Does it Pay to be First? Sequential Locational Choice and Foreclosure

Abstract

We analyze the sequential choices of locations in the Hotelling [0, 1] space of variety-differentiated products. n firms locate in sequence, one at a time. In stage n+1, all firms choose prices simultaneously. Firms anticipate correctly the decisions of subsequent entrants, as well as the equilibrium prices, so we analyze subgame-perfect equilibria. We analyze two games. In the first, the number of firms is fixed. In the second, the number of firms is determined by free entry, i.e., entry continues until the last entrant makes nonnegative profits. When the number of firms is fixed, the ordering of profits follows the order of action. When the number of firms is determined by free entry, for a range of fixed costs, early entrants choose their positions strategically so as to keep out potential entrants. For a range of fixed costs, early actors reduce the distances among them to foreclose entry even though these actions reduce their profits given the number of active firms. For low enough fixed costs, entry cannot be prevented any more and a new firm enters resulting in a complete disruption of the locational pattern. In the game with a fixed number of firms, we find that the order of the profits of the firms is the same as the order of action, so that it pays to be first. In contrast, in the free entry game it does not always pay to be first. We also note that entry of a new firm significantly reduces the pre-entry profits of incumbents. Thus, if a technology is available that would increase the costs of both incumbents and entrants ( raising both rivals and own costs ), it will be used to deter entry.