Group strategy-proofness in private good economies without money: matching, division and house allocation

• Authors: Salvador Barberà.
• BSE Working Paper: 110099 | September 15
• Keywords: strategy-proofness , matching , group strategy-proofness , division , house allocation , group monotonicity , non-bossiness
• JEL codes: C78, D71, D78
• strategy-proofness
• matching
• group strategy-proofness
• division
• house allocation
• group monotonicity
• non-bossiness

We observe that three salient solutions to matching, division and house allocation problems are not only (partially) strategy-proof, but (partially) group strategy-proof as well, in appropriate domains of definition. That is the case for the Gale-Shapley mechanism, the uniform rule and the top trading cycle solution, respectively. We embed these three types of problems into a general framework. We then notice that the three rules, as well as many others, do share a common set of properties, which together imply their (partial) group strategy-proofness. This proves that the equivalence between individual and group strategy-proofness in all these cases is not a fortuitous event, but results from the structure of the functions under consideration.