Abstract: There are objects of diﬀerent quality to be assigned to agents. Agents can be assigned at most one object and there are not enough high quality objects for every agent. The social planner is unable to use transfers to give incentives for agents to convey their private information; instead, she is able to imperfectly verify their reports. We characterize a mechanism that maximizes welfare, where agents face diﬀerent lotteries over the various objects, depending on their report. We then apply our main result to the case of college admissions. We ﬁnd that optimal mechanisms are, in general, ex-post ineﬃcient and do strictly better than the standard mechanisms that are typically studied in the matching literature.
JEL classiﬁcation: C7, D8.
Keywords: imperfect veriﬁcation, evidence, mechanism design.