{"title":"Equivalent Choice Functions and Stable Mechanisms","authors":"Jan Christoph Schlegel","doi":"10.2139/ssrn.3306009","DOIUrl":null,"url":null,"abstract":"We study conditions for the existence of stable and group-strategy-proof mechanisms in a many-to-one matching model with contracts if students' preferences are monotone in contract terms. We show that \"equivalence\", properly defined, to a choice profile under which contracts are substitutes and the law of aggregate holds is a necessary and sufficient condition for the existence of a stable and group-strategy-proof mechanism. \nOur result can be interpreted as a (weak) embedding result for choice functions under which contracts are observable substitutes and the observable law of aggregate demand holds.","PeriodicalId":165362,"journal":{"name":"ERN: Discrete Regression & Qualitative Choice Models (Single) (Topic)","volume":"57 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ERN: Discrete Regression & Qualitative Choice Models (Single) (Topic)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2139/ssrn.3306009","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
We study conditions for the existence of stable and group-strategy-proof mechanisms in a many-to-one matching model with contracts if students' preferences are monotone in contract terms. We show that "equivalence", properly defined, to a choice profile under which contracts are substitutes and the law of aggregate holds is a necessary and sufficient condition for the existence of a stable and group-strategy-proof mechanism.
Our result can be interpreted as a (weak) embedding result for choice functions under which contracts are observable substitutes and the observable law of aggregate demand holds.
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