Optimization-based Mechanisms for the Course Allocation Problem

Abstract

In recent years, several universities have adopted an algorithmic approach to the allocation of seats in courses, for which students place bids (typically by ordering or scoring desirable courses), and then seats are awarded according to a predetermined procedure or mechanism. Designing the appropriate mechanism for translating bids into student schedules has received attention in the literature, but there is currently no consensus on the best mechanism in practice. In this paper, we introduce five new algorithms for this course-allocation problem, using various combinations of matching algorithms, second-price concepts, and optimization, and compare our new methods with the natural benchmarks from the literature: the (proxy) draft mechanism and the (greedy) bidding-point mechanism. Using simulation, we compare the algorithms on metrics of fairness, efficiency, and incentive compatibility, measuring their ability to encourage truth telling among boundedly rational agents. We find good results for all of our methods and that a two-stage, full-market optimization performs best in measures of fairness and efficiency but with slightly worse incentives to act strategically compared with the best of the mechanisms. We also find generally negative results for the bidding-point mechanism, which performs poorly in all categories. These results can help guide the decision of selecting a mechanism for course allocation or for similar assignment problems, such as project team assignments or sports drafts, for example, in which efficiency and fairness are of utmost importance but incentives must also be considered. Additional robustness checks and comparisons are provided in the online supplement.