Product Differentiation with Multiple Qualities

We study subgame-perfect equilibria of the classical quality-price, multistage game of vertical product differentiation. Each firm can choose the levels of an arbitrary number of qualities. Consumers' valuations are drawn from independent and general distributions. The unit cost of production is increasing and convex in qualities. We characterize equilibrium prices, and the equilibrium effects of qualities on the rival's price in the general model. We present necessary and sufficient conditions for equilibrium differentiation in any of the qualities.