Group incentive compatibility in a market with indivisible goods

In a market where each trader has one unit of an indivisible good, there are procedures for exchanging goods which result in competitive allocations. One of these procedures, the top trading cycle, has the property that it is in each trader's best interest to report his true preferences over the set of goods. This note shows that no subset of traders can misrepresent their preferences and improve the allocation for all members of the subset. Additionally, if there are no indifferences in the preferences, then some traders in a subset that misrepresents preferences do worse.