On the design of group strategy-proof mechanisms: domains, ranges and special conditions

Group strategy-proofness is a very attractive requirement of incentive compatibility. But in many cases it is hard or impossible to .nd nontrivial social choice functions satisfying even the weakest condition of individual strategy-proofness. However, there are a number of economically signi.cant domains where interesting rules satisfying individual strategy-proofness can be de.ned, and for some of them, all these rules turn out to also satisfy the stronger requirement of group strategy-proofness. In other cases, this equivalence does not hold. In a previous paper we pro- vide su¢ cient conditions de.ning domains of preferences guaranteeing that individual and group strategy-proofness are equivalent for all rules de.ned on these domains. In this paper, we show that our results extend in two directions. On the one hand, to intermediate versions of strategy- proofness, de.ned to exclude manipulations by small group of agents. On the other hand, we provide guidelines on how to restrict the ranges of functions de.ned on domains that only satisfy our condition partially. Finally, we provide a partial answer regarding the necessity of our condition and give applications to particular settings. Some applications of our results are also provided