The Core of Housing Markets from an Agent’s Perspective: Is It Worth Sprucing up Your Home?
研究了Shapley-Scarf住房市场中，给定代理人能否在核心分配中获得特定房屋的计算复杂性，并证明核心分配在房屋价值提升时具有改进性质。
We study housing markets as introduced by Shapley and Scarf. 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 [Formula: see text]-hard to find an allocation in the core of H in which (i) a receives a certain house, (ii) a does not receive a certain house, or (iii) a receives a house other than a’s own. We prove that the core of housing markets respects improvement in the following sense: given an allocation in the core of H in which agent a receives a house h, if the value of the house owned by a increases, then the resulting housing market admits an allocation in its core in which a receives either h or a house that a 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. Funding: This work was supported by the Hungarian Scientific Research Fund [Grants K124171, K128611]. I. Schlotter is supported by the Hungarian Academy of Sciences under its Momentum Programme (LP2021-2) and its János Bolyai Research Scholarship. The research reported in this paper and carried out by T. Fleiner at the Budapest University of Technology and Economics was supported by the “TKP2020, National Challenges Program” of the National Research Development and Innovation Office [BME NC TKP2020 and OTKA K143858] and by the Higher Education Excellence Program of the Ministry of Human Capacities in the frame of the Artificial Intelligence research area of the Budapest University of Technology and Economics (BME FIKP-MI/SC). P. Biró gratefully acknowledges financial support from the Hungarian Scientific Research Fund, OTKA [Grant K143858] and the Hungarian Academy of Sciences [Momentum Grant LP2021-2].