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Random assignment under weak preferences

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  • YIlmaz, Özgür

Abstract

The natural preference domain for many practical settings of the assignment problems is the one in which agents are allowed to be indifferent between objects, the weak preference domain. Most of the existing work on assignment problems assumes strict preferences. There are important exceptions, but they provide solutions only to the assignment problems with a social endowment, where agents own objects collectively and there are no private endowments. We consider the general class of assignment problems with private endowments and a social endowment. Our main contribution is a recursive solution for the weak preference domain. Our solution satisfies individual rationality, ordinal efficiency and a recently introduced fairness axiom, no justified-envy.

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Bibliographic Info

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

Volume (Year): 66 (2009)
Issue (Month): 1 (May)
Pages: 546-558

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Handle: RePEc:eee:gamebe:v:66:y:2009:i:1:p:546-558

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

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Keywords: Random assignment Ordinal efficiency No justified-envy Parametric maximum flow algorithm;

References

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  1. Alvin E. Roth & Tayfun Sönmez & M. Utku Ünver, 2004. "Pairwise Kidney Exchange," Game Theory and Information 0408001, EconWPA, revised 16 Feb 2005.
  2. Tayfun Sönmez & Alvin E. Roth & M. Utku Ünver, 2007. "Efficient Kidney Exchange: Coincidence of Wants in Markets with Compatibility-Based Preferences," American Economic Review, American Economic Association, vol. 97(3), pages 828-851, June.
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  4. Tayfun Sönmez & M. Utku Ünver, 2001. "House Allocation with Existing Tenants: An Equivalence," Game Theory and Information 0112002, EconWPA, revised 26 Sep 2002.
  5. Tayfun Sönmez & M. Utku Ünver, 2006. "Kidney Exchange with Good Samaritan Donors: A Characterization," Boston College Working Papers in Economics 640, Boston College Department of Economics.
  6. Anna Bogomolnaia & Herve Moulin, 2004. "Random Matching Under Dichotomous Preferences," Econometrica, Econometric Society, vol. 72(1), pages 257-279, 01.
  7. Abdulkadiroglu, Atila & Sonmez, Tayfun, 2003. "Ordinal efficiency and dominated sets of assignments," Journal of Economic Theory, Elsevier, vol. 112(1), pages 157-172, September.
  8. Szilvia Papai, 2000. "Strategyproof Assignment by Hierarchical Exchange," Econometrica, Econometric Society, vol. 68(6), pages 1403-1434, November.
  9. Atila Abdulkadiroglu & Tayfun Sonmez, 1998. "Random Serial Dictatorship and the Core from Random Endowments in House Allocation Problems," Econometrica, Econometric Society, vol. 66(3), pages 689-702, May.
  10. McLennan, Andrew, 2002. "Ordinal Efficiency and the Polyhedral Separating Hyperplane Theorem," Journal of Economic Theory, Elsevier, vol. 105(2), pages 435-449, August.
  11. Alvin E. Roth & Tayfun Sonmez & M. Utku Unver, 2003. "Kidney Exchange," Game Theory and Information 0308002, EconWPA.
  12. Katta, Akshay-Kumar & Sethuraman, Jay, 2006. "A solution to the random assignment problem on the full preference domain," Journal of Economic Theory, Elsevier, vol. 131(1), pages 231-250, November.
  13. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
  14. Lars-Gunnar Svensson, 1999. "Strategy-proof allocation of indivisible goods," Social Choice and Welfare, Springer, vol. 16(4), pages 557-567.
  15. Zhou, Lin, 1990. "On a conjecture by gale about one-sided matching problems," Journal of Economic Theory, Elsevier, vol. 52(1), pages 123-135, October.
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Citations

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Cited by:
  1. Kesten, Onur & Ünver, M. Utku, 0. "A theory of school choice lotteries," Theoretical Economics, Econometric Society.
  2. HOUGAARD, Jens L. & moreno-ternero, JUAN D. & OSTERDAL, Lars P., 2013. "Assigning agents to a line," CORE Discussion Papers 2013015, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. YIlmaz, Özgür, 2011. "Kidney exchange: An egalitarian mechanism," Journal of Economic Theory, Elsevier, vol. 146(2), pages 592-618, March.
  4. 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.
  5. Alcalde, Jose & Silva-Reus, José Ángel, 2013. "Allocating via Priorities," QM&ET Working Papers 13-3, Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica.
  6. YIlmaz, Özgür, 2010. "The probabilistic serial mechanism with private endowments," Games and Economic Behavior, Elsevier, vol. 69(2), pages 475-491, July.
  7. Stergios Athanassoglou & Jay Sethuraman, 2011. "House allocation with fractional endowments," International Journal of Game Theory, Springer, vol. 40(3), pages 481-513, August.

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