Incentives and efficiency in matching with transfers : towards nonquasilinear package auctions

We study the package assignment model and its consequences for themodel of matching with transfers. We show that on rich domains, strategy-proofness,joint monotonicity (of Barberà, Berga, and Moreno [American Economic Review,106 (2016)]), anonymity in welfare, and continuity in welfare together imply con-ditional efficiency: the allocation cannot be improved by re-allocation of packages,keeping packages intact. Thus, rules are restricted to choosing, for each problem, aset of objects to distribute and a partitioning of these.Labor markets are auctions with unit demand, once anonymity is modified toaccount for productivity differences. In this case, conditional efficiency is no blocking(by matched pairs), the core component of the standard solution concept of stability.Thus, while it is known that stable outcomes can be strategy-proof, we show thata component of stability is necessary for incentives.These results are derived from the following result, also discovered here, on therestricted quasilinear domain: weak pairwise strategy-proofness, anonymity in wel-fare, and continuity in welfare imply no-envy