Abstract
We study housing markets as introduced by Shapley and Scarf [39]. We investigate the computational complexity of various questions regarding the situation of an agent a in a housing market H: we show that it is \(\mathsf {NP}\)-hard to find an allocation in the core of H where (i) a receives a certain house, (ii) a does not receive a certain house, or (iii) a receives a house other than her own. We prove that the core of housing markets respects improvement in the following sense: given an allocation in the core of H where agent a receives a house h, if the value of the house owned by a increases, then the resulting housing market admits an allocation where a receives either h, or a house that she prefers to h; moreover, such an allocation can be found efficiently. We further show an analogous result in the Stable Roommates setting by proving that stable matchings in a one-sided market also respect improvement.
Supported by the Hungarian Academy of Sciences (Momentum Programme LP2021-2) and the Hungarian Scientific Research Fund (NFKIH grants K128611, K124171).
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Notes
- 1.
Throughout the paper we will use the term partial ordering in the sense of an irreflexive (or strict) partial ordering.
- 2.
In fact, these are the two factors for which acceptability thresholds can be set by the patients in the UK program [8].
- 3.
Proofs marked by an asterisk can be found in the full version of our paper [38].
- 4.
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Schlotter, I., Biró, P., Fleiner, T. (2022). The Core of Housing Markets from an Agent’s Perspective: Is It Worth Sprucing Up Your Home?. In: Feldman, M., Fu, H., Talgam-Cohen, I. (eds) Web and Internet Economics. WINE 2021. Lecture Notes in Computer Science(), vol 13112. Springer, Cham. https://doi.org/10.1007/978-3-030-94676-0_14
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