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Random Matching under Priorities: Stability and No Envy Concepts

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  • Haris Aziz
  • Bettina Klaus

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.

Suggested Citation

  • Haris Aziz & Bettina Klaus, 2017. "Random Matching under Priorities: Stability and No Envy Concepts," Cahiers de Recherches Economiques du Département d'économie 17.09bis, Université de Lausanne, Faculté des HEC, Département d’économie.
    • Handle: RePEc:lau:crdeep:17.09bis
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    Cited by:

    1. Niclas Boehmer & Edith Elkind, 2020. "Stable Roommate Problem with Diversity Preferences," Papers 2004.14640, arXiv.org.
    2. Aziz, Haris & Brandl, Florian, 2022. "The vigilant eating rule: A general approach for probabilistic economic design with constraints," Games and Economic Behavior, Elsevier, vol. 135(C), pages 168-187.
    3. Haris Aziz & Florian Brandl, 2020. "The Vigilant Eating Rule: A General Approach for Probabilistic Economic Design with Constraints," Papers 2008.08991, arXiv.org, revised Jul 2021.
    4. Mehdi Feizi, 2023. "The object allocation problem with favoring upper ranks," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(2), pages 370-383, June.
    5. Schlegel, J. C. & Mamageishvili, A., 2017. "Welfare theorems for random assignments with priorities," Working Papers 17/05, Department of Economics, City University London.
    6. Schlegel, J. C., 2017. "A Note on Ex-Ante Stable Lotteries," Working Papers 17/06, Department of Economics, City University London.

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    More about this item

    Keywords

    Matching Theory; Stability Concepts; Fairness; Random Matching;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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