This paper studies the relationship between horizontal product differentiation and the welfare effects of third-degree price discrimination in oligopoly. By deriving linear demand from a representative consumer's utility and focusing on the symmetric equilibrium of a pricing game, we characterize the conditions relating to such demand properties as substitutability and complementarity for price discrimination to improve social welfare. In particular, we show that price discrimination can improve social welfare if firms' brands are substitutes in a market where the discriminatory price is higher and complements in one where it is lower, but welfare never improves in the reverse situation. We verify, however, that consumer surplus is never improved by price discrimination; welfare improvement by price discrimination is solely due to an increase in the firms' profits. This means that there is no chance that firms suffer from a prisoners' dilemma, that is, firms are better off by switching from uniform pricing to price discrimination.
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