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Stochastic Sequential Screening

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  • Hao Li
  • Xianwen Shi

Abstract

We study when and how randomization can help improve the seller's revenue in the sequential screening setting. In a model with discrete ex ante types and a continuum of ex post valuations, the standard approach based on solving a relaxed problem that keeps only local downward incentive compatibility constraints often fails. Under a strengthening of first-order stochastic dominance ordering on the valuation distribution functions of ex ante types, we introduce and solve a modified relaxed problem by retaining all local incentive compatibility constraints, provide necessary and sufficient conditions for optimal mechanisms to be stochastic, and characterize optimal stochastic contracts. Our analysis mostly focuses on the case of three ex ante types, but our methodology of solving the modified problem, as well as the necessary and sufficient conditions for randomization to be optimal, can be extended to any finite number of ex ante types.

Suggested Citation

  • Hao Li & Xianwen Shi, 2025. "Stochastic Sequential Screening," Working Papers tecipa-793, University of Toronto, Department of Economics.
    • Handle: RePEc:tor:tecipa:tecipa-793
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    References listed on IDEAS

    as
    1. Bergemann, Dirk & Castro, Francisco & Weintraub, Gabriel Y., 2020. "The scope of sequential screening with ex post participation constraints," Journal of Economic Theory, Elsevier, vol. 188(C).
    2. John Riley & Richard Zeckhauser, 1983. "Optimal Selling Strategies: When to Haggle, When to Hold Firm," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 98(2), pages 267-289.
    3. Richard J. Gilbert & Paul Klemperer, 2000. "An Equilibrium Theory of Rationing," RAND Journal of Economics, The RAND Corporation, vol. 31(1), pages 1-21, Spring.
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    More about this item

    Keywords

    Sequential Screening; Stochastic Mechanism;

    JEL classification:

    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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