IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/24351.html
   My bibliography  Save this paper

House allocation with fractional endowments

Author

Listed:
  • Athanassoglou, Stergios
  • Sethuraman, Jay

Abstract

This paper studies a generalization of the well known house allocation problem in which agents may own fractions of different houses summing to an arbitrary quantity, but have use for only the equivalent of one unit of a house. It departs from the classical model by assuming that arbitrary quantities of each house may be available to the market. Justified envy considerations arise when two agents have the same initial endowment, or when an agent is in some sense disproportionately rewarded in comparison to her peers. For this general model, an algorithm is designed to find a fractional allocation of houses to agents that satisfies ordinal efficiency, individual rationality, and no justified envy. The analysis extend to the full preference domain. Individual rationality, ordinal efficiency, and no justified envy conflict with weak strategyproofness. Moreover, individual rationality, ordinal efficiency and strategyproofness are shown to be incompatible. Finally, two reasonable notions of envy-freeness, no justified envy and equal-endowment no envy, conflict in the presence of ordinal efficiency and individual rationality. All of the impossibility results hold in the strict preference domain.

Suggested Citation

  • Athanassoglou, Stergios & Sethuraman, Jay, 2010. "House allocation with fractional endowments," MPRA Paper 24351, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:24351
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/24351/1/MPRA_paper_24351.pdf
    File Function: original version
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    4. YIlmaz, Özgür, 2009. "Random assignment under weak preferences," Games and Economic Behavior, Elsevier, vol. 66(1), pages 546-558, May.
    5. Abdulkadiroglu, Atila & Sonmez, Tayfun, 1999. "House Allocation with Existing Tenants," Journal of Economic Theory, Elsevier, vol. 88(2), pages 233-260, October.
    6. 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.
    7. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Han, Xiang, 2016. "On the consistency of random serial dictatorship," Economics Letters, Elsevier, vol. 145(C), pages 168-171.
    2. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Østerdal, Lars Peter, 2014. "Assigning agents to a line," Games and Economic Behavior, Elsevier, vol. 87(C), pages 539-553.
    3. Onur Kesten & Morimitsu Kurino & Alexander S. Nesterov, 2017. "Efficient lottery design," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 31-57, January.
    4. YIlmaz, Özgür, 2009. "Random assignment under weak preferences," Games and Economic Behavior, Elsevier, vol. 66(1), pages 546-558, May.
    5. Le, Phuong, 2013. "Competitive Equilibrium in the Random Assignment Problem," MPRA Paper 66290, University Library of Munich, Germany.
    6. Balbuzanov, Ivan & Kotowski, Maciej H., 2017. "Endowments, Exclusion, and Exchange," Working Paper Series rwp17-016, Harvard University, John F. Kennedy School of Government.
    7. repec:bla:ijethy:v:13:y:2017:i:4:p:369-385 is not listed on IDEAS
    8. Ünver, M. Utku & Kesten, Onur & Kurino, Morimitsu & Hashimoto, Tadashi & Hirata, Daisuke, 2014. "Two axiomatic approaches to the probabilistic serial mechanism," Theoretical Economics, Econometric Society, vol. 9(1), January.
    9. Kesten, Onur & Kurino, Morimitsu & Nesterov, Alexander, 2015. "Efficient lottery design," Discussion Papers, Research Unit: Market Behavior SP II 2015-203, Social Science Research Center Berlin (WZB).
    10. Kesten, Onur & Ünver, M. Utku, 2015. "A theory of school choice lotteries," Theoretical Economics, Econometric Society, vol. 10(2), May.
    11. Heo, Eun Jeong, 2014. "Probabilistic assignment problem with multi-unit demands: A generalization of the serial rule and its characterization," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 40-47.
    12. repec:spr:sochwe:v:49:y:2017:i:2:d:10.1007_s00355-017-1059-3 is not listed on IDEAS
    13. repec:eee:matsoc:v:88:y:2017:i:c:p:3-10 is not listed on IDEAS
    14. repec:eee:matsoc:v:90:y:2017:i:c:p:56-62 is not listed on IDEAS
    15. Eun Jeong Heo & Vikram Manjunath, 2017. "Implementation in stochastic dominance Nash equilibria," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 5-30, January.
    16. Tayfun Sönmez & M. Utku Ünver, 2015. "Enhancing the Efficiency of and Equity in Transplant Organ Allocation via Incentivized Exchange," Boston College Working Papers in Economics 868, Boston College Department of Economics.

    More about this item

    Keywords

    house allocation; fractional endowments; fairness; individual rationality;

    JEL classification:

    • 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
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    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:pra:mprapa:24351. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter) or (Rebekah McClure). General contact details of provider: http://edirc.repec.org/data/vfmunde.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.