Influencing Waiting Lists

In many settings, randomly arriving objects are offered successively to agents according to their fixed order in a waiting list. Though it is costly to wait, an agent may prefer to decline an offered object in order to wait for a better one (e.g. as in perhaps the most significant of such environments, the assignment of donor organs to queued patients). We consider the welfare consequences of influencing such accept/decline decisions. Examples of influence could be: encouraging agents to accept lower quality objects than they otherwise would; disallowing the right to defer offered objects; disallowing agents in certain waiting list positions to accept certain types of objects; etc. We consider a general, abstract definition of “influence” capturing these examples as special cases. We show that such influence necessarily leads to weakly Paretodominated outcomes: influencing behavior in any one position in the list cannot improve the expected continuation payoff to any single position in the waiting list. The same conclusion holds under (CARA) risk-aversion. These results also can be viewed as generalizations of a (reinterpreted) optimization result for the problem of assigning jobs to a set of parallel processors. We also consider the interests of a party averse to uncertainty in an agent’s waiting time (e.g. a treatment provider whose efficiency ∗Kellogg School of Management, MEDS Department, Northwestern University. Email: [email protected]. This work was presented under its original title “Waiting for Prizes” in Summer 2014. I thank Hyoduk Shin for initial discussion on an earlier version of this model that eventually motivated this paper. I also thank Nick Anosti, Anna Bogomolnaia, and Tayfun Sönmez for comments.