Strategic Behavior in Multi-unit Assignment Problems: Theory and Evidence from Course Allocations

Abstract

This paper analyses the assignment problem when agents have multi-unit demand. Applications include task assignment in a team, course allocation, sport drafts and any other allocation problem where money does not play a role in balancing supply and demand. There is no known allocation mechanism that is ex-post efficient, strategyproof and minimally fair, and practical solutions must therefore trade off these different aspects. We study such a specific mechanism used at Harvard Business School to allocate courses to students. We argue that students in the HBS mechanism have an incentive to overreport their preferences for popular courses, that this incentive does not vanish with the size of the market and that it results in increased congestion. We confirm these predictions with detailed data on reported preferences and behavior in the HBS mechanism. We show that strategic behavior hurts students but that it might still be preferable to random serial dictatorship over course bundles, a strategyproof alternative.