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Sequential Competitive Location on Networks

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Dominik Kreß

This book deals with classical competitive location problems where two players, leader and follower, sequentially enter markets with given numbers of facilities. The markets under consideration are represented as networks. The book provides a detailed overview of the literature on competitive and voting location, and it presents extensions and variations of the classical models, with a focus on the incorporation of proportional choice rules, non-discrete demand (edge demand), or additional pricing decisions of the players. It provides corresponding mathematical models, insights into the computational complexity of the resulting problems and proposes and analyzes adequate solution methods.

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Chapter 2. Sequential Competitive Locationon Networks: Literature Review

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Chapter 2 Sequential Competitive Location on Networks: Literature Review Eiselt and Laporte presented a survey of sequential competitive location prob- lems in 1996. Various publications in this field have appeared since then. We will therefore extend Eiselt and Laporte (1996) by reviewing some of these recent developments in this chapter as in Kress and Pesch (2012d). The scope of review is as follows: • We restrict ourselves to detailed descriptions of publications that have appeared after Eiselt and Laporte (1996). • We include voting location problems. • Our focus is on models where potential locations are not a priori re- stricted to a finite set of points, as one finds up-to-date reviews con- cerning discrete models in Current et al. (2002); Daskin (2008); ReVelle et al. (2008); Serra and ReVelle (1995). • Furthermore, we restrict our attention to problems defined on networks. Since a line, i.e. an interval of one-dimensional real space, may be interpreted as a special type of network and because models defined on lines might contain ideas worth adapting in more general network models, we include these models as well, yet without describing them in detail for the sake of brevity. 16 Chapter 2. Sequential Competitive Location on Networks: Literature Review • We explicitly exclude location decisions in political issue spaces and refer the reader to Osborne (1995) and the references therein. • Furthermore, for the most part, we exclude coverage problems as an ex- cellent, very recent survey is Berman et al. (2010). Only indispensable models are surveyed in this...

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