The Multi-unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard

2237 Educational institutions commonly place limits on the number of students in any particular class. These class-size limits create an instance of the multi-unit assignment problem: if it is not possible for all students to take their most desired schedule of courses, then how should seats in courses be allocated? Other examples of multi-unit assignment problems include the assignment of tasks or shifts to workers, players to sports teams, shared scientific resources to their users, and airport takeoffand-landing slots to airlines. Perhaps the central difference between how practitioners and economists have approached multi-unit assignment and other similar market design problems is the attention paid to incentives. Practitioners often design mechanisms that would lead to economically desirable outcomes if agents told the truth about their preferences, but which fail to provide agents with an incentive to do so. Economists try where possible to design mechanisms where truthful reporting not only leads