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

Francisco Sánchez Sánchez ()
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Francisco Sánchez Sánchez: Centro de Investigación en Matemáticas A.C.

Group Decision and Negotiation, 2022, vol. 31, issue 3, No 8, 703-721

Abstract: 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.

Keywords: Rental harmony problem; Envy-free; Assignment; Rent division (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10726-022-09779-w

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