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Non-technical abstractThis paper addresses the problem of price discrimination in an oligopoly context where firms have imperfect information about consumers' characteristics. The economics of price discrimination under imperfect information is well understood under monopoly conditions but not entirely under oligopoly. The purpose of the paper is to characterise competition between two rival firms that offer discriminatory contracts. The problem is addressed in a stylised market where consumers have heterogeneous preferences both over a horizontal parameter (brand) and a vertical one (quality). The difference in consumer types over the vertical parameter gives a rationale for non-linear contracts, while the horizontal dimension is used to control for the intensity of price competition.Discriminatory contracts are characterised for different market structures: monopoly, collusive duopoly and competitive duopoly.Matters are more complex in an oligopolistic setting that under monopoly because the presence of more than one firm gives the customer the right to buy products from different suppliers. In a competitive environment, contracts should not only perform the standard function as a screening device that gives the right incentive to customer to reveal their type, but also they should not give room to rivals. Since firms typically differ in the relative appeal to customers, I study the properties of equilibrium contracts with different intensity of competition.In the context of the model analysed, I show that oligopolistic interaction between firms can be reduced to reformulating the participation constraints that become typedependent, so that the solution can be thought of as a monopolist's problem with nonstandard binding constraints. It is shown how there are three different mechanisms at work according to the intensity of competition. When competition from a rival is very mild, the basic discriminatory mechanism is the same one as under monopoly, and competition simply redistributes surplus. When competition becomes more intense, the presence of a rival good diminishes the screening ability of an incumbent firm, so that there are also efficiency gains. In particular, quality distortions are reduced so that prices can go up, reflecting higher product quality. Finally, any distortion is eliminated and no screening is possible when brand preferences are not too strong or consumer heterogeneity over vertical parameters is suffic...