Waitlist engineering in discrete object allocations with outside option

This study pursues how waitlists should be designed to achieve desirable outcomes in object allocation models with outside option. We adapt the usual stability notion to our setting and call it “sure stability." Our first mechanism—Deferred Acceptance with Straightforward Waitlists (DSW)—is surely stable, and it dominates other surely stable mechanisms unless waitlists are capped, otherwise, it is not even constrained efficient. Given this inefficiency of DSW, we propose Deferred Acceptance with Augmented Waitlists (DAW) mechanism. It is surely stable and improves DSW. Sure stability is incompatible with strategy-proofness, hence both mechanisms are manipulable. We also show that increasing the waitlist capacities is always at least weakly welfare-improving under each of them.