Simple Paired Combinatorial Assignment

Consider a university assigning students to courses and dorms. While many mechanisms are available, they each have their own drawbacks. Running serial dictatorship once for all goods is highly unfair, but running serial dictatorship separately for each matching problem is inefficient-Pareto improvements can be found via students jointly trading their allocated course and dorm. Alternatively, competitive equilibrium from equal incomes scales combinatorially in the number of items, making implementation and preference elicitation difficult. This paper considers paired serial dictatorship: a novel mechanism where agents signal relative preferences that determine their priority in each market. Any deterministic allocation that arises in equilibrium is Pareto efficient and envy-free, highlighting how seemingly innocuous tie-breaking is the key barrier to optimality and fairness. When agents differ only in relative preferences, paired serial dictatorship ex-ante Pareto dominates running random serial dictatorship independently in each market. Such gains exist even when agents behave simplistically.