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Random Matching under Priorities: Stability and No Envy Concepts

Listed author(s):
  • Haris Aziz
  • Bettina Klaus

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.

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Paper provided by Université de Lausanne, Faculté des HEC, DEEP in its series Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) with number 17.09.

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Length: 61 pp.
Date of creation: Jul 2017
Handle: RePEc:lau:crdeep:17.09
Contact details of provider: Postal:
Université de Lausanne, Faculté des HEC, DEEP, Internef, CH-1015 Lausanne

Phone: ++41 21 692.33.20
Web page: http://www.hec.unil.ch/deep/publications/cahiers/series
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