In the standard auction model, we provide a necessary and sufficient condition on the value domain under which non-trivial mechanisms exist that satisfy group strategy-proofness and symmetry. In particular, this condition is satisfied (violated) if values are drawn from a finite set (an interval)

A principal wants to procure a discrete number of homogeneous units from a finite set of agents. Each agent has an increasing and convex cost function, whose exact shape is unknown to the principal. Utility is quasilinear in money. We characterize the set of mechanisms that are strategy-proof...