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