Computer Science > Computer Science and Game Theory
[Submitted on 13 Jun 2021]
Title:On the Complexity of Fair House Allocation
View PDFAbstract:We study fairness in house allocation, where $m$ houses are to be allocated among $n$ agents so that every agent receives one house. We show that maximizing the number of envy-free agents is hard to approximate to within a factor of $n^{1-\gamma}$ for any constant $\gamma>0$, and that the exact version is NP-hard even for binary utilities. Moreover, we prove that deciding whether a proportional allocation exists is computationally hard, whereas the corresponding problem for equitability can be solved efficiently.
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