Incentivizing Agents through Ratings: The Value of Randomization

Peiran Xiao

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Abstract: I study the optimal design of ratings to motivate an agent's investment in quality when transfers are unavailable. The principal designs a (possibly stochastic) rating scheme that maps quality to a distribution over signals. The agent privately knows his ability and chooses a quality level. A competitive market then offers the agent a wage equal to his expected quality given the signal. I reduce the rating design problem to a mechanism design problem with a majorization constraint. When the principal maximizes expected quality, randomization has no value if the ability density is log-concave or increasing: lower censorship is then optimal among all rating schemes, and pass/fail tests are also optimal if the density is increasing. By contrast, every optimal rating scheme involves randomization if the density is decreasing and sufficiently log-convex---roughly, if intermediate ability is scarce relative to high and low ability.

Date: 2024-07, Revised 2026-09
New Economics Papers: this item is included in nep-cta, nep-des and nep-mic
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