Hotelling’s duopoly on a tree

This paper considers Hotelling’s duopoly model on a tree. It is shown that if both competitiors have price and location as decision variables, no equilibrium exists. If prices are fixed in advance by the competitors, equilibria may exist. Conditions for this case are developed. Then the related sequential location problem is investigated. It is shown that it is usually beneficial for a facility not to locate first but to react to its competitor’s location choice.