Strategy-proof Pareto-improvement

We consider a model where each agent has an outside option of privately known value. At a given allocation, we call the set of agents who do not exercise their outside options the "participants." We show that one strategy-proof and individually rational mechanism weakly Pareto-improves another if and only if, at each preference profile, it weakly expands (in terms of set inclusion) the set of participants. Corollaries include: a sufficient condition for a mechanism to be on the Pareto-efficient frontier of strategy-proof mechanisms; uniqueness of strategy-proof Pareto-improvements under true preferences over certain normatively meaningful benchmark allocation rules; and a characterization of the pivotal mechanism. (C) 2019 Elsevier Inc. All rights reserved.