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The difference indifference makes in strategy-proof allocation of objects

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  • Jaramillo, Paula
  • Manjunath, Vikram

Abstract

We study problems of allocating objects among people. Some objects may be initially owned and the rest are unowned. Each person needs exactly one object and initially owns at most one object. We drop the common assumption of strict preferences. Without this assumption, it suffices to study problems where each person initially owns an object and every object is owned. For such problems, when preferences are strict, the “top trading cycles” algorithm provides the only rule that is efficient, strategy-proof, and individually rational Ma (1994) [1]. Our contribution is to generalize this algorithm to accommodate indifference without compromising on efficiency and incentives.

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  • Jaramillo, Paula & Manjunath, Vikram, 2012. "The difference indifference makes in strategy-proof allocation of objects," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1913-1946.
  • Handle: RePEc:eee:jetheo:v:147:y:2012:i:5:p:1913-1946
    DOI: 10.1016/j.jet.2012.05.017
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    Cited by:

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    3. Alcalde-Unzu, Jorge & Molis, Elena, 2011. "Exchange of indivisible goods and indifferences: The Top Trading Absorbing Sets mechanisms," Games and Economic Behavior, Elsevier, vol. 73(1), pages 1-16, September.
    4. Haris Aziz, 2018. "Mechanisms for House Allocation with Existing Tenants under Dichotomous Preferences," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 3(1), pages 97-110, December.
    5. Ahmad, Ghufran, 2021. "Group incentive compatibility in the housing market problem with weak preferences," Games and Economic Behavior, Elsevier, vol. 126(C), pages 136-162.
    6. Ehlers, Lars, 2014. "Top trading with fixed tie-breaking in markets with indivisible goods," Journal of Economic Theory, Elsevier, vol. 151(C), pages 64-87.
    7. Carbajal, Juan Carlos & McLennan, Andrew & Tourky, Rabee, 2013. "Truthful implementation and preference aggregation in restricted domains," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1074-1101.
    8. Diebold, Franz & Bichler, Martin, 2017. "Matching with indifferences: A comparison of algorithms in the context of course allocation," European Journal of Operational Research, Elsevier, vol. 260(1), pages 268-282.
    9. Youngsub Chun & Eun jeong Heo & Sunghoon Heo, 2017. "Kidney exchange with immunosuppressants," Vanderbilt University Department of Economics Working Papers 17-00012, Vanderbilt University Department of Economics.
    10. Tommy ANDERSSON & Ágnes CSEH & Lars EHLERS & Albin ERLANSON, 2018. "Organizing Time Banks : Lessons from Matching Markets," Cahiers de recherche 11-2018, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    11. William Thomson, 2016. "Non-bossiness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(3), pages 665-696, October.
    12. Han, Xiang, 2018. "Stable and efficient resource allocation under weak priorities," Games and Economic Behavior, Elsevier, vol. 107(C), pages 1-20.
    13. Nicolò, Antonio & Rodríguez-Álvarez, Carmelo, 2017. "Age-based preferences in paired kidney exchange," Games and Economic Behavior, Elsevier, vol. 102(C), pages 508-524.
    14. Raghavan, Madhav, 2020. "Influence in private-goods allocation," Journal of Mathematical Economics, Elsevier, vol. 89(C), pages 14-28.
    15. Fujinaka, Yuji & Miyakawa, Toshiji, 2020. "Ex-post incentive compatible and individually rational assignments in housing markets with interdependent values," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 157-164.
    16. Erdil, Aytek & Ergin, Haluk, 2017. "Two-sided matching with indifferences," Journal of Economic Theory, Elsevier, vol. 171(C), pages 268-292.
    17. Barberà, Salvador & Berga, Dolors & Moreno, Bernardo, 2012. "Two necessary conditions for strategy-proofness: On what domains are they also sufficient?," Games and Economic Behavior, Elsevier, vol. 75(2), pages 490-509.
    18. C. Gizem Korpeoglu, 2018. "Allocation of an indivisible object on the full preference domain: axiomatic characterizations," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 6(1), pages 41-53, April.
    19. Rajnish Kunar & Kriti Manocha & Josue Ortega, 2020. "On the integration of Shapley-Scarf housing markets," Papers 2004.09075, arXiv.org, revised Oct 2020.
    20. Jingsheng Yu & Jun Zhang, 2020. "Fractional Top Trading Cycle on the Full Preference Domain," Papers 2005.09340, arXiv.org.
    21. Jingsheng Yu & Jun Zhang, 2020. "Efficient and fair trading algorithms in market design environments," Papers 2005.06878, arXiv.org, revised May 2021.
    22. Manjunath, Vikram & Westkamp, Alexander, 2021. "Strategy-proof exchange under trichotomous preferences," Journal of Economic Theory, Elsevier, vol. 193(C).
    23. Marek Pycia & M. Utku Ünver, 2016. "Arrovian Efficiency in Allocation of Discrete Resources," Boston College Working Papers in Economics 916, Boston College Department of Economics.
    24. Madhav Raghavan, 2018. "Influence in Private-Good Economies," Cahiers de Recherches Economiques du Département d'économie 18.05, Université de Lausanne, Faculté des HEC, Département d’économie.
    25. Bade, Sophie, 2019. "Matching with single-peaked preferences," Journal of Economic Theory, Elsevier, vol. 180(C), pages 81-99.

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    More about this item

    Keywords

    Strategy-proofness; Indivisible goods; Indifference; Housing market; House allocation; Existing tenants; Top trading cycles;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • 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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