It is well known that the core of an exchange market with indivisible
goods is always non empty, although it may contain Pareto inefficient
allocations. The strict core solves this shortcoming when
indifferences are not allowed, but when agents' preferences are weak
orders the strict core may be empty. On the other hand, when
indifferences are allowed, the core or the strict core may fail to be
stable sets, in the von Neumann and Morgenstern sense.
We introduce a new solution concept that improves the behaviour of the
strict core, in the sense that it solves the emptiness problem of the
strict core when indifferences are allowed in the individuals'
preferences and whenever the strict core is non-empty, our solution is
included in it. We define our proposal, the MS-set, by using
a stability property (m-stability) that the strict core
fulfills. Finally, we provide a min-max interpretation for this new