We examine the tradeoffs between two variants of group strategyproofness, efficiency and budget balance in queueing models. In general, group strategyproofness is incompatible with efficiency and budget balance. Weakening budget balance to feasibility, we show that the incompatibility persists with strong group strategyproofness. We then identify a necessary condition for weak group strategyproofness and efficiency and use it to show that these two requirements are incompatible with budget balance unless there are exactly three agents. We also demonstrate the compatibility when there are three agents. Finally, we identify a class of efficient and weak group strategyproof mechanisms that we call k-pivotal mechanisms and identify the complete subclass of these mechanisms that are feasible.
