A general solution to the quasi linear screening problem

Carlier, Guillaume; Dupuis, Xavier; Rochet, Jean-Charles; Thanassoulis, John

doi:10.1016/j.jmateco.2024.103025

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2024

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A duality and free boundary approach to adverse selection

McCann,

Zhang

2024

Math. Models Methods Appl. Sci.

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Adverse selection is a version of the principal-agent problem that includes monopolist nonlinear pricing, where a monopolist with known costs seeks a profit-maximizing price menu facing a population of potential consumers whose preferences are known only in the aggregate. For multidimensional spaces of agents and products, Rochet and Choné (Econometrica, 1998) reformulated this problem as a concave maximization over the set of convex functions, by assuming agent preferences combine bilinearity in the product and agent parameters with a quasilinear sensitivity to prices. We characterize solutions to this problem by identifying a dual minimization problem. This duality allows us to reduce the solution of the square example of Rochet–Choné to a novel free boundary problem, giving the first analytical description of an overlooked market segment.

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