Theoretical Economics 18 (2023), 1407–1439
Conveying value via categories
Paula Onuchic, Debraj Ray
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 monotone categorization of quality. We characterize the sender's optimal monotone categorization, the optimality of full pooling or full separation, and make precise a sense in which pooling is dominant relative to separation. As an application, we study the design of a grading scheme by an educational institution which seeks to signal student qualities and simultaneously incentivize students to learn. We show how these incentive constraints are embedded as a distortion of the school's prior over student qualities, generating a monotone categorization problem with distinct sender and receiver priors.
Keywords: Monotonic categorization, heterogeneous priors, information design
JEL classification: D82, D83
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