Undergraduate Course Allocation through Pseudo-Markets

We consider a many-to-many matching problem with a priority structure such as the one in undergraduate course allocation. In order to incorporate course priorities, we develop a deterministic pseudo-market mechanism with priority-specific prices that is based on the approximate competitive equilibrium from equal incomes. This novel mechanism, the Pseudo-Market with Priorities mechanism, prevents justified course envy, prevents Pareto improvements among students respecting the priority structure, is strategy-proof in the large, bounds envy by a single course among students at the same level of priority, and maintains a small upper bound on the market-clearing error. In a simulated environment, we show that this mechanism increases student utility and outcome fairness when compared to the commonly used in practice Random Serial Dictatorship