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Conveying Value via Categories

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  • Paula Onuchic
  • Debraj Ray

Abstract

A sender sells an object of unknown quality to a receiver who pays his expected value for it. Sender and receiver might hold different priors over quality. The sender commits to a monotonic categorization of quality. We characterize the sender's optimal monotonic categorization. Using our characterization, we study the optimality of full pooling or full separation, the alternation of pooling and separation, and make precise a sense in which pooling is dominant relative to separation. We discuss applications, extensions and generalizations, among them the design of a grading scheme by a profit-maximizing school which seeks to signal student qualities and simultaneously incentivize students to learn. Such incentive constraints force monotonicity, and can also be embedded as a distortion of the school's prior over student qualities, generating a categorization problem with distinct sender and receiver priors.

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  • Paula Onuchic & Debraj Ray, 2021. "Conveying Value via Categories," Papers 2103.12804, arXiv.org.
  • Handle: RePEc:arx:papers:2103.12804
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    References listed on IDEAS

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    1. Yeon-Koo Che & Navin Kartik, 2009. "Opinions as Incentives," Journal of Political Economy, University of Chicago Press, vol. 117(5), pages 815-860, October.
    2. ,, 2009. "Monopolistic group design with peer effects," Theoretical Economics, Econometric Society, vol. 4(1), March.
    3. Popov, Sergey V. & Bernhardt, Dan, 2010. "University Competition, Grading Standards and Grade Inflation," MPRA Paper 26461, University Library of Munich, Germany.
    4. Raphael Boleslavsky & Christopher Cotton, 2015. "Grading Standards and Education Quality," American Economic Journal: Microeconomics, American Economic Association, vol. 7(2), pages 248-279, May.
    5. Simone Galperti, 2019. "Persuasion: The Art of Changing Worldviews," American Economic Review, American Economic Association, vol. 109(3), pages 996-1031, March.
    6. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    7. Alonso, Ricardo & Câmara, Odilon, 2016. "Bayesian persuasion with heterogeneous priors," Journal of Economic Theory, Elsevier, vol. 165(C), pages 672-706.
    8. Kolotilin, Anton, 2018. "Optimal information disclosure: a linear programming approach," Theoretical Economics, Econometric Society, vol. 13(2), May.
    9. Piotr Dworczak & Giorgio Martini, 2019. "The Simple Economics of Optimal Persuasion," Journal of Political Economy, University of Chicago Press, vol. 127(5), pages 1993-2048.
    10. Navin Kartik & Frances Xu Lee & Wing Suen, 2021. "Information Validates the Prior: A Theorem on Bayesian Updating and Applications," American Economic Review: Insights, American Economic Association, vol. 3(2), pages 165-182, June.
    11. Skreta, Vasiliki & Veldkamp, Laura, 2009. "Ratings shopping and asset complexity: A theory of ratings inflation," Journal of Monetary Economics, Elsevier, vol. 56(5), pages 678-695, July.
    12. Eric Van den Steen, 2009. "Authority versus Persuasion," American Economic Review, American Economic Association, vol. 99(2), pages 448-453, May.
    13. Elliot Lipnowski & Doron Ravid, 2020. "Cheap Talk With Transparent Motives," Econometrica, Econometric Society, vol. 88(4), pages 1631-1660, July.
    14. Alonso, Ricardo & Câmara, Odilon, 2016. "Political disagreement and information in elections," Games and Economic Behavior, Elsevier, vol. 100(C), pages 390-412.
    15. Rayo Luis, 2013. "Monopolistic Signal Provision†," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 13(1), pages 27-58, May.
    16. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    17. Eric Van den Steen, 2010. "On the origin of shared beliefs (and corporate culture)," RAND Journal of Economics, RAND Corporation, vol. 41(4), pages 617-648, December.
    18. Michael Ostrovsky & Michael Schwarz, 2010. "Information Disclosure and Unraveling in Matching Markets," American Economic Journal: Microeconomics, American Economic Association, vol. 2(2), pages 34-63, May.
    19. repec:bla:ecinqu:v:51:y:2013:i:3:p:1764-1778 is not listed on IDEAS
    20. Gregorio Curello & Ludvig Sinander, 2022. "The comparative statics of persuasion," Papers 2204.07474, arXiv.org, revised Oct 2024.
    21. Laura Doval & Vasiliki Skreta, 2018. "Constrained Information Design," Papers 1811.03588, arXiv.org, revised Aug 2022.
    22. Maryam Saeedi & Ali Shourideh, 2020. "Optimal Rating Design under Moral Hazard," Papers 2008.09529, arXiv.org, revised Jul 2023.
    23. Muhamet Yildiz, 2004. "Waiting to Persuade," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(1), pages 223-248.
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    Cited by:

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    More about this item

    JEL classification:

    • 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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