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Locational equilibrium of two facilities on a tree. (English) Zbl 0734.90048

Summary: This paper considers the location of two facilities on a tree. In particular, conditions for the existence of an equilibrium are derived and an efficient computational procedure is described for finding such an equilibrium, if one exists. Secondly, conditions for the so-called “first-entry paradox” are examined: in this, the first entrant to a market may not always have an advantage over his opponent as commonly thought. Relationships between the occurrence of this paradox and the existence of a Nash equilibrium are demonstrated.

MSC:

90B80 Discrete location and assignment
91B50 General equilibrium theory
91B24 Microeconomic theory (price theory and economic markets)
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