Discussion Papers on Economics,
University of Southern Denmark, Department of Economics

Abstract: We study the package assignment model and its consequences for the model 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 conditional efficiency: the allocation cannot be improved by re-allocation of packages, keeping packages intact. Thus, rules are restricted to choosing, for each problem, a set of objects to distribute and a partitioning of these. Labor markets are auctions with unit demand, once anonymity is modified to account 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 that a component of stability is necessary for incentives. These results are derived from the following result, also discovered here, on the restricted quasilinear domain: weak pairwise strategy-proofness, anonymity in welfare, and continuity in welfare imply no-envy.

Keywords: Assignment game; Package auctions; Strategy-proofness

JEL-codes: C78; D44; D47

Language: English

46 pages, April 22, 2022

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