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 …