The vigilant eating rule: A general approach for probabilistic economic design with constraints

• Published in: Games and economic behavior Vol. 135; pp. 168 - 187
• Main Authors: Aziz, Haris, Brandl, Florian
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.09.2022
• Subjects: Algorithms; Market design; Matching under constraints; Matching under preferences; Probabilistic matching; Market design; Matching under constraints; Algorithms; Probabilistic matching; Matching under preferences
• ISSN: 0899-8256; 1090-2473
• DOI: 10.1016/j.geb.2022.06.002

We consider probabilistic allocation of objects under ordinal preferences and constraints on allocations. We devise an allocation mechanism, called the vigilant eating rule (VER), that applies to nearly arbitrary constraints. It is constrained ordinally efficient, can be computed efficiently for a large class of constraints, and treats agents equally if they have the same preferences and are subject to the same constraints. When the set of feasible allocations is convex, it is characterized by ordinal egalitarianism. As a case study, we assume objects have priorities for agents and apply VER to sets of probabilistic allocations that are constrained by stability. While VER always returns a stable and constrained efficient allocation, it fails to be strategyproof, unconstrained efficient, and envy-free. We show, however, that each of these three properties is incompatible with stability and constrained efficiency.