Cournot Competition on the Hotelling Line Yields at Most Three Varieties

This paper reexamines the equilibrium product choices in a spatial Cournot n- oligopoly on the linear market by considering the case of output that accidentally harms consumers and firms that are subject to product liability. We characterize the resulting spatial pattern in terms of uniqueness and stability. For low levels of the unit cost of accident, central agglomeration is the unique and stable location equilibrium. For a high enough unit cost of accident, multiple equilibria exist: from central agglomeration to partial dispersion (both asymmetric and symmetric). In this case we show that asymmetric dispersion equilibria as well as symmetrical three-variety equilibria are unstable, whereas there always exists a symmetrical two-variety location equilibrium that is stable. Finally, complete dispersion appears as a very specific case that is limited to duopoly and triopoly: For markets with more firms, equilibrium product differentiation involves partial clustering on three varieties/locations.