Strategy-proofness and Pareto-efficiency in quasi-linear exchange economies

In this paper, we revisit a long-standing question on the structure of strategy-proof and Pareto-efficient social choice functions (SCFs) in classical exchange economies (Hurwicz (1972)). Using techniques developed by Myerson in the context of auction-design, we show that in a specific quasi-linear domain, every Pareto-efficient and strategy-proof SCF satisfying non-bossiness and a mild continuity property is dictatorial. The result holds for an arbitrary number of agents but the two-person version does not require either the non-bossiness or continuity assumptions. It also follows that the dictatorship conclusion holds on any superset of this domain. We also provide a minimum consumption guarantee result in the spirit of Serizawa and Weymark (2003).