Hotelling Games with Three, Four, and More Players*

Abstract

. This paper extends the interval Hotelling model with quadratic transport costs to the n-player case. For a large set of locations including potential equilibrium configurations, we show for n > 2 that firms neither maximize differentiation—as in the duopoly model—nor minimize differentiation—as in the multi-firm 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 firm locations. Results are driven by an asymmetry between firms. Interior firms are weaker competitors than their rivals at the corners. Increasing the number of firms shifts even more power to the corner firms. As a result, there is too much differentiation from the social perspective if n ≤ 3, while adding firms leads to a level of differentiation in equilibrium below the social optimum.