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Markovian assignment rules

Author

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  • Francis Bloch

    () (Department of Economics, Ecole Polytechnique - Polytechnique - X - CNRS - Centre National de la Recherche Scientifique)

  • David Cantala

    (El Colegio de Mexico - El Colegio de México)

Abstract

We analyze dynamic assignment problems where agents successively receive different objects (positions, offices, etc.). A finite set of n vertically differentiated indivisible objects are assigned to n agents who live n periods. At each period, a new agent enters society, and the oldest agent retires, leaving his object to be reassigned. We define independent assignment rules (where the assignment of an object to an agent is independent of the way other objects are allocated to other agents), efficient assignment rules (where there does not exist another assignment rule with larger expected surplus), and fair assignment rules (where agents experiencing the same circumstances have identical histories in the long run). When agents are homogenous, we characterize efficient, independent and fair rules as generalizations of the seniority rule. When agents draw their types at random, we prove that independence and efficiency are incompatible, and that efficient and fair rules only exist when there are two types of agents. We characterize two simple rules (type-rank and type-seniority) which satisfy both efficiency and fairness criteria in dichotomous settings.

Suggested Citation

  • Francis Bloch & David Cantala, 2008. "Markovian assignment rules," Working Papers hal-00356304, HAL.
  • Handle: RePEc:hal:wpaper:hal-00356304 Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00356304
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Monte, Daniel & Tumennasan, Norovsambuu, 2015. "Centralized allocation in multiple markets," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 74-85.
    2. Anno, Hidekazu & Kurino, Morimitsu, 2016. "On the operation of multiple matching markets," Games and Economic Behavior, Elsevier, vol. 100(C), pages 166-185.
    3. John Kennes & Daniel Monte & Norovsambuu Tumennasan, 2015. "Dynamic Matching Markets and the Deferred Acceptance Mechanism," Economics Working Papers 2015-23, Department of Economics and Business Economics, Aarhus University.
    4. Francis Bloch & David Cantala, 2014. "Dynamic Allocation of Objects to Queuing Agents: The Discrete Model," Documents de travail du Centre d'Economie de la Sorbonne 14066, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    5. Francis Bloch & Nicolas Houy, 2012. "Optimal assignment of durable objects to successive agents," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(1), pages 13-33, September.
    6. Francis Bloch & David Cantala, 2017. "Dynamic Assignment of Objects to Queuing Agents," American Economic Journal: Microeconomics, American Economic Association, vol. 9(1), pages 88-122, February.
    7. Lawrence M. Ausubel & Thayer Morrill, 2014. "Sequential Kidney Exchange," American Economic Journal: Microeconomics, American Economic Association, vol. 6(3), pages 265-285, August.
    8. Pereyra, Juan Sebastián, 2013. "A dynamic school choice model," Games and Economic Behavior, Elsevier, vol. 80(C), pages 100-114.
    9. Morimitsu Kurino, 2014. "House Allocation with Overlapping Generations," American Economic Journal: Microeconomics, American Economic Association, vol. 6(1), pages 258-289, February.
    10. Kawasaki, Ryo, 2015. "Roth–Postlewaite stability and von Neumann–Morgenstern stability," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 1-6.

    More about this item

    Keywords

    dynamic assignment; finite Markov chains; seniority; promotion rules; Appariements dynamiques; chaînes de Markov finies; ancienneté; règles de promotion;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D73 - Microeconomics - - Analysis of Collective Decision-Making - - - Bureaucracy; Administrative Processes in Public Organizations; Corruption
    • M51 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Personnel Economics - - - Firm Employment Decisions; Promotions

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