Locational equilibrium of two facilities on a tree

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.