Two-sided matching with indifferences

• 成果类型: Article
• 署名作者: Erdil, Aytek; Ergin, Haluk
• 署名单位: University of Cambridge; University of California System; University of California Berkeley
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2017.07.002
• 发表日期: 2017
• 页码: 268-292
• 关键词: Two-sided matching; Matching with ties; Matching with indifferences; Efficient and stable matching

摘要

Most of the two-sided matching literature maintains the assumption that agents are never indifferent between any two members of the opposite side. In practice, however, ties in preferences arise naturally and are widespread. Market design needs to handle ties carefully, because in the presence of indifferences, stability no longer implies Pareto efficiency, and the deferred acceptance algorithm cannot be applied to produce a Pareto efficient or a worker-optimal stable matching. We allow ties in preference rankings and show that the Pareto dominance relation on stable matchings can be captured by two simple operations which involve rematching of workers and firms via cycles or chains. Likewise, the Pareto relation defined via workers' welfare can also be broken down to two similar procedures which preserve stability. Using these structural results we design fast algorithms to compute a Pareto efficient and stable matching, and a worker -optimal stable matching. (C) 2017 Elsevier Inc. All rights reserved.