This paper considers truncation strategies in housing markets. First, we characterize the top trading cycles rule in housing markets by the following two groups of axioms: individual rationality, Pareto efficiency, truncation-invariance; individual rationality, endowments-swapping-proofness, truncation-invariance. The new characterizations refine Ma (1994), Fujinaka and Wakayama (2018), and Chen and Zhao (2021) simultaneously, because truncation-invariance is weaker than both strategy-proofness and rank monotonicity. Second, we show that the characterization result of the current paper can no longer be obtained by further weakening truncation-invariance to truncation-proofness.
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