Product differentiation with multiple qualities

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We study subgame-perfect equilibria of the classical quality-price, multistage game of vertical product differentiation. Each of two firms 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 effects of qualities on the rival’s equilibrium price in the general model. Equilibrium qualities depend on what we call the Spence and price-reaction effects. For any equilibrium, we characterize conditions for quality differentiation.