On rank dominance of tie-breaking rules

• 成果类型: Article
• 署名作者: Allman, Maxwell; Ashlagi, Itai; Nikzad, Afshin
• 署名单位: Stanford University; University of Southern California
• 刊物名称: THEORETICAL ECONOMICS
• ISSN/ISSBN: 1933-6837
• DOI: 10.3982/TE4762
• 发表日期: 2023-05-01
• 页码: 707-748
• 关键词: Matching; deferred acceptance; tiebreaking; C78; D47

摘要

Lotteries are a common way to resolve ties in assignment mechanisms that ration resources. We consider a model with a continuum of agents and a finite set of resources with heterogeneous qualities, where the agents' preferences are generated from a multinomial-logit (MNL) model based on the resource qualities. We show that all agents prefer a common lottery to independent lotteries at each resource if every resource is popular, meaning that the mass of agents ranking that resource as their first choice exceeds its capacity. We then prove a stronger result where the assumption that every resource is popular is not required and agents' preferences are drawn from a (more general) nested MNL model. By appropriately adapting the notion of popularity to resource types, we show that a hybrid tie-breaking rule in which the objects in each popular type share a common lottery dominates independent lotteries at each resource.