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

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  • ALCALDE-UNZU, Jorge

    ()
    (Department of Applied Economics IV (Mathematics), UPV-EHU. Bilbao, Spain)

  • MOLIS, Elena

    ()
    (Facultés Universitaires Saint-Louis, CEREC, Bruxelles ; Université Catholique de Louvain, CORE, Louvain-la-Neuve)

Abstract

There is a wide range of economic problems involving the exchange of indivisible goods without monetary transfers, starting from the housing market model of the seminal paper of Shapley and Scarf [10] and including other problems like the kidney exchange or the school choice problems. For many of these models, the classical solution is the application of an algorithm/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, that generalizes the Top Trading Cycles for the general case in which individuals can report indifferences, and preserves all its desirable properties.

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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2009062.

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Date of creation: 01 Oct 2009
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Handle: RePEc:cor:louvco:2009062

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Keywords: housing market; indifferences; top trading cycles; absorbing sets;

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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. Alvin E. Roth & Tayfun Sonmez & M. Utku Unver, 2004. "Pairwise Kidney Exchange," NBER Working Papers 10698, National Bureau of Economic Research, Inc.
  3. Ehlers, Lars, 2002. "Coalitional Strategy-Proof House Allocation," Journal of Economic Theory, Elsevier, vol. 105(2), pages 298-317, August.
  4. Tayfun Sönmez & M. Utku Ünver, 2009. "Matching, Allocation, and Exchange of Discrete Resources," Boston College Working Papers in Economics 717, Boston College Department of Economics.
  5. Thomas Quint & Jun Wako, 2004. "On Houseswapping, the Strict Core, Segmentation, and Linear Programming," Yale School of Management Working Papers ysm373, Yale School of Management.
  6. E. Kalai & D. Schmeidler, 1975. "An Admissible Set Occurring in Various Bargaining Situations," Discussion Papers 191, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Roth, Alvin & Ünver, M. Utku & Sönmez, Tayfun, 2004. "Kidney Exchange," Scholarly Articles 2580565, Harvard University Department of Economics.
  8. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
  9. YIlmaz, Özgür, 2009. "Random assignment under weak preferences," Games and Economic Behavior, Elsevier, vol. 66(1), pages 546-558, May.
  10. Bird, Charles G., 1984. "Group incentive compatibility in a market with indivisible goods," Economics Letters, Elsevier, vol. 14(4), pages 309-313.
  11. Roth, Alvin E. & Postlewaite, Andrew, 1977. "Weak versus strong domination in a market with indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 131-137, August.
  12. Roth, Alvin E., 1982. "Incentive compatibility in a market with indivisible goods," Economics Letters, Elsevier, vol. 9(2), pages 127-132.
  13. Abdulkadiroglu, Atila & Sonmez, Tayfun, 1999. "House Allocation with Existing Tenants," Journal of Economic Theory, Elsevier, vol. 88(2), pages 233-260, October.
  14. Ma, Jinpeng, 1994. "Strategy-Proofness and the Strict Core in a Market with Indivisibilities," International Journal of Game Theory, Springer, vol. 23(1), pages 75-83.
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Cited by:
  1. Antonio Nicolò & Carmelo Rodríguez-Álvarez, 2013. "Age based preferences in paired kidney exchange," Documentos de Trabajo del ICAE 2013-38, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
  2. Alcalde, José & Romero-Medina, Antonio, 2011. "Fair School Placement," QM&ET Working Papers 11-1, Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica.
  3. EHLERS, Lars, 2012. "Top Trading with Fixed Tie-Breaking in Markets with Indivisible Goods," Cahiers de recherche 2012-02, Universite de Montreal, Departement de sciences economiques.
  4. 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.
  5. Lars EHLERS, 2014. "Strategy-Proofness and Essentially Single-Valued Cores Revisited," Cahiers de recherche 05-2014, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  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. José Alcalde Pérez & Begoña Subiza Martínez, 2012. "On integration policies and schooling," Working Papers. Serie AD 2012-06, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  8. Aziz, Haris & Brandt, Felix & Harrenstein, Paul, 2013. "Pareto optimality in coalition formation," Games and Economic Behavior, Elsevier, vol. 82(C), pages 562-581.
  9. Alcalde, José & Subiza, Begoña, 2012. "Affirmative Action and School Choice," QM&ET Working Papers 12-3, Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica.

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