Paired Course and Dorm Allocation

Consider a university administrator who must assign students to both courses and dorms and runs (random) serial dictatorship independently in each market. While serial dictatorship is efficient for each individual matching problem holding the other fixed, Pareto improvements can be found via students jointly trading their allocated course and dorm. To align priorities with students’ relative preferences between courses and dorms, we introduce paired serial dictatorship: a novel mechanism where students signal relative preferences to influence their priority in each market. Any deterministic allocation that arises in equilibrium is Pareto efficient, pointing towards ad-hoc tie-breaking as the key barrier to optimality. When students differ only in relative preferences, paired serial dictatorship ex-ante Pareto dominates running random serial dictatorship in each market. Such gains are realized despite students never reporting full preferences, a key advantage over other combinatorial allocation mechanisms that scale poorly with problem size.