In Hotelling style duopoly location games the product variety (or firm locations) is typically not socially optimal. This occurs because the competitive outcome is driven by the density of consumers at the margin while the socially optimal outcome depends on the whole distribution of consumer...

Theoretical models of spatial competition usually assume an uniform consumer distribution. In the real world, firms frequently compete for consumers who are not uniformly located. The equilibrium duopoly locations of several types of commonly used distributions were discussed in Meagher, Teo and...