We study the balanced exchange of indivisible objects without monetary transfers when agents may be endowed with (and consume) more than one object. We propose a natural domain of preferences that we call trichotomous. In this domain, each agent’s preference over bundles of objects is responsive to an ordering over objects that has the following three indifference classes, in decreasing order of preferences: desirable objects, objects that she is endowed with but does not consider desirable, and objects that she neither is endowed with nor finds desirable.
For this domain, we define a class of individually rational, Pareto-efficient, and strategy-proof mechanisms that are also computationally efficient.