🤖 AI Summary
This study addresses the problem of random assignment under two-sided capacity constraints—specifically, minimum and maximum demand requirements for objects, such as enrollment caps and floors in course allocation. To tackle this challenge, the paper proposes the Minimum-demand Probabilistic Serial (MPS) mechanism, which, for the first time, simultaneously achieves Pareto efficiency, envy-freeness, and weak strategy-proofness in settings with such bidirectional constraints. The MPS mechanism generalizes the classical Probabilistic Serial mechanism by integrating insights from random assignment theory and first-order stochastic dominance analysis. The resulting allocation rule strikes a favorable balance between desirable theoretical properties and practical implementability, thereby filling a critical gap in the literature on efficient and fair random assignment mechanisms that accommodate minimum-demand constraints.
📝 Abstract
We study stochastic object assignment problems in which objects may have minimum and maximum requirements, such as with classes with upper and lower enrollment bounds. We construct a new random assignment mechanism, the minimums probabilistic serial (MPS) mechanism, which generalizes the Probabilistic Serial mechanism of Bogomolnaia and Moulin (2001). The random allocation produced by MPS is guaranteed to be Pareto efficient; that is, there is no other implementable allocation that all agents prefer via first order stochastic dominance. We also show that MPS is i) envy-free, in that no agent will strictly prefer another agent's assignment, and ii) weak strategyproof, in that agents cannot achieve a better assignment by misreporting their preferences.