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Test design under voluntary participation

Author

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  • Rosar, Frank
Abstract
An agent who is imperfectly informed about his binary quality can voluntarily participate in a test that generates a public signal. I study the design of the test that allows for optimal learning of the agent's quality when the agent strives for a high perception of his quality but is averse towards perception risk. For a large class of reduced-form utility functions that reflect these properties, the optimal test is binary and not subject to false positives. I uncover the forces that drive this result and show how the problem with endogenous participation can be transformed into a problem to that the concavification approach from the Bayesian persuasion literature applies. Furthermore, for a non-reduced version of my model where the designer estimates the agent's quality but suffers either more from false positives or from false negatives, I show that the same type of test is optimal.

Suggested Citation

  • Rosar, Frank, 2017. "Test design under voluntary participation," Games and Economic Behavior, Elsevier, vol. 104(C), pages 632-655.
    • Handle: RePEc:eee:gamebe:v:104:y:2017:i:c:p:632-655
    DOI: 10.1016/j.geb.2017.06.002
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Perez-Richet, Eduardo & Vigier, Adrien & Bizzotto, Jacopo, 2019. "Information Design with Agency," CEPR Discussion Papers 13868, C.E.P.R. Discussion Papers.
    2. Eduardo Perez‐Richet & Vasiliki Skreta, 2022. "Test Design Under Falsification," Econometrica, Econometric Society, vol. 90(3), pages 1109-1142, May.
    3. Jacopo Bizzotto & Eduardo Perez-Richet & Adrien Vigier, 2020. "Communication via Third Parties," Working Papers 202006, Oslo Metropolitan University, Oslo Business School.
    4. Escudé, Matteo & Sinander, Ludvig, 2023. "Slow persuasion," Theoretical Economics, Econometric Society, vol. 18(1), January.
      • Matteo Escud'e & Ludvig Sinander, 2019. "Slow persuasion," Papers 1903.09055, arXiv.org, revised Apr 2022.
    5. Laura Doval & Alex Smolin, 2024. "Persuasion and Welfare," Journal of Political Economy, University of Chicago Press, vol. 132(7), pages 2451-2487.
    6. Alonso, Ricardo & Câmara, Odilon, 2018. "On the value of persuasion by experts," Journal of Economic Theory, Elsevier, vol. 174(C), pages 103-123.
    7. Ginzburg, Boris, 2019. "A Simple Model of Competitive Testing," MPRA Paper 99463, University Library of Munich, Germany.
    8. Nikolaus Schweizer & Nora Szech, 2018. "Optimal Revelation of Life-Changing Information," Management Science, INFORMS, vol. 64(11), pages 5250-5262, November.
    9. Choi, Jay Pil & Mukherjee, Arijit, 2019. "Optimal certification policy, entry, and investment in the presence of public signals," Working Papers 2019-6, Michigan State University, Department of Economics.
    10. Marta Serra-Garcia & Nora Szech, 2023. "Incentives and Defaults Can Increase COVID-19 Vaccine Intentions and Test Demand," Management Science, INFORMS, vol. 69(2), pages 1037-1049, February.
    11. Smolin, Alex & Doval, Laura, 2021. "Information Payoffs: An Interim Perspective," TSE Working Papers 21-1247, Toulouse School of Economics (TSE).
    12. Jacopo Bizzotto & Adrien Vigier, 2022. "A Case for Tiered School Systems," Working Papers 202205, Oslo Metropolitan University, Oslo Business School.
    13. Jay Pil Choi & Arijit Mukherjee, 2020. "Optimal certification policy, entry, and investment in the presence of public signals," RAND Journal of Economics, RAND Corporation, vol. 51(4), pages 989-1013, December.
    14. Jacopo Bizzotto & Adrien Vigier, 2022. "Sorting and Grading," Papers 2208.10894, arXiv.org, revised Feb 2024.
    15. Emir Kamenica & Kyungmin Kim & Andriy Zapechelnyuk, 2021. "Bayesian persuasion and information design: perspectives and open issues," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(3), pages 701-704, October.

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    More about this item

    Keywords

    Test design; Bayesian learning; Concavification; False positive; Asymmetric information; Voluntary participation;
    All these keywords.

    JEL classification:

    • D02 - Microeconomics - - General - - - Institutions: Design, Formation, Operations, and Impact
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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