Geodesic
Competitive facility location models
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 6, pp. 1037-1054

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Two classes of competitive facility location models are considered, in which several persons (players) sequentially or simultaneously open facilities for serving clients. The first class consists of discrete two-level programming models. The second class consists of game models with several independent players pursuing selfish goals. For the first class, its relationship with pseudo-Boolean functions is established and a novel method for constructing a family of upper and lower bounds on the optimum is proposed. For the second class, the tight PLS-completeness of the problem of finding Nash equilibriums is proved. 
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     author = {A. V. Kononov and Yu. A. Kochetov and A. V. Plyasunov},
     title = {Competitive facility location models},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1037--1054},
     publisher = {mathdoc},
     volume = {49},
     number = {6},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_6_a7/}
}
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A. V. Kononov; Yu. A. Kochetov; A. V. Plyasunov. Competitive facility location models. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 6, pp. 1037-1054. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_6_a7/