Hotelling’s Model with Firms Located Close to Each Other

Hotelling’s model—which is commonly referred to as the “linear city” model—is perhaps the most widely-used model of competition in differentiated products. However, pure-strategy Nash equilibria in prices do not exist unless the firms are located either sufficiently far apart from each other or at the same place. In fact, pure-strategy Nash equilibrium prices exist in only about 15 percent of all possible locations of firms in the linear city. This paper applies the undercut-proof equilibrium concept to solve for equilibrium prices for all possible locations of firms in the linear city.