Department of Economics2024-11-0920221434-474210.1007/s10058-021-00280-52-s2.0-85122828292http://dx.doi.org/10.1007/s10058-021-00280-5https://hdl.handle.net/20.500.14288/12281A central stability notion for allocation problems when there are private endowments is core: no coalition should be able to block the allocation. But, for an exchange economy of discrete resources, core can be empty. An alternative stability axiom is the bargaining set a la Aumann and Maschler (Advances in game theory, Annals of mathematics studies, Princeton University Press, Princeton, pp 443-476, 1964): a blocking by a coalition is justified only if there is no counter-objection to it and an allocation is in the bargaining set if there does not exist a justified blocking. Allowing for weak preferences, we prove that any allocation obtained by the well-known Top Trading Cycles class is in the bargaining set, but not all allocations in the bargaining set can be obtained by this class.EconomicsJournal Article1434-4750741856400001Q49691