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Mix and match: A strategyproof mechanism for multi-hospital kidney exchange

Author

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  • Ashlagi, Itai
  • Fischer, Felix
  • Kash, Ian A.
  • Procaccia, Ariel D.

Abstract

As kidney exchange programs are growing, manipulation by hospitals becomes more of an issue. Assuming that hospitals wish to maximize the number of their own patients who receive a kidney, they may have an incentive to withhold some of their incompatible donor–patient pairs and match them internally, thus harming social welfare. We study mechanisms for two-way exchanges that are strategyproof, i.e., make it a dominant strategy for hospitals to report all their incompatible pairs. We establish lower bounds on the welfare loss of strategyproof mechanisms, both deterministic and randomized, and propose a randomized mechanism that guarantees at least half of the maximum social welfare in the worst case. Simulations using realistic distributions for blood types and other parameters suggest that in practice our mechanism performs much closer to optimal.

Suggested Citation

  • Ashlagi, Itai & Fischer, Felix & Kash, Ian A. & Procaccia, Ariel D., 2015. "Mix and match: A strategyproof mechanism for multi-hospital kidney exchange," Games and Economic Behavior, Elsevier, vol. 91(C), pages 284-296.
    • Handle: RePEc:eee:gamebe:v:91:y:2015:i:c:p:284-296
    DOI: 10.1016/j.geb.2013.05.008
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    References listed on IDEAS

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    1. Tayfun Sönmez & Alvin E. Roth & M. Utku Ünver, 2007. "Efficient Kidney Exchange: Coincidence of Wants in Markets with Compatibility-Based Preferences," American Economic Review, American Economic Association, vol. 97(3), pages 828-851, June.
    2. Roth, Alvin E. & Sonmez, Tayfun & Utku Unver, M., 2005. "Pairwise kidney exchange," Journal of Economic Theory, Elsevier, vol. 125(2), pages 151-188, December.
    3. Alvin E. Roth & Tayfun Sönmez & M. Utku Ünver, 2004. "Kidney Exchange," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(2), pages 457-488.
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    Citations

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    Cited by:

    1. Carvalho, Margarida & Lodi, Andrea, 2023. "A theoretical and computational equilibria analysis of a multi-player kidney exchange program," European Journal of Operational Research, Elsevier, vol. 305(1), pages 373-385.
    2. John P. Dickerson & Ariel D. Procaccia & Tuomas Sandholm, 2019. "Failure-Aware Kidney Exchange," Management Science, INFORMS, vol. 65(4), pages 1768-1791, April.
    3. Radu-Stefan Mincu & Péter Biró & Márton Gyetvai & Alexandru Popa & Utkarsh Verma, 2021. "IP solutions for international kidney exchange programmes," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(2), pages 403-423, June.
    4. Blom, Danny & Smeulders, Bart & Spieksma, Frits, 2024. "Rejection-proof mechanisms for multi-agent kidney exchange," Games and Economic Behavior, Elsevier, vol. 143(C), pages 25-50.
    5. Christian Haas & Margeret Hall, 2019. "Two-Sided Matching for mentor-mentee allocations—Algorithms and manipulation strategies," PLOS ONE, Public Library of Science, vol. 14(3), pages 1-27, March.
    6. Tayfun Sönmez & M Utku Ünver, 2017. "Market design for living-donor organ exchanges: an economic policy perspective," Oxford Review of Economic Policy, Oxford University Press and Oxford Review of Economic Policy Limited, vol. 33(4), pages 676-704.
    7. Klimentova, Xenia & Viana, Ana & Pedroso, João Pedro & Santos, Nicolau, 2021. "Fairness models for multi-agent kidney exchange programmes," Omega, Elsevier, vol. 102(C).
    8. Avrim Blum & Paul Golz, 2021. "Incentive-Compatible Kidney Exchange in a Slightly Semi-Random Model," Papers 2106.11387, arXiv.org.

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    More about this item

    Keywords

    Approximate mechanisms without money; Kidney exchange;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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