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 -