Multiple cartel-like equilibria in Hotelling’s model

We study Hotelling’s two-stage model of spatial competition with quadratic transportation costs, where two firms first simultaneously choose locations in the unit interval and then set prices. Relative to the standard framework, we relax the assumption that the reservation price is sufficiently high to ensure full market coverage. Consequently, the market is covered only if the equilibrium prices are low enough. We identify local subgame-perfect equilibria and, using numerical methods, explore their properties. For intermediate reservation prices, our results indicate the existence of multiple equilibria characterized by full market coverage and a cartel-like structure: firms set prices at the highest level consistent with full market coverage, such that the indifferent consumer receives zero utility. We also find intervals of reservation prices in which differentiation either decreases or increases as the reservation price rises. In all cases, consumers located at the endpoints of the Hotelling line have zero utility from purchasing the good.