Equilibria in unidirectional spatial models

This paper (a) characterizes the unique Nash equilibrium of the unidirectional Hotelling–Downs game in which firms maximize their market shares, for any distribution of the consumers, and (b) analyzes equilibrium behavior in the variation of the game in which each firm aims to secure a larger market share than its competitor. In the first case, firms employ identical mixed strategies and each of them serves (in expected terms) a fraction (1/e) of the market and in both cases no firm ever locates in a position to the left of the first quartile of the consumers’ distribution.