Peiran Xiao

Research

Incentivizing Agents through Ratings

I study the optimal design of performance or product ratings to motivate agents’ performance or investment in product quality. The principal designs a rating that maps their quality (performance) to possibly stochastic scores.  Agents have private information about their abilities (cost of effort/quality) and choose their quality. The market observes the scores and offers a wage equal to the agent’s expected quality [resp. ability]. For example, a school incentivizes learning through a grading policy that reveals students’ quality to the job market.

I first show that an incentive-compatible interim wage function can be induced by a rating (i.e., feasible) if and only if it is a mean-preserving spread of quality [resp. ability]. Thus, I reduce the principal's rating design problem to the design of a feasible interim wage. When restricted to deterministic ratings, the optimal rating design is equivalent to the optimal delegation with participation constraints (Amador and Bagwell, 2022). Using optimal control theory, I provide necessary and sufficient conditions under which lower censorship is optimal within deterministic ratings and solve for the optimal deterministic ratings in general. In particular, when the principal elicits maximal effort (quality), lower censorship [resp. pass/fail] is optimal if the density is unimodal [resp. increasing]. For general ratings, I provide sufficient conditions under which lower censorship remains optimal. In the effort-maximizing case, a pass/fail test remains optimal if the density is increasing. 

Tournament with Managerial Discretion (with Hashim Zaman)

We study the optimal design of a two-player tournament in which one player has discretion over hiring the other. The manager hires an agent of a certain ability and competes with him in a Lazer-Rosen-style tournament. In the tournament, both players produce at heterogeneous marginal costs (abilities), and the one with higher output wins a fraction of the total output. The principal determines the payout ratio and the head start (or handicap) to the manager—an advantage (or disadvantage) when comparing output.  We find the optimal contract offers just enough head start to induce the manager to hire the best candidate. However, in a two-period model where the first-period winner is retained for the future, the principal with succession concerns may allow hiring sabotage to prevail in equilibrium but will ensure the new hire has a higher ability than the manager.