The strong core of housing markets
with partial order preferences
We study the strong core of housing markets when agents’ preferences over houses are expressed as partial orders. 
We provide a structural characterization of the strong core, and propose an efficient algorithm that finds an allocation in the strong core or decides that it is empty, even in the presence of forced and forbidden arcs. The algorithm satisfies the property of weak group-strategyproofness. Additionally, we show that certain results known for the strong core in the case where agents’ preferences are weak orders can be extended to the setting with partial order preferences; among others, we show that the strong core in such housing markets satisfies the property of respecting improvements.
