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

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  • 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
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    References listed on IDEAS

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    4. Diamantaras, Dimitrios & Thomson, William, 1990. "A refinement and extension of the no-envy concept," Economics Letters, Elsevier, vol. 33(3), pages 217-222, July.
    5. Azrieli, Yaron & Shmaya, Eran, 2014. "Rental harmony with roommates," Journal of Economic Theory, Elsevier, vol. 153(C), pages 128-137.
    6. 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.
    7. 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.
    8. 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.
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