Welfare-Maximizing Assignment of Agents to Hierarchical Positions

We consider an environment where agents must be allocated to one of three kinds of hierarchical positions with limited capacities. No monetary transfers are allowed. We assume that agentspayo¤s for being assigned to medium positions are their pri-vate information, and we consider bayesian incentive-compatible direct mechanisms. We solve for utilitarian and Rawlsian welfare-maximizing rules. Interestingly, the two optimal mechanisms are implemented by Hylland and Zeckhauser (1979)s pseudomar-ket mechanism with equal budgets (PM) and the Boston mechanism without priorities (BM), for a variety of cases. When the market is tough (i.e., when medium positions are overdemanded), then utilitarian optimal, Rawlsian optimal, PM, and BM assign-ments coincide. Otherwise, when the market is mild, PM and BM di¤er, and each one implements the two optimal mechanisms under di¤erent assumptions on the curvature of the payo ¤ distribution of the medium positions. When we allow medium positions to be the favorite for some agent types, PM and BM may still be optimal in tough markets, and a bias in favor of BM rather than PM appears in mild markets