Individual versus group strategy-proofness: when do they coincide?

32 pages, 2 figures.-- JEL Classification Number: D71.A social choice function is group strategy-proof on a domain if no group of agents can manipulate its final outcome to their own benefit by declaring false preferences on that domain. Group strategy-proofness is a very attractive requirement of incentive compatibility. But in many cases it is hard or impossible to find nontrivial social choice functions satisfying even the weakest condition of individual strategy-proofness. However, there are a number of economically significant domains where interesting rules satisfying individual strategy-proofness can be defined, and for some of them, all these rules turn out to also satisfy the stronger requirement of group strategy-proofness. This is the case, for example, when preferences are single-peaked or single-dipped. In other cases, this equivalence does not hold. We provide sufficient conditions defining domains of preferences guaranteeing that individual and group strategy-proofness are equivalent for all rules defined on these domains. Our results extend to intermediate versions of strategy-proofness, defined to exclude manipulations by small group of agents. They also provide guidelines on how to restrict the ranges of functions defined on domains that only satisfy our condition partially. Finally, we provide a partial answer regarding the necessity of our conditions.Salvador Barberà acknowledges the support of the Barcelona Graduate School of Economics where he is an affiliated professor, through its Research Recognition Programme. His work is also supported through grants SEJ2006-2789-E and ECO2008-04756 (Grupo Consolidado-C) from the Spanish Ministry of Science and Innovation, and by the Distinció per la Promoció de la Recerca Universitària from the Generalitat de Catalunya. Dolors Berga acknowledges the support of the Spanish Ministry of Science and Innovation through grant SEJ2007-60671 and of Generalitat de Catalunya through grant 2005SGR-213. She also acknowledges the Research Recognition Programme of the Barcelona GSE. Bernardo Moreno acknowledges financial support from Junta de Andalucía through Proyecto de Excelencia 522 and the ECO2008-03674 from the Spanish Ministry of Science and Innovation.Peer reviewe