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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.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 73 (2011)
Issue (Month): 1 (September)
Pages: 1-16

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Handle: RePEc:eee:gamebe:v:73:y:2011:i:1:p:1-16

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Web page: http://www.elsevier.com/locate/inca/622836

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Keywords: Housing market Indifferences Top trading cycles Absorbing sets;

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References

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  1. Alvin E. Roth & Tayfun Sonmez & M. Utku Unver, 2004. "Pairwise Kidney Exchange," Levine's Bibliography 122247000000000350, UCLA Department of Economics.
  2. 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.
  3. Roth, Alvin & Ünver, M. Utku & Sönmez, Tayfun, 2004. "Kidney Exchange," Scholarly Articles 2580565, Harvard University Department of Economics.
  4. Abdulkadiroglu, Atila & Sonmez, Tayfun, 1999. "House Allocation with Existing Tenants," Journal of Economic Theory, Elsevier, vol. 88(2), pages 233-260, October.
  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. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
  7. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
  8. 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.
  9. 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.
  10. Ehlers, Lars, 2002. "Coalitional Strategy-Proof House Allocation," Journal of Economic Theory, Elsevier, vol. 105(2), pages 298-317, August.
  11. Bird, Charles G., 1984. "Group incentive compatibility in a market with indivisible goods," Economics Letters, Elsevier, vol. 14(4), pages 309-313.
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Citations

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Cited by:
  1. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2011. "Two Necessary Conditions for Strategy-Proofness: on What Domains are they also Sufficient?," UFAE and IAE Working Papers 892.11, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  2. 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.
  3. 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.
  4. 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.
  5. 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).
  6. Alcalde, Jose & Romero-Medina, Antonio, 2011. "Re-Reforming the Bostonian System: A Novel Approach to the Schooling Problem," MPRA Paper 28206, University Library of Munich, Germany.
  7. Aziz, Haris & Brandt, Felix & Harrenstein, Paul, 2013. "Pareto optimality in coalition formation," Games and Economic Behavior, Elsevier, vol. 82(C), pages 562-581.

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