Selecting a winner with external referees.

We consider a problem of mechanism design without money, where a planner selects a winner among a set of agents with binary types and receives outside signals (like the report of external referees). We show that there is a gap between the optimal Dominant Strategy Incentive Compatible (DSIC) mechanism and the optimal Bayesian Incentive Compatible (BIC) mechanism. In the optimal BIC mechanism, the planner can leverage the outside signal to elicit information about agents' types. BIC mechanisms are lexicographic mechanisms, where the planner first shortlists agents who receive high reports from the referees and then uses agents' reports to break ties among agents in the shortlist. We compare the "self-evaluation" mechanism with a "peer evaluation" mechanism where agents evaluate other agents, and show that for the same signal precision, the self- evaluation mechanism outperforms the peer evaluation mechanism. We show that optimal Ex Post Incentive Compatible (EPIC) mechanisms give the planner an intermediate value between the optimal DSIC and BIC mechanisms & COPY; 2023 Elsevier Inc. All rights reserved.