Competitive Imperfect Price Discrimination and Market Power

Two duopolists compete in price on the market for a homogeneous product. They can 'profile' consumers, i.e., 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.