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Exchange of indivisible goods and indifferences: The Top Trading Absorbing Sets mechanisms

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  • Alcalde-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.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:gamebe:v:73:y:2011:i:1:p:1-16
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    Cited by:

    1. repec:eee:jetheo:v:176:y:2018:i:c:p:393-407 is not listed on IDEAS
    2. 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.
    3. José Alcalde & Antonio Romero-Medina, 2017. "Fair student placement," Theory and Decision, Springer, vol. 83(2), pages 293-307, August.
    4. Balbuzanov, Ivan & Kotowski, Maciej H., 2017. "Endowments, Exclusion, and Exchange," Working Paper Series rwp17-016, Harvard University, John F. Kennedy School of Government.
    5. Lars Ehlers, 2012. "Top Trading with Fixed Tie-Breaking in Markets with Indivisible Goods," Cahiers de recherche 03-2012, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    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. Alcalde, Jose & Subiza, Begoña, 2011. "On Integration Policies and Schooling," MPRA Paper 29145, University Library of Munich, Germany.
    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. Lars EHLERS, 2014. "Strategy-Proofness and Essentially Single-Valued Cores Revisited," Cahiers de recherche 05-2014, 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. 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.
    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. 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.
    15. Ahamad, Mazbahul, 2016. "Envious Preferences in Two-sided Matching," 2016 Annual Meeting, July 31-August 2, Boston, Massachusetts 235482, Agricultural and Applied Economics Association.
    16. repec:eee:jetheo:v:171:y:2017:i:c:p:268-292 is not listed on IDEAS
    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. Aziz, Haris & Brandt, Felix & Harrenstein, Paul, 2013. "Pareto optimality in coalition formation," Games and Economic Behavior, Elsevier, vol. 82(C), pages 562-581.

    More about this item

    Keywords

    Housing market Indifferences Top trading cycles Absorbing sets;

    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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