Spatial Duopoly with a Reservation Price

Introducing a finite reservation price in Hotelling’s spatial duopoly with linear transportation costs shows that (i) there dose not exist a pure strategy symmetric location equilibrium of the reservation price is 'high’, (ii) there exists a unique pure strategy symmetric location equilibrium (in which the two firms compete with each other and cover the entire market) if the reservation price is 'intermediate’. The equilibrium distance between the two firms in the latter case is at least a quarter and at most half the length of the market.