We stress the importance that Arrow attached to studying the role of domain conditions in determining the validity of his impossibility theorem, a subject to which he devoted two chapters of Social Choice and Individual Values. Then we partially survey recent results about the role of domain...

We study the possibility of designing satisfactory ex post incentive compatible single valued direct mechanisms in interdependent values environments, characterized by the set of agents type profiles and by their induced preference profiles. For environments that we call knit and strict, only...

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...

We introduce a new notion of non-manipulability by groups, based on the idea that some of the agreements among a set of potential manipulators may be credible, while others may not. The derived notion of immunity to credible manipulations by groups is intermediate between individual and group...

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...