Conveying Value via Categories

TL;DR

This paper analyzes how a sender can optimally categorize object qualities to convey value, considering different priors and incentives, with applications in grading schemes and signaling.

Contribution

It characterizes the optimal monotonic categorization strategy for a sender with different priors, extending signaling models to include incentive constraints and applications.

Findings

Full pooling or separation are not always optimal.

Pooling can be more effective than separation in certain settings.

Incentive constraints influence the design of categorization schemes.

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.