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Matching with single-peaked preferences

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  • Bade, Sophie

Abstract

The crawler is a new efficient, strategyproof, and individually rational mechanism for housing markets with single-peaked preferences. In a housing market each agent is endowed with exactly one house. These houses are ordered – by their size for example – and all agents preferences are single-peaked with respect to that order. The crawler screens agents in order of their houses' sizes, starting with the smallest. The first agent who does not want to move to a larger house is matched with his most preferred house. Agents who currently occupy houses sized between this agent's original and chosen houses “crawl” to the next largest unmatched house. This process is repeated until all agents are matched. The crawler is easier to understand than Gale's top trading cycles and can be extended to allow for indifferences.

Suggested Citation

  • Bade, Sophie, 2019. "Matching with single-peaked preferences," Journal of Economic Theory, Elsevier, vol. 180(C), pages 81-99.
    • Handle: RePEc:eee:jetheo:v:180:y:2019:i:c:p:81-99
    DOI: 10.1016/j.jet.2018.12.004
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Morrill, Thayer & Roth, Alvin E., 2024. "Top trading cycles," Journal of Mathematical Economics, Elsevier, vol. 112(C).
    2. Gogulapati Sreedurga & Soumyarup Sadhukhan & Souvik Roy & Yadati Narahari, 2022. "Characterization of Group-Fair Social Choice Rules under Single-Peaked Preferences," Papers 2207.07984, arXiv.org.
    3. Hu, Xinquan & Zhang, Jun, 2024. "Characterization of Top Trading Cycles with single-dipped preferences," Economics Letters, Elsevier, vol. 241(C).
    4. Chatterji, Shurojit & Roy, Souvik & Sadhukhan, Soumyarup & Sen, Arunava & Zeng, Huaxia, 2022. "Probabilistic fixed ballot rules and hybrid domains," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    5. Ingalagavi, Chinmay & Sadhukhan, Soumyarup, 2023. "On a class of strategy-proof social choice correspondences with single-peaked utility functions," Journal of Mathematical Economics, Elsevier, vol. 109(C).
    6. Chen, Yajing & Zhao, Fang, 2021. "Alternative characterizations of the top trading cycles rule in housing markets," Economics Letters, Elsevier, vol. 201(C).
    7. Tamura, Yuki & Hosseini, Hadi, 2022. "The crawler: Three equivalence results for object (re)allocation problems when preferences are single-peaked," Journal of Economic Theory, Elsevier, vol. 203(C).
    8. Mandal, Pinaki & Roy, Souvik, 2021. "Strategy-proof Allocation of Indivisible Goods when Preferences are Single-peaked," MPRA Paper 105320, University Library of Munich, Germany.
    9. Tamura, Yuki, 2023. "Object reallocation problems with single-dipped preferences," Games and Economic Behavior, Elsevier, vol. 140(C), pages 181-196.
    10. Rajnish Kunar & Kriti Manocha & Josue Ortega, 2020. "On the integration of Shapley-Scarf housing markets," Papers 2004.09075, arXiv.org, revised Jan 2022.
    11. Yajing Chen & Zhenhua Jiao & Chenfeng Zhang & Luosai Zhang, 2021. "The Machiavellian frontier of top trading cycles," Papers 2106.14456, arXiv.org, revised Apr 2024.
    12. Yuki Tamura, 2022. "Object reallocation problems under single-peaked preferences: two characterizations of the crawler," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(3), pages 537-565, November.
    13. Di Feng, 2023. "Efficiency in Multiple-Type Housing Markets," Papers 2308.14989, arXiv.org, revised Dec 2023.
    14. Ping Zhan, 2019. "A simple construction of complete single-peaked domains by recursive tiling," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(3), pages 477-488, December.
    15. Arlegi, Ricardo & Teschl, Miriam, 2022. "Pareto rationalizability by two single-peaked preferences," Mathematical Social Sciences, Elsevier, vol. 118(C), pages 1-11.
    16. Louis Golowich & Shengwu Li, 2021. "On the Computational Properties of Obviously Strategy-Proof Mechanisms," Papers 2101.05149, arXiv.org, revised Oct 2022.
    17. Zhang, Jun, 2020. "When are efficient and fair assignment mechanisms group strategy-proof?," Games and Economic Behavior, Elsevier, vol. 119(C), pages 251-266.
    18. Mandal, Pinaki & Roy, Souvik, 2022. "On obviously strategy-proof implementation of fixed priority top trading cycles with outside options," Economics Letters, Elsevier, vol. 211(C).
    19. Shengwu Li, 2024. "Designing Simple Mechanisms," Papers 2403.18694, arXiv.org, revised Jul 2024.
    20. Clayton Thomas, 2020. "Classification of Priorities Such That Deferred Acceptance is Obviously Strategyproof," Papers 2011.12367, arXiv.org, revised Feb 2021.

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    More about this item

    Keywords

    Matching; Single-peaked preferences; Gale's top trading cycles; Obvious strategyproofness;
    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

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