Welfare-maximizing assignment of agents to hierarchical positions

We allocate agents to three kinds of hierarchical positions: top, medium, and low. No monetary transfers are allowed. We solve for the incentive-compatible (IC) mechanisms that maximize a family of weighted social welfares that includes utilitarian and Rawlsian welfares. When the market is tough (all agents bear positive risk of obtaining a low position in any IC and feasible mechanism), then the pseudomarket mechanism with equal budgets (PM) and the Boston mechanism without priorities (BM) yield identical assignments which are always optimal. Otherwise, when the market is mild, PM and BM differ and each one implements the optimal rule under different assumptions on the curvature of virtual valuations. We also establish that both BM and PM mechanisms guarantee IC Pareto-optimal assignments for a domain of preference distributions satisfying weak assumptions.