Sequential multi-store location in a duopoly

This paper focuses on multi-store sequential locations between two firms within a confined geographical area over the short term. Based on the model of Teitz (1968), we incorporate a fixed cost for opening stores, as well as every possible asymmetry regarding an upper limit on the number of store openings. These two factors have an impact on firms' location strategies as constraints, which yield only two opposing types of equilibrium strategies for the leader. One is the segmentation strategy, where the leader monopolizes a market segment by partially deterring the follower's entry. The other is the equidistant location strategy, where stores are opened at equidistant locations throughout the market. Both maximum and minimum differentiation can result in equilibrium at the firm level. This seems to reflect real-world location patterns well, particularly those observed in some retail industries such as cafes and fast fashion retailers. We also obtain welfare implications of multi-store competition by analyzing the case where the social planner can optimize the upper limit on the number of store openings.