Geodesic
Migration-Proof Organization of a Linear World: Existence Theorem
The Bulletin of Irkutsk State University. Series Mathematics, Tome 6 (2013) no. 2, pp. 57-68

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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, non-atomic games, migration-proofness, Nash stability
Mots-clés : group structures, Nikaido–Gale–Debre Lemma. 
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     author = {A. V. Savvateev},
     title = {Migration-Proof {Organization} of a {Linear} {World:} {Existence} {Theorem}},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {57--68},
     publisher = {mathdoc},
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     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2013_6_2_a5/}
}
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A. V. Savvateev. Migration-Proof Organization of a Linear World: Existence Theorem. The Bulletin of Irkutsk State University. Series Mathematics, Tome 6 (2013) no. 2, pp. 57-68. http://geodesic.mathdoc.fr/item/IIGUM_2013_6_2_a5/