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Exchange of indivisible goods and indifferences: the top trading absorbing sets mechanisms

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  • ALCADE-UNZU, Jorge
  • MOLIS, Elena

Abstract

There is a wide range of economic problems that involve the exchange of indivisible goods with no monetary transfers, starting from the housing market model of the seminal paper by Shapley and Scarf (1974) to problems such as the kidney exchange or the school choice problem. The classical solution to many of these models is to apply a mechanism called Top Trading Cycles, attributed to David Gale, which satisfies good properties for the case of strict preferences. In this paper, we propose a family of mechanisms, called Top Trading Absorbing Sets mechanisms, which generalize the Top Trading Cycles to the general case in which individuals are allowed to report indifferences, while preserving a maximal possible set of its desirable properties.
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Suggested Citation

  • ALCADE-UNZU, Jorge & MOLIS, Elena, 2011. "Exchange of indivisible goods and indifferences: the top trading absorbing sets mechanisms," LIDAM Reprints CORE 2331, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvrp:2331
    Note: In : Games and Economic Behavior, 73(1), 1-16, 2011
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    References listed on IDEAS

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    1. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    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.
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    Cited by:

    1. 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.
    2. 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.
    3. William Thomson, 2016. "Non-bossiness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(3), pages 665-696, October.
    4. Ehlers, Lars, 2018. "Strategy-proofness and essentially single-valued cores revisited," Journal of Economic Theory, Elsevier, vol. 176(C), pages 393-407.
    5. José Alcalde & Antonio Romero-Medina, 2017. "Fair student placement," Theory and Decision, Springer, vol. 83(2), pages 293-307, August.
    6. 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.
    7. 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.
    8. Ahamad, Mazbahul, 2016. "Envious Preferences in Two-sided Matching," 2016 Annual Meeting, July 31-August 2, Boston, Massachusetts 235482, Agricultural and Applied Economics Association.
    9. Ivan Balbuzanov & Maciej H. Kotowski, 2019. "Endowments, Exclusion, and Exchange," Econometrica, Econometric Society, vol. 87(5), pages 1663-1692, September.
    10. Erdil, Aytek & Ergin, Haluk, 2017. "Two-sided matching with indifferences," Journal of Economic Theory, Elsevier, vol. 171(C), pages 268-292.
    11. 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.
    12. Tommy ANDERSSON & Lars EHLERS & Lars-Gunnar SVENSSON & Ryan TIERNEY, 2018. "Gale's Fixed Tax for Exchanging Houses," Cahiers de recherche 08-2018, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    13. Jingsheng Yu & Jun Zhang, 2020. "Fractional Top Trading Cycle on the Full Preference Domain," Papers 2005.09340, arXiv.org.
    14. José Alcalde & Begoña Subiza, 2014. "Affirmative action and school choice," International Journal of Economic Theory, The International Society for Economic Theory, vol. 10(3), pages 295-312, September.
    15. Nicolò, Antonio & Rodríguez-Álvarez, Carmelo, 2017. "Age-based preferences in paired kidney exchange," Games and Economic Behavior, Elsevier, vol. 102(C), pages 508-524.
    16. Alcalde, Jose & Subiza, Begoña, 2011. "On Integration Policies and Schooling," MPRA Paper 29145, University Library of Munich, Germany.
    17. Aziz, Haris & Brandt, Felix & Harrenstein, Paul, 2013. "Pareto optimality in coalition formation," Games and Economic Behavior, Elsevier, vol. 82(C), pages 562-581.
    18. Rajnish Kunar & Kriti Manocha & Josue Ortega, 2020. "On the integration of Shapley-Scarf housing markets," Papers 2004.09075, arXiv.org, revised Oct 2020.
    19. Bade, Sophie, 2019. "Matching with single-peaked preferences," Journal of Economic Theory, Elsevier, vol. 180(C), pages 81-99.
    20. 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.
    21. 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.
    22. 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.
    23. Jingsheng Yu & Jun Zhang, 2020. "Efficient and fair trading algorithms in market design environments," Papers 2005.06878, arXiv.org, revised May 2021.

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    More about this item

    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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