IDEAS home Printed from https://ideas.repec.org/p/udc/wpaper/wp547.html
   My bibliography  Save this paper

Coalitional Stability and Incentives in Housing Markets with Incomplete Preferences

Author

Listed:
  • Emilio Guaman
  • Juan Pablo Torres-Martinez

Abstract

We study the non-monetary exchange of indivisible goods when agents may not know how to compare some of them. Adding incomplete preferences to the Shapley-Scarf housing market model, we introduce two concepts of coalitional stability -the core and the strong core- that differ by the conditions required by a group of agents to block a housing allocation. The core is the set of allocations immune to blocking coalitions that improve the well-being of house-switching members, while the strong core is the set of allocations immune to blocking coalitions that may leave some members with a house incomparable to the original. We show that the core coincides with the set of allocations obtained by applying the Top Trading Cycles algorithm to the transitive completions of agents preferences. This result allows us to find a family of core-selecting and group strategy-proof mechanisms. Although the strong core may be an empty set, in the preference domain in which it is non-empty and the incompleteness of preferences is transitive, we show that there are strong-core-selecting and weakly group strategy-proof mechanisms. We also extend these results to housing allocation problems in which existing tenants and newcomers may coexist.

Suggested Citation

  • Emilio Guaman & Juan Pablo Torres-Martinez, 2023. "Coalitional Stability and Incentives in Housing Markets with Incomplete Preferences," Working Papers wp547, University of Chile, Department of Economics.
    • Handle: RePEc:udc:wpaper:wp547
    as

    Download full text from publisher

    File URL: https://econ.uchile.cl/uploads/publicacion/2962657aaf40fe510b804d1024c0f39f2b73b79d.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Lars-Gunnar Svensson, 1999. "Strategy-proof allocation of indivisible goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(4), pages 557-567.
    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. Xinsheng Xiong & Xianjia Wang & Kun He, 2022. "A new allocation rule for the housing market problem with ties," Journal of Combinatorial Optimization, Springer, vol. 43(1), pages 98-115, January.
    6. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    7. 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.
    8. Mandler, Michael, 2005. "Incomplete preferences and rational intransitivity of choice," Games and Economic Behavior, Elsevier, vol. 50(2), pages 255-277, February.
    9. Yasunori Okumura, 2023. "Consistent Linear Orders for Supermajority Rules," Papers 2304.09419, arXiv.org, revised Oct 2023.
    10. Minoru Kitahara & Yasunori Okumura, 2023. "On extensions of partial priorities in school choice," Papers 2305.00641, arXiv.org, revised Oct 2023.
    11. Hylland, Aanund & Zeckhauser, Richard, 1979. "The Efficient Allocation of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 87(2), pages 293-314, April.
    12. Ma, Jinpeng, 1994. "Strategy-Proofness and the Strict Core in a Market with Indivisibilities," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(1), pages 75-83.
    13. Minoru Kitahara & Yasunori Okumura, 2021. "Improving efficiency in school choice under partial priorities," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(4), pages 971-987, December.
    14. Ehlers, Lars, 2002. "Coalitional Strategy-Proof House Allocation," Journal of Economic Theory, Elsevier, vol. 105(2), pages 298-317, August.
    15. Thomas Quint & Jun Wako, 2004. "On Houseswapping, the Strict Core, Segmentation, and Linear Programming," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 861-877, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nicolò, Antonio & Rodríguez-Álvarez, Carmelo, 2017. "Age-based preferences in paired kidney exchange," Games and Economic Behavior, Elsevier, vol. 102(C), pages 508-524.
    2. 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.
    3. Afacan, Mustafa Oğuz & Hu, Gaoji & Li, Jiangtao, 2024. "Housing markets since Shapley and Scarf," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    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. Murat Yılmaz & Özgür Yılmaz, 2022. "Stability of an allocation of objects," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 561-580, December.
    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. Rajnish Kunar & Kriti Manocha & Josue Ortega, 2020. "On the integration of Shapley-Scarf housing markets," Papers 2004.09075, arXiv.org, revised Jan 2022.
    8. Kumar, Rajnish & Manocha, Kriti & Ortega, Josué, 2022. "On the integration of Shapley–Scarf markets," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    9. Han, Xiang, 2018. "Stable and efficient resource allocation under weak priorities," Games and Economic Behavior, Elsevier, vol. 107(C), pages 1-20.
    10. Morrill, Thayer & Roth, Alvin E., 2024. "Top trading cycles," Journal of Mathematical Economics, Elsevier, vol. 112(C).
    11. Will Sandholtz & Andrew Tai, 2023. "House-Swapping with Objective Indifferences," Papers 2306.09529, arXiv.org.
    12. 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.
    13. Pycia, Marek & Ãœnver, M. Utku, 2020. "Arrovian Efficiency and Auditability in the Allocation of Discrete Resources," CEPR Discussion Papers 15377, C.E.P.R. Discussion Papers.
    14. Marek Pycia & M. Utku Ünver, 2022. "Outside options in neutral allocation of discrete resources," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 581-604, December.
    15. 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.
    16. 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.
    17. Atila Abdulkadiroglu & Tommy Andersson, 2022. "School Choice," NBER Working Papers 29822, National Bureau of Economic Research, Inc.
    18. Ehlers, Lars & Klaus, Bettina & Papai, Szilvia, 2002. "Strategy-proofness and population-monotonicity for house allocation problems," Journal of Mathematical Economics, Elsevier, vol. 38(3), pages 329-339, November.
    19. Sönmez, Tayfun & Ünver, M. Utku, 2010. "House allocation with existing tenants: A characterization," Games and Economic Behavior, Elsevier, vol. 69(2), pages 425-445, July.
    20. Marek Pycia & M. Utku Ünver, 2016. "Arrovian Efficiency in Allocation of Discrete Resources," Boston College Working Papers in Economics 916, Boston College Department of Economics.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:udc:wpaper:wp547. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohit Karnani (email available below). General contact details of provider: https://edirc.repec.org/data/deuclcl.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.