Migration-Proof Organization of a Linear World: Existence Theorem

A. V. Savvateev<sup>abcdefg

a</sup> CEMI RAS
^b Yandex (Moscow)
^c ISTU (Irkutsk)
^d MIPT
^e DRESP ISC SB RAS
^f NES
^g IMEI ISU

Abstract: In the paper, a uni-dimensional version of the uncapacitated facility location problem is analysed from the angle of Nash-type (i.e. migrational) stability of group structures. A general result is proved that, under arbitrary population distribution admitting a strictly positive density, migration-proof solution comprised of prescribed number of groups always exists. To prove the theorem, a celebrated Nikaido–Gale–Debre Lemma is being utilized.

Keywords: Uncapacitated facility location problem, group structures, non-atomic games, migration-proofness, Nash stability, Nikaido–Gale–Debre Lemma.

MSC: 91A13, 91A44, 91, 90, 06, 52