Competitive imperfect price discrimination and market power

Two duopolists compete on price in the market for a homogeneous product. They can “profile” consumers, that is, identify their valuations with some probability. If both firms can profile consumers but with different abilities, then they achieve positive expected profits at equilibrium. This provides a rationale for firms to (partially and unequally) share data about consumers or for data brokers to sell different customer analytics to competing firms. Consumers prefer that both firms profile exactly the same set of consumers or that only one firm profiles consumers as this entails marginal cost pricing (so does a policy requiring list prices to be public). Otherwise, more protective privacy regulations have ambiguous effects on consumer surplus.