Hotelling Games with Three, Four, and More Players

This paper extends the standard Hotelling model with quadratic transport costs to the multi-firm case. Considering locational equilibria we show that neither holds the Principle of Maximum Differentiation - as in the duopoly model - nor does the Principle of Minimum Differentiation - as in the multiple firms game with linear transport cost. Subgame perfect equilibria for games with up to nine players are characterized by a U-shaped price structure and interior corner firms locations. In equilibrium the level of differentiation is almost at the socially optimal level if the number of firms is larger than three. Otherwise, there is too little differentiation.