Random Matching under Priorities: Stability and No Envy Concepts

Haris Aziz and Bettina Klaus (bettina.klaus@unil.ch)

Cahiers de Recherches Economiques du Département d'économie from Université de Lausanne, Faculté des HEC, Département d’économie

Abstract: We consider stability concepts for random matchings where agents have preferences over objects and objects have priorities for the agents. When matchings are deterministic, the standard stability concept also captures the fairness property of no (justified) envy. When matchings can be random, there are a number of natural stability / fairness concepts that coincide with stability / no envy whenever matchings are deterministic. We formalize known stability concepts for random matchings for a general setting that allows weak preferences and weak priorities, unacceptability, and an unequal number of agents and objects. We then present a clear taxonomy of the stability concepts and identify logical relations between them.Furthermore, we provide no envy / claims interpretations for some of the stability concepts that are based on a consumption process interpretation of random matchings. Finally, we present a transformation from the most general setting to the most restricted setting, and show how almost all our stability concepts are preserved by that transformation.

Keywords: Matching Theory; Stability Concepts; Fairness; Random Matching (search for similar items in EconPapers)
JEL-codes: C63 C70 C71 C78 (search for similar items in EconPapers)
Pages: 61 pp.
Date: 2017-07
New Economics Papers: this item is included in nep-des and nep-gth
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Related works:
Journal Article: Random matching under priorities: stability and no envy concepts (2019)
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Persistent link: https://EconPapers.repec.org/RePEc:lau:crdeep:17.09bis

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