The core of housing markets from an agent's perspective: Is it worth sprucing up your home?
Ildik\'o Schlotter, P\'eter Bir\'o, Tam\'as Fleiner

TL;DR
This paper examines the computational complexity of core allocations in housing markets, showing NP-hardness for certain allocation questions and demonstrating that core stability respects improvements in house value, with efficient solutions.
Contribution
It establishes NP-hardness results for core-related questions in housing markets and proves that core stability respects improvements in house value, including efficient algorithms for certain cases.
Findings
NP-hardness of finding specific core allocations
Core stability respects house value improvements
Efficient algorithms for certain core allocation adjustments
Abstract
We study housing markets as introduced by Shapley and Scarf (1974). We investigate the computational complexity of various questions regarding the situation of an agent in a housing market : we show that it is -hard to find an allocation in the core of where (i) receives a certain house, (ii) does not receive a certain house, or (iii) 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 where agent receives a house , if the value of the house owned by increases, then the resulting housing market admits an allocation in its core in which receives either , or a house that prefers to ; moreover, such an allocation can be found efficiently. We further show an analogous result in the Stable Roommates setting by proving that…
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Taxonomy
TopicsAuction Theory and Applications · Economic theories and models · Game Theory and Voting Systems
