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Markovian assignment rules

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  • Francis Bloch

    ()
    (Ecole Polytechnique)

  • David Cantala

    ()
    (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.

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Bibliographic Info

Paper provided by El Colegio de México, Centro de Estudios Económicos in its series Serie documentos de trabajo del Centro de Estudios Económicos with number 2010-18.

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Date of creation: Dec 2010
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Handle: RePEc:emx:ceedoc:2010-18

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Web page: http://www.colmex.mx/centros/cee/
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Related research

Keywords: dynamic assignment; finite Markov chains; seniority; promotion rules;

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References

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  1. Dirk Bergemann & Juuso Valimaki, 2008. "The Dynamic Pivot Mechanism," Cowles Foundation Discussion Papers 1672R, Cowles Foundation for Research in Economics, Yale University, revised Dec 2009.
  2. Roth,Alvin E. & Sotomayor,Marilda A. Oliveira, 1992. "Two-Sided Matching," Cambridge Books, Cambridge University Press, number 9780521437882, October.
  3. Alex Gershkov & Benny Moldovanu, 2009. "Learning about the Future and Dynamic Efficiency," American Economic Review, American Economic Association, vol. 99(4), pages 1576-87, September.
  4. William Thomson, 2007. "Fair Allocation Rules," RCER Working Papers 539, University of Rochester - Center for Economic Research (RCER).
  5. Alex Gershkov & Benny Moldovanu, 2009. "Dynamic Revenue Maximization with Heterogeneous Objects: A Mechanism Design Approach," American Economic Journal: Microeconomics, American Economic Association, vol. 1(2), pages 168-98, August.
  6. David Cantala & Francisco Sánchez, 2008. "Welfare and stability in senior matching markets," International Journal of Game Theory, Springer, vol. 36(3), pages 369-392, March.
  7. Dirk Bergemann & Juuso Valimaki, 2006. "Efficient Dynamic Auctions," Cowles Foundation Discussion Papers 1584, Cowles Foundation for Research in Economics, Yale University.
  8. Morimitsu Kurino, 2009. "House Allocation with Overlapping Agents: A Dynamic Mechanism Design Approach," Jena Economic Research Papers 2009-075, Friedrich-Schiller-University Jena, Max-Planck-Institute of Economics.
  9. Susan Athey & Ilya Segal, 2007. "An Efficient Dynamic Mechanism," Levine's Bibliography 122247000000001134, UCLA Department of Economics.
  10. Cantala, David, 2004. "Restabilizing matching markets at senior level," Games and Economic Behavior, Elsevier, vol. 48(1), pages 1-17, July.
  11. Blum, Yosef & Roth, Alvin E. & Rothblum, Uriel G., 1997. "Vacancy Chains and Equilibration in Senior-Level Labor Markets," Journal of Economic Theory, Elsevier, vol. 76(2), pages 362-411, October.
  12. Moulin, Herve & Stong, Richard, 2001. "Fair Queuing and Other Probabilistic Allocation Methods," Working Papers 2000-09, Rice University, Department of Economics.
  13. Abdulkadiroglu, Atila & Sonmez, Tayfun, 1999. "House Allocation with Existing Tenants," Journal of Economic Theory, Elsevier, vol. 88(2), pages 233-260, October.
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Citations

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Cited by:
  1. Francis Bloch & Nicolas Houy, 2012. "Optimal assignment of durable objects to successive agents," Economic Theory, Springer, vol. 51(1), pages 13-33, September.
  2. Monte, Daniel & Tumennasan, Norovsambuu, 2013. "Centralized allocation in multiple markets," Textos para discussão 322, Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil).
  3. Pereyra, Juan Sebastián, 2013. "A dynamic school choice model," Games and Economic Behavior, Elsevier, vol. 80(C), pages 100-114.

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