Scheduling with Opting Out : Improving Upon Random Priority

In a scheduling problem where agents can opt out, we show that the familiar Random Priority (RP)a rule can be improved upon by another mechanism dubbed Probabilistic Serial (PS). Both mechanisms are nonmanipulable in a strong sense, but the latter is Pareto superior to the former and serves a larger (expected number of agents. The PS equilibrium outcome is easier to compute than the RP outcome; on the other hand RP is easier to implement than PS. We show that the improvement of PS over RP is significant but small: at most a couple of percentage points in the relative welfare gain and the relative difference in quantity served. We conjecture that the latter never exceeds 8.33 %. Both gains vanish when the number of agents is large