{"title":"Characterizing priorities for deferred acceptance with or without outside options","authors":"Xiang Han, Junxiao Zhang","doi":"10.1007/s00199-024-01586-5","DOIUrl":null,"url":null,"abstract":"<p>In a model of priority-based allocation of indivisible objects where there may not be outside options, we characterize the priority structures under which the deferred acceptance algorithm (DA) satisfies various desiderata. We first identify an acyclicity condition that is necessary and sufficient for DA to be group strategy-proof, robustly stable, weakly group robustly stable, or to implement the stable allocation correspondence in Nash equilibria. When there is no outside option and there are more agents than total resources, the condition becomes considerably weaker, and no longer requires the priorities between any pair of objects to be similar. We further find a condition on priorities that is necessary and sufficient for the efficiency or consistency of DA, which is in general stronger than the above incentive properties for this mechanism.</p>","PeriodicalId":47982,"journal":{"name":"Economic Theory","volume":"22 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Economic Theory","FirstCategoryId":"96","ListUrlMain":"https://doi.org/10.1007/s00199-024-01586-5","RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ECONOMICS","Score":null,"Total":0}
引用次数: 0
Abstract
In a model of priority-based allocation of indivisible objects where there may not be outside options, we characterize the priority structures under which the deferred acceptance algorithm (DA) satisfies various desiderata. We first identify an acyclicity condition that is necessary and sufficient for DA to be group strategy-proof, robustly stable, weakly group robustly stable, or to implement the stable allocation correspondence in Nash equilibria. When there is no outside option and there are more agents than total resources, the condition becomes considerably weaker, and no longer requires the priorities between any pair of objects to be similar. We further find a condition on priorities that is necessary and sufficient for the efficiency or consistency of DA, which is in general stronger than the above incentive properties for this mechanism.
在一个基于优先权的不可分割对象分配模型中，可能没有外部选择，我们描述了延迟接受算法（DA）满足各种需求的优先权结构。我们首先确定了一个非周期性条件，该条件是延迟接受算法具有群体策略保护、稳健稳定、弱群体稳健稳定或在纳什均衡中实现稳定分配对应关系的必要且充分条件。当没有外部选择且代理人数量多于总资源时，该条件就会变得相当弱，不再要求任何一对对象之间的优先级相似。我们进一步找到了一个优先权条件，它是 DA 效率或一致性的必要且充分条件，一般来说，它比该机制的上述激励属性更强。
期刊介绍：
The purpose of Economic Theory is to provide an outlet for research - in all areas of economics based on rigorous theoretical reasoning, and
- on specific topics in mathematics which is motivated by the analysis of economic problems. Economic Theory''s scope encompasses - but is not limited to - the following fields. - classical and modern equilibrium theory
- cooperative and non-cooperative game theory
- macroeconomics
- social choice and welfare
- uncertainty and information, intertemporal economics (including dynamical systems)
- public economics
- international and developmental economics
- financial economics, money and banking
- industrial organization Economic Theory also publishes surveys if they clearly picture the basic ideas at work in some areas, the essential technical apparatus which is used and the central questions which remain open. The development of a productive dialectic between stylized facts and abstract formulations requires that economic relevance be at the forefront. Thus, correct, and innovative, mathematical analysis is not enough; it must be motivated by - and contribute to - the understanding of substantive economic problems.
Officially cited as: Econ Theory
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