Transparency versus Opacity: Personalized pricing and firm competition under network effects

We study firms' strategic choice between transparent and opaque personalized pricing in a duopoly with differentiated network goods with both within-firm and between-firm network effects. Under transparent pricing, consumers observe prices offered to others and internalize the resulting network benefits. In contrast, under opaque pricing, such information remains private, limiting consumers' ability to coordinate their purchasing decisions. Consumers are heterogeneous in baseline valuations and firm-specific preferences. We show that, unlike in monopoly settings, opaque pricing is more profitable than transparent pricing in competitive markets whenever firms' networks are not perfectly compatible. This is because transparency intensifies competition by allowing consumers to respond strategically to expected network participation, whereas opacity doesn't allow the same, enabling firms to sustain higher prices. Endogenizing firms' choice of pricing schemes, we show that when firms' network compatibility is relatively high, or consumers are sufficiently heterogeneous, or firms' marginal cost differences are high, (Opaque, Opaque) is the unique Nash equilibrium. In other cases, firms' pricing schemes become strategic complements, giving rise to both (Transparent, Transparent) and (Opaque, Opaque) as Nash equilibria; however, the latter is Pareto-dominant. We further show that transparent pricing can induce strategic subsidization, whereby a high-cost firm prices below cost for low-valuation consumers to signal stronger network benefits. In a sequential purchasing environment, we show that firms earn higher profits than under transparent pricing, but lower profits than under opaque pricing. Finally, we show that prohibiting personalized pricing always lowers firms' profits in a duopoly.