Respecting improvement in markets with indivisible goods

Abstract

We study markets with indivisible goods where monetary compensations are fixed (or are not possible). Each individual is endowed with an object and a preference relation over all objects. Respect for improvement means that when the ranking of an agent’s endowment improves in some other agent’s preference (while keeping other preferences unchanged), then this agent weakly benefits from it. As a main result we show that on the strict domain individual rationality, strategy-proofness, and non-bossiness imply respecting improvement. As a consequence we obtain that top trading with fixed-tie breaking and random tie-breaking, respectively, satisfy respecting improvement on the weak domain. We further show that trading cycles rules with fixed tie-breaking satisfy respecting improvement. Finally, we put our results in the contexts of generalized matching problems, roommate problems and school choice.