# Strategy-Proof Exchange under Trichotomous Preferences

Strategy-Proof Exchange under Trichotomous Preferences

We study the exchange of indivisible objects without monetary transfers when each agent may be endowed with and consume more than one object. We assume that each agent has trichotomous preferences in the sense that she
(A) partitions objects into three: desirable, obligatory, and undesirable ones,
(B) considers a bundle acceptable if and only if it contains no undesirable objects, and
(C) ranks acceptable bundles by their numbers of desirable objects.
On this domain, we show that there is an individually rational, Pareto-efficient, and strategy-proof mechanism that is also computationally efficient.