Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
Spatial equilibrium in a multidimensional space : An immigration-consistent division into countries centered at barycenter. / Marakulin, Valeriy.
Mathematical Optimization Theory and Operations Research - 18th International Conference, MOTOR 2019, Proceedings. ed. / Michael Khachay; Panos Pardalos; Yury Kochetov. Springer-Verlag GmbH and Co. KG, 2019. p. 651-672 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11548 LNCS).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
}
TY - GEN
T1 - Spatial equilibrium in a multidimensional space
T2 - 18th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2019
AU - Marakulin, Valeriy
PY - 2019/1/1
Y1 - 2019/1/1
N2 - 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.
AB - 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.
KW - Barycenter
KW - Generalized fixed point theorems
KW - Migration stable partitions
KW - Tiebout equilibrium
UR - http://www.scopus.com/inward/record.url?scp=85067680525&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-22629-9_46
DO - 10.1007/978-3-030-22629-9_46
M3 - Conference contribution
AN - SCOPUS:85067680525
SN - 9783030226282
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 651
EP - 672
BT - Mathematical Optimization Theory and Operations Research - 18th International Conference, MOTOR 2019, Proceedings
A2 - Khachay, Michael
A2 - Pardalos, Panos
A2 - Kochetov, Yury
PB - Springer-Verlag GmbH and Co. KG
Y2 - 8 July 2019 through 12 July 2019
ER -
ID: 20643555