs
Publication statusPublished - 1 Jan 2019
Event18th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2019 - Ekaterinburg, Russian Federation
Duration: 8 Jul 201912 Jul 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11548 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference18th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2019
CountryRussian Federation
CityEkaterinburg
Period08.07.201912.07.2019

Keywords

  • Barycenter
  • Generalized fixed point theorems
  • Migration stable partitions
  • Tiebout equilibrium

Fingerprint Dive into the research topics of 'Spatial equilibrium in a multidimensional space: An immigration-consistent division into countries centered at barycenter'. Together they form a unique fingerprint.

Cite this