The object allocation problem with random priorities

• 成果类型: Article
• 署名作者: Afacan, Mustafa Oguz
• 署名单位: Sabanci University
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2018.03.010
• 发表日期: 2018
• 页码: 71-89
• 关键词: Constrained probabilistic serial mechanism; Probabilistic deferred acceptance mechanism; Constrained sd-efficiency; Claimwise stability

摘要

The existing priority-based object allocation literature restricts objects' priorities to be deterministic. However, agents might be probabilistically prioritized ex-ante, for instance, through a non-uniform tie-breaking rule. This paper generalizes the deterministic setting by allowing priorities to be random. In this probabilistic environment, we first introduce a fairness notion called claimwise stability in the spirit of the usual stability of Gale and Shapley (1962). We show that the natural generalization of the deferred acceptance mechanism (Gale and Shapley, 1962), so called probabilistic deferred acceptance mechanism, is claimwise stable, but with the downside that it is stochastically dominated by another claimwise stable rule. We then introduce a new mechanism called the constrained probabilistic serial, which is built on the probabilistic serial mechanism of Bogomolnaia and Moulin (2001). It is both claimwise stable and constrained sd-efficient. The paper then systematically compares the probabilistic deferred acceptance and constrained probabilistic serial mechanisms in terms of their strategic and fairness properties. (C) 2018 Elsevier Inc. All rights reserved.