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Université de Lausanne
Faculté des HEC
Département d'économétrie et d'économie politique

Cahier de recherches économiques du DEEP No. 17.09

Haris Aziz and Bettina Klaus

Random Matching under Priorities: Stability and No Envy Concepts

July 5, 2017

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.

JEL Classification: C63, C70, C71, C78

Keywords: Matching Theory; Stability Concepts; Fairness; Random Matching

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