On the "group non-bossiness" property

We extend the concept of non-bossiness to groups of agents and say that a mechanism is group non-bossy if no group of agents can change the assignment of someone else while theirs being unaffected by misreporting their preferences. First, we show that they are not equivalent properties. We, then, prove that group strategy-proofness is sufficient for group non-bossiness. While this result implies that the top trading cycles mechanism is group non-bossy, it also provides a characterization of the market structures in which the deferred acceptance algorithm is group non-bossy.