Product differentiation and entry timing in a continuous-time spatial competition model with vertical relations

We study the entry timing and location decisions of two exclusive buyer-supplier relationships in a continuous-time spatial competition model. In each relationship, the firms determine their entry timing and location, and negotiate a wholesale price through Nash bargaining. Then, the downstream firm immediately determines its retail price. Our findings are as follows. Ordinarily, if the supplier of the first entrant (called the leader pair) has strong bargaining power, the equilibrium location of the leader will be closer to the center, inducing a delay in entry by the second entrant (called the follower pair). This delay implies the stronger bargaining power of the supplier in the leader pair can also benefit the buyer of the pair. The location of the leader pair can change non-monotonically with an increase in the supplier's bargaining power, which has a substantial impact on the entry timing of the follower pair. However, the greater the bargaining power of the supplier in the follower pair, the closer the leader pair will be to the edge. This implies that having greater bargaining power will enhance the profitability of the supplier in the follower pair.