Information Design for Congested Social Services: Optimal Need-Based\n Persuasion

We study the effectiveness of information design in reducing congestion in\nsocial services catering to users with varied levels of need. In the absence of\nprice discrimination and centralized admission, the provider relies on sharing\ninformation about wait times to improve welfare. We consider a stylized model\nwith heterogeneous users who differ in their private outside options: low-need\nusers have an acceptable outside option to the social service, whereas\nhigh-need users have no viable outside option. Upon arrival, a user decides to\nwait for the service by joining an unobservable first-come-first-serve queue,\nor leave and seek her outside option. To reduce congestion and improve social\noutcomes, the service provider seeks to persuade more low-need users to avail\ntheir outside option, and thus better serve high-need users. We characterize\nthe Pareto-optimal signaling mechanisms and compare their welfare outcomes\nagainst several benchmarks. We show that if either type is the overwhelming\nmajority of the population, information design does not provide improvement\nover sharing full information or no information. On the other hand, when the\npopulation is a mixture of the two types, information design not only Pareto\ndominates full-information and no-information mechanisms, in some regimes it\nalso achieves the same welfare as the "first-best", i.e., the Pareto-optimal\ncentralized admission policy with knowledge of users' types.\n