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Strategy-proof and fair assignment is wasteful

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  • Martini, Giorgio

Abstract

I prove there exists no assignment mechanism that is strategy-proof, non-wasteful and satisfies equal treatment of equals. When outside options may exist, this strengthens the impossibility result of Bogomolnaia and Moulin (2001) by weakening ordinal efficiency to non-wastefulness. My result solves an open question posed by Erdil (2014) and complements his results on the efficient frontier of random assignment mechanisms.

Suggested Citation

  • Martini, Giorgio, 2016. "Strategy-proof and fair assignment is wasteful," Games and Economic Behavior, Elsevier, vol. 98(C), pages 172-179.
    • Handle: RePEc:eee:gamebe:v:98:y:2016:i:c:p:172-179
    DOI: 10.1016/j.geb.2016.06.007
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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.
    2. 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.
    3. Kojima, Fuhito & Manea, Mihai, 2010. "Incentives in the probabilistic serial mechanism," Journal of Economic Theory, Elsevier, vol. 145(1), pages 106-123, January.
    4. Erdil, Aytek, 2014. "Strategy-proof stochastic assignment," Journal of Economic Theory, Elsevier, vol. 151(C), pages 146-162.
    5. Hylland, Aanund & Zeckhauser, Richard, 1979. "The Efficient Allocation of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 87(2), pages 293-314, April.
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    Citations

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    Cited by:

    1. Feizi, Mehdi & Ramezanian, Rasoul, 2023. "A new impossibility result for random assignments," Journal of Mathematical Economics, Elsevier, vol. 107(C).
    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, 2023. "Strategy-proof allocation with outside option," Games and Economic Behavior, Elsevier, vol. 137(C), pages 50-67.
    4. Zhang, Jun, 2020. "When are efficient and fair assignment mechanisms group strategy-proof?," Games and Economic Behavior, Elsevier, vol. 119(C), pages 251-266.
    5. Jun Zhang, 2023. "On wastefulness of random assignments in discrete allocation problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(1), pages 289-310, July.
    6. Basteck, Christian & Ehlers, Lars, 2023. "Strategy-proof and envy-free random assignment," Journal of Economic Theory, Elsevier, vol. 209(C).
    7. Basteck, Christian & Ehlers, Lars H., 2022. "Strategy-proof and envy-free random assignment," Discussion Papers, Research Unit: Market Behavior SP II 2022-208, WZB Berlin Social Science Center.
    8. Basteck, Christian & Ehlers, Lars, 2021. "Strategy-Proof and Envy-Free Random Assignment," Rationality and Competition Discussion Paper Series 307, CRC TRR 190 Rationality and Competition.
    9. Demeulemeester, Tom & Goossens, Dries & Hermans, Ben & Leus, Roel, 2023. "A pessimist’s approach to one-sided matching," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1087-1099.
    10. 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.
    11. Priyanka Shende & Manish Purohit, 2020. "Strategy-proof and Envy-free Mechanisms for House Allocation," Papers 2010.16384, arXiv.org.
    12. Zhang, Jun, 2019. "Efficient and fair assignment mechanisms are strongly group manipulable," Journal of Economic Theory, Elsevier, vol. 180(C), pages 167-177.

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    More about this item

    Keywords

    Random assignment; Random serial dictatorship; Strategy-proofness; Ordinal efficiency; Non-wastefulness;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis

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