Abstract: We show that under horizontal differentiation pure equilibria exist if firms react to a rise in competitors' output in such a way that their market price does not rise. This condition is related to strategic complementarity, but not to convexity or differentiability. We rule out multiple equilibria under some additional conditions and discuss stability and regularity of equilibria with ordinal methods. Following entry equilibrium price decreases only if competitors' outputs enter inverse demand aggregated into a single number, otherwise it may increase even in stable equilibria. The comparative statics of quantities and profits for all equilibria are given.