Weak group strategy‐proof and queue‐efficient mechanisms for the queueing problem with multiple machines

We first provide the complete characterization of mechanisms that satisfy weak group strategy‐proofness and queue‐efficiency in the multiple machine queueing problem with two agents. For any such mechanism, there can be at most one point of discontinuity in the transfer map. We then state a necessary condition for mechanisms to satisfy queue‐efficiency, weak group strategy‐proofness and continuity, with more than two agents. Finally, we provide a class of mechanisms that satisfy queue‐efficiency, weak group strategy‐proofness and continuity.