Pair-efficient Reallocation of Indivisible Objects

We revisit the classical object reallocation problem under strict preferences. When attention is constrained to the set of Pareto-efficient rules, it is known that top trading cycles (TTC) is the only rule that is strategyproof and individually-rational. We relax this constraint and consider pair-efficiency. A rule is pair-efficient if it never induces an allocation at which a pair of agents gain from trading their assigned objects. Remarkably, even in the larger set of pair-efficient rules, we find that TTC is still the only rule that is strategyproof and individually-rational. Pair-efficiency is a minimal efficiency notion, ruling out gainful trades between only pairs of agents. Individual-rationality is a minimal voluntary participation constraint, assuring agents only that they never receive objects worse than their endowments. Therefore, our characterization result, by showing that TTC is the only strategyproof rule satisfying these two minimal conditions, gives strong support to the use of TTC in object reallocation problems. Our proof technique is based on a metric that measures the level of similarity of an arbitrary rule with TTC. We define our similarity metric by exploiting TTC's procedural nature. In future studies, we believe defining and working with similarity metrics, as done in our paper, can become functional when studying the properties of other procedural rules.