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Incompatibility of efficiency and strategyproofness in the random assignment setting with indifferences

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  • Aziz, Haris
  • Luo, Pang
  • Rizkallah, Christine

Abstract

A fundamental resource allocation setting is the random assignment problem in which agents express preferences over objects that are then randomly allocated to the agents. In 2001, Bogomolnaia and Moulin presented the probabilistic serial (PS) mechanism that is an anonymous, Pareto optimal, and weak strategyproof mechanism when the preferences are considered with respect to stochastic dominance. The result holds when agents have strict preferences over individual objects. It has been an open problem whether there exists a mechanism that satisfies the same properties when agents may have indifference among the objects. We show that for this more general domain, there exists no extension of PS that is ex post efficient and weak strategyproof. The result is surprising because it does not even require additional symmetry or fairness conditions such as anonymity, neutrality, or equal treatment of equals. Our result further demonstrates that the lack of weak SD-strategyproofness of the extended PS mechanism of Katta and Sethuraman (2006) is not a design flaw but is due to an inherent incompatibility of efficiency and strategyproofness of PS in the full preference domain.

Suggested Citation

  • Aziz, Haris & Luo, Pang & Rizkallah, Christine, 2017. "Incompatibility of efficiency and strategyproofness in the random assignment setting with indifferences," Economics Letters, Elsevier, vol. 160(C), pages 46-49.
    • Handle: RePEc:eee:ecolet:v:160:y:2017:i:c:p:46-49
    DOI: 10.1016/j.econlet.2017.08.010
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    References listed on IDEAS

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    1. Atila Abdulkadiroglu & Tayfun Sonmez, 1998. "Random Serial Dictatorship and the Core from Random Endowments in House Allocation Problems," Econometrica, Econometric Society, vol. 66(3), pages 689-702, May.
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    4. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
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    More about this item

    Keywords

    Social choice theory; Random assignment problem; Probabilistic serial; Strategyproofness; Stochastic dominance;
    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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