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arXiv · 2301.07660

A duality and free boundary approach to adverse selection

Robert J. McCann·Kelvin Shuangjian Zhang
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Abstract

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 Chon\'e (1998) reformulated this problem to 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-Chon\'e to a novel free boundary problem, giving the first analytical description of an overlooked market segment.

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Robert J. McCann, Kelvin Shuangjian Zhang. 2023-01-18. A duality and free boundary approach to adverse selection. https://arxiv.org/abs/2301.07660

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