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Optimal truncation in matching markets

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  • Coles, Peter
  • Shorrer, Ran

Abstract

Although no stable matching mechanism can induce truth-telling as a dominant strategy for all participants (Roth, 1982), recent studies have presented conditions under which truthful reporting by all agents is close to optimal (Immorlica and Mahdian, 2005; Kojima and Pathak, 2009; Lee, 2011). Our results demonstrate that in large, uniform markets using the Men-Proposing Deferred Acceptance Algorithm, each woman's best response to truthful behavior by all other agents is to truncate her list substantially. In fact, the optimal degree of truncation for such a woman goes to 100% of her list as the market size grows large. In general one-to-one markets we provide comparative statics for optimal truncation strategies: reduction in risk aversion and reduced correlation across preferences each lead agents to truncate more. So while several recent papers focused on the limits of strategic manipulation, our results serve as a reminder that without pre-conditions ensuring truthful reporting, there exists a potential for significant manipulation even in settings where agents have little information.

Suggested Citation

  • Coles, Peter & Shorrer, Ran, 2014. "Optimal truncation in matching markets," Games and Economic Behavior, Elsevier, vol. 87(C), pages 591-615.
    • Handle: RePEc:eee:gamebe:v:87:y:2014:i:c:p:591-615
    DOI: 10.1016/j.geb.2014.01.005
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    Cited by:

    1. Paula Jaramillo & Çaǧatay Kayı & Flip Klijn, 2014. "On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 793-811, April.
    2. Braun, Sebastian & Dwenger, Nadja & Kübler, Dorothea & Westkamp, Alexander, 2014. "Implementing quotas in university admissions: An experimental analysis," Games and Economic Behavior, Elsevier, vol. 85(C), pages 232-251.
    3. Marcelo Ariel Fernandez & Kirill Rudov & Leeat Yariv, 2022. "Centralized Matching with Incomplete Information," American Economic Review: Insights, American Economic Association, vol. 4(1), pages 18-33, March.
    4. Rustamdjan Hakimov & Dorothea Kübler & Siqi Pan, 2023. "Costly information acquisition in centralized matching markets," Quantitative Economics, Econometric Society, vol. 14(4), pages 1447-1490, November.
    5. Marco Castillo & Ahrash Dianat, 2021. "Strategic uncertainty and equilibrium selection in stable matching mechanisms: experimental evidence," Experimental Economics, Springer;Economic Science Association, vol. 24(4), pages 1365-1389, December.
    6. Itai Ashlagi & Mark Braverman & Amin Saberi & Clayton Thomas & Geng Zhao, 2020. "Tiered Random Matching Markets: Rank is Proportional to Popularity," Papers 2009.05124, arXiv.org, revised Jan 2021.
    7. Janine Balter & Michela Rancan & Olena Senyuta, 2014. "Truncation in the Matching Markets and Market Ineffciency," RSCAS Working Papers 2014/04, European University Institute.
    8. Castillo, Marco & Dianat, Ahrash, 2016. "Truncation strategies in two-sided matching markets: Theory and experiment," Games and Economic Behavior, Elsevier, vol. 98(C), pages 180-196.
    9. Qiufu Chen & Yuanmei Li & Xiaopeng Yin & Luosai Zhang & Siyi Zhou, 2024. "The Machiavellian frontier of stable mechanisms," Papers 2405.12804, arXiv.org, revised Jul 2024.
    10. Martin Van der Linden, 2019. "Deferred acceptance is minimally manipulable," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 609-645, June.
    11. Rheingans-Yoo, Ross, 2024. "Large random matching markets with localized preference structures can exhibit large cores," Games and Economic Behavior, Elsevier, vol. 144(C), pages 71-83.
    12. 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.
    13. Vincent Meisner, 2023. "Report-Dependent Utility and Strategy-Proofness," Management Science, INFORMS, vol. 69(5), pages 2733-2745, May.
    14. Ashlagi, Itai & Nikzad, Afshin & Romm, Assaf, 2019. "Assigning more students to their top choices: A comparison of tie-breaking rules," Games and Economic Behavior, Elsevier, vol. 115(C), pages 167-187.
    15. Assaf Romm, 2014. "Implications of capacity reduction and entry in many-to-one stable matching," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(4), pages 851-875, December.
    16. Christian Haas, 2021. "Two-Sided Matching with Indifferences: Using Heuristics to Improve Properties of Stable Matchings," Computational Economics, Springer;Society for Computational Economics, vol. 57(4), pages 1115-1148, April.
    17. Benjamin N. Roth & Ran I. Shorrer, 2021. "Making Marketplaces Safe: Dominant Individual Rationality and Applications to Market Design," Management Science, INFORMS, vol. 67(6), pages 3694-3713, June.
    18. Itai Ashlagi & Mark Braverman & Yash Kanoria & Peng Shi, 2020. "Clearing Matching Markets Efficiently: Informative Signals and Match Recommendations," Management Science, INFORMS, vol. 66(5), pages 2163-2193, May.

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    More about this item

    Keywords

    Matching; Deferred acceptance; Truncation; Market design; Manipulation;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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