A Solution for General Exchange Markets with Indivisible Goods when Indifferences are Allowed

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 solution