IDEAS home Printed from https://ideas.repec.org/a/spr/grdene/v31y2022i3d10.1007_s10726-022-09779-w.html
   My bibliography  Save this article

Envy-Free Solutions to the Problem of Room Assignment and Rent Division

Author

Listed:
  • Francisco Sánchez Sánchez

    (Centro de Investigación en Matemáticas A.C.)

Abstract

We have 3 students who wish to share the rent of an apartment together. There is a problem. The bedrooms have different characteristics. How does one assign the bedrooms?. How much will each one pay?. In this article based on the students’ preferences, we will find all envy-free solutions to this problem. In addition, given an efficient assignment, we find all the extreme points of the set of prices that make up these solutions. An efficient assignment together with the centroid of the set of prices is suggested as a solution. In the model there is an implicit proposal of how to obtain envy-free solutions in economies with indivisible goods. Also, the same model can be used to divide a set of chores fairly among agents.

Suggested Citation

  • Francisco Sánchez Sánchez, 2022. "Envy-Free Solutions to the Problem of Room Assignment and Rent Division," Group Decision and Negotiation, Springer, vol. 31(3), pages 703-721, June.
    • Handle: RePEc:spr:grdene:v:31:y:2022:i:3:d:10.1007_s10726-022-09779-w
    DOI: 10.1007/s10726-022-09779-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10726-022-09779-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10726-022-09779-w?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Diamantaras, Dimitrios & Thomson, William, 1990. "A refinement and extension of the no-envy concept," Economics Letters, Elsevier, vol. 33(3), pages 217-222, July.
    2. Steven J. Brams & D. Marc Kilgour, 2001. "Competitive Fair Division," Journal of Political Economy, University of Chicago Press, vol. 109(2), pages 418-443, April.
    3. Alkan, Ahmet & Demange, Gabrielle & Gale, David, 1991. "Fair Allocation of Indivisible Goods and Criteria of Justice," Econometrica, Econometric Society, vol. 59(4), pages 1023-1039, July.
    4. Gabrielle Demange & Ahmet Alkan & David Gale, 1991. "Fair Allocation of Indivisible Goods and Money and Criteria of Justice," Post-Print halshs-00670945, HAL.
    5. Tadenuma, Koichi & Thomson, William, 1991. "No-Envy and Consistency in Economies with Indivisible Goods," Econometrica, Econometric Society, vol. 59(6), pages 1755-1767, November.
    6. Flip Klijn, 2000. "An algorithm for envy-free allocations in an economy with indivisible objects and money," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(2), pages 201-215.
    7. Azrieli, Yaron & Shmaya, Eran, 2014. "Rental harmony with roommates," Journal of Economic Theory, Elsevier, vol. 153(C), pages 128-137.
    8. Claus-Jochen Haake & Matthias G. Raith & Francis Edward Su, 2002. "Bidding for envy-freeness: A procedural approach to n-player fair-division problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(4), pages 723-749.
    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. Andersson, T. & Svensson, L.-G. & Yang, Z., 2010. "Constrainedly fair job assignments under minimum wages," Games and Economic Behavior, Elsevier, vol. 68(2), pages 428-442, March.
    2. Atila Abdulkadiroğlu & Tayfun Sönmez & M. Utku Ünver, 2004. "Room assignment-rent division: A market approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(3), pages 515-538, June.
    3. Erel Segal-Halevi, 2019. "Generalized Rental Harmony," Papers 1912.13249, arXiv.org, revised Feb 2020.
    4. Thomson, William, 2011. "Chapter Twenty-One - Fair Allocation Rules," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 2, chapter 21, pages 393-506, Elsevier.
    5. Rodrigo A. Velez, 2017. "Equitable rent division," Working Papers 20170818-001, Texas A&M University, Department of Economics.
    6. Tommy ANDERSSON & Lars EHLERS, 2013. "An Algorithm for Identifying Agent-k-Linked Allocations in Economies with Indivisibilities," Cahiers de recherche 17-2013, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    7. Tommy Andersson & Christer Andersson, 2009. "Solving House Allocation Problems with Risk-Averse Agents," Computational Economics, Springer;Society for Computational Economics, vol. 33(4), pages 389-401, May.
    8. , & , & ,, 2014. "Budget-balance, fairness and minimal manipulability," Theoretical Economics, Econometric Society, vol. 9(3), September.
    9. Haake, Claus-Jochen & Raith, Matthias G. & Su, Francis Edward, 2017. "Bidding for envy freeness," Center for Mathematical Economics Working Papers 311, Center for Mathematical Economics, Bielefeld University.
    10. Azacis, Helmuts, 2008. "Double implementation in a market for indivisible goods with a price constraint," Games and Economic Behavior, Elsevier, vol. 62(1), pages 140-154, January.
    11. Johannes Brustle & Jack Dippel & Vishnu V. Narayan & Mashbat Suzuki & Adrian Vetta, 2019. "One Dollar Each Eliminates Envy," Papers 1912.02797, arXiv.org.
    12. Meertens, Marc & Potters, Jos & Reijnierse, Hans, 2002. "Envy-free and Pareto efficient allocations in economies with indivisible goods and money," Mathematical Social Sciences, Elsevier, vol. 44(3), pages 223-233, December.
    13. Chun, Youngsub & Mitra, Manipushpak & Mutuswami, Suresh, 2019. "Egalitarianism in the queueing problem," Journal of Mathematical Economics, Elsevier, vol. 81(C), pages 48-56.
    14. Nicolò, Antonio & Velez, Rodrigo A., 2017. "Divide and compromise," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 100-110.
    15. Andersson, Tommy & Ehlers, Lars & Svensson, Lars-Gunnar, 2014. "Least manipulable Envy-free rules in economies with indivisibilities," Mathematical Social Sciences, Elsevier, vol. 69(C), pages 43-49.
    16. Duygu Yengin, 2017. "No-envy and egalitarian-equivalence under multi-object-demand for heterogeneous objects," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 81-108, January.
    17. Banerjee, Sreoshi, 2023. "Stability and fairness in sequencing games: optimistic approach and pessimistic scenarios," MPRA Paper 118680, University Library of Munich, Germany.
    18. Rodrigo A. Velez, 2017. "Sharing an increase of the rent fairly," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 59-80, January.
    19. Ning Sun & Zaifu Yang, 2009. "Strategy Proof And Privacy Preserving Fair Allocation Mechanism," The Japanese Economic Review, Japanese Economic Association, vol. 60(2), pages 143-151, June.
    20. Fujinaka, Yuji & Sakai, Toyotaka, 2007. "Maskin monotonicity in economies with indivisible goods and money," Economics Letters, Elsevier, vol. 94(2), pages 253-258, February.

    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:spr:grdene:v:31:y:2022:i:3:d:10.1007_s10726-022-09779-w. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.