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A duality and free boundary approach to adverse selection

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  • Robert J. McCann
  • Kelvin Shuangjian Zhang

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. "A duality and free boundary approach to adverse selection," Papers 2301.07660, arXiv.org, revised Nov 2023.
    • Handle: RePEc:arx:papers:2301.07660
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    References listed on IDEAS

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    6. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
    7. J. A. Mirrlees, 1971. "An Exploration in the Theory of Optimum Income Taxation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(2), pages 175-208.
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    Cited by:

    1. Federico Echenique & Joseph Root & Fedor Sandomirskiy, 2024. "Stable matching as transportation," Papers 2402.13378, arXiv.org.

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