The unidirectional Hotelling model with spatial price discrimination

The unidirectional Hotelling model where consumers can buy only from firms located on their right (left) is extended to allow for price discriminating firms and a general class of transportation costs. In a two-stage location-price game one firm locates at 1/2 and the other locates at 1 (0). We also study collusion in an infinitely repeated game. The maximum collusive profits sustainable in equilibrium monotonically increase (decrease) with the location of the firm located at the right (left), while initially increase and then decrease with the location of the firm located at the left (right). A higher reservation price of consumers makes perfect collusion less sustainable in equilibrium, but allows firms to agree on higher (albeit imperfect) collusive profits.