Unicity of the equilibrium in the unconstrained Hotelling model

Abstract

A spatial duopoly is described, where firms are free to locate along the real axis, while consumers are distributed along a linear city of finite length. By adding a preplay stage where firms are required to set the timing of moves, one can analyze issues such as the endogenous choice of roles and the nature of differentiation at equilibrium. The distribution of roles is discussed both at the location stage and at the price stage. The game exhibits a unique subgame perfect equilibrium in pure strategies (up to a permutation), where firms play simultaneously in locations and sequentially in prices. Moreover, the results highlight the relevance of endogenous differentiation in altering some of the conclusions reached by previous literature. Finally, it turns out that the nature of differentiation may be heavily affected by the sequence of decisions.