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Let  $X = \{h_{1}, \ldots, h_{n} \}$ and $D$ be all the unitary subsets of $X$;
$N = \{1, \ldots, n\}$ and preferences given by linear orders (complete and
strict rankings) over $D$. This is the housing market introduced by
\cite{shapley_cores_1974}.

\section{Procedures}

\subsection{Top trading procedures}

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In the classic housing assignment problem, Gale's {\em top trade cycles} (TTC)
algorithm yields an efficient allocation that is in the core.

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