Strategy-proof Pareto-improvement under voluntary participation*

We consider a general framework where each agent has an outside option of privately known value. First, we show that if the designer seeks to (weakly) Pareto-improve an individually rational and participation-maximal benchmark mechanism, there is at most one strategy-proof candidate. Consequently, many known mechanisms are on the Pareto frontier of strategy-proof mechanisms. Second, we characterize the Paretoimprovement relation over strategy-proof and individually rational mechanisms: one of these mechanisms Pareto-improves another if and only if it weakly expands the set of participants. Third, when utility is transferable, we provide a characterization of the pivotal mechanism and a revenue equivalence theorem.