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Efficient and fair assignment mechanisms are strongly group manipulable

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  • Zhang, Jun

Abstract

We study the assignment of indivisible objects to agents without using monetary transfers. We prove that, regardless of whether the number of objects is sufficient, a mechanism that satisfies ex-post Pareto efficiency, equal treatment of equals, equal total assignment (ETA), and uniform-head fairness (UHF) must be strongly manipulable by a group of agents. In other words, by misreporting their preferences, all group members can obtain lotteries that strictly first-order stochastically dominate the lotteries they would have obtained by reporting their true preferences. ETA requires that agents obtain equal total probability shares of objects. UHF requires that if all agents have equal preferences over a subset of objects and prefer the objects in that subset to the remaining objects, then they obtain equal probability shares of the objects in that subset. The random priority and probabilistic serial mechanisms satisfy our axioms.

Suggested Citation

  • Zhang, Jun, 2019. "Efficient and fair assignment mechanisms are strongly group manipulable," Journal of Economic Theory, Elsevier, vol. 180(C), pages 167-177.
    • Handle: RePEc:eee:jetheo:v:180:y:2019:i:c:p:167-177
    DOI: 10.1016/j.jet.2018.12.005
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    13. Bade, Sophie, 2016. "Fairness and group-strategyproofness clash in assignment problems," Journal of Economic Theory, Elsevier, vol. 165(C), pages 257-262.
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    Cited by:

    1. Georgios Gerasimou, 2019. "Simple Preference Intensity Comparisons," Discussion Paper Series, School of Economics and Finance 201905, School of Economics and Finance, University of St Andrews, revised 27 Apr 2020.
    2. Ramezanian, Rasoul & Feizi, Mehdi, 2022. "Robust ex-post Pareto efficiency and fairness in random assignments: Two impossibility results," Games and Economic Behavior, Elsevier, vol. 135(C), pages 356-367.
    3. Zhang, Jun, 2020. "When are efficient and fair assignment mechanisms group strategy-proof?," Games and Economic Behavior, Elsevier, vol. 119(C), pages 251-266.
    4. Basteck, Christian & Ehlers, Lars, 2023. "Strategy-proof and envy-free random assignment," Journal of Economic Theory, Elsevier, vol. 209(C).
    5. Basteck, Christian & Ehlers, Lars H., 2023. "On the constrained efficiency of strategy-proof random assignment," Discussion Papers, Research Unit: Market Behavior SP II 2023-202, WZB Berlin Social Science Center.
    6. Morimoto, Shuhei, 2022. "Group strategy-proof probabilistic voting with single-peaked preferences," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    7. Shende, Priyanka & Purohit, Manish, 2023. "Strategy-proof and envy-free mechanisms for house allocation," Journal of Economic Theory, Elsevier, vol. 213(C).

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    More about this item

    Keywords

    Random assignment; Efficiency; Fairness; Strong group manipulation;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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