Group Strategy-Proofness in Private Good Economies

We observe that many salient rules to allocate private goods are not only (partially) strategy-proof, but also (partially) group strategy-proof, in appropriate domains of definition. That is so for solutions to matching, division, cost sharing, house allocation and auctions, in spite of the substantive disparity between these cases. In a general framework that encompasses all of them, we remark that those strategy-proof rules share a common set of properties, which together imply their group strategy-proofness. Hence, the equivalence between the two forms of strategy-proofness is due to the underlying common structure of all these rules, irrespectively of their specific application.