Rating Multiple Agents with Career Concerns

Abstract

A principal designs ratings for multiple career-concerned agents with correlated talents, mapping outputs into arbitrary finite-variance statistics. Peer output both benchmarks effort and signals talent, making full disclosure suboptimal under confidential ratings. Relaxing Bayes plausibility to linear orthogonality yields a closed-form rating and computable effort bounds for general priors; under normality, the relaxation is exact. Optimal confidential ratings combine the full-disclosure wage with the Fisher score for effort: they are relative-performance when individual output is informative about talent and team-based when it is noisy. Public ratings must satisfy joint Bayes plausibility, weakening incentives; hence, the principal prefers confidential ratings, whereas agents prefer public ratings. A spectral decomposition characterizes public ratings under normality: small cost heterogeneity implies full disclosure regardless of the noise structure, whereas large cost heterogeneity or strong effort spillovers can induce partial disclosure to reallocate incentives. The results bear on performance ratings and pay transparency.