Nonlinear Pricing in Oligopoly: How Brand Preferences Shape Market Outcomes

We study oligopolistic competition by firms engaging in second-degree price discrimination. In line with the large empirical literature on demand estimation, our theory allows for comovements between consumers' taste for quality and propensity to switch brands. If low-type consumers are sufficiently less (more) brand loyal than high types, (i) quality provision is inefficiently low at the bottom (high at the top) of the product line, and (ii) informational rents are negative (positive) for high types, while positive (negative) for low types. We produce several testable comparative statics on pricing and quality provision, and show that more competitive markets (in the sense that consumers are less brand-loyal) may produce lower welfare. Interestingly, pure-strategy equilibria fail to exist whenever brand loyalty is sufficiently different across consumers types. Accordingly, our theory identifies a new rationale for price/quality dispersion; namely, the interplay between self-selection constraints and heterogeneity in brand loyalty.