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

Social services often face the challenge of congestion due to their limited capacity relative to their demand. The congestion partly stems from the inclusionary intent of such services: a toll-free road is available to everyone, even those able to afford alternative tolled ones. A broad range of low- and middle-income households are eligible to apply for public housing. How can a social service provider reduce congestion and thus the efficiency loss associated with service delay? In this context, the two controls commonly used for managing congestion, pricing and centralized admission control, are inapplicable due to fairness and implementation considerations. However, the service provider may have control over the information about the system state that it shares with the users. Local traffic managers and public housing authorities have accurate information about the level of congestion for their corresponding services. As such, the service provider can leverage this informational advantage to persuade some of those with lower needs to forgo the service and reduce congestion in the system. In this paper, we study how effective such an informational lever is. To investigate this question, we develop a stylized model that captures the key features of such a system. We consider a single server queueing system where each user, upon arrival, decides to either wait for the service by joining an unobservable queue or seek her outside option. To capture the disparity that users face in the quality of their outside options, we categorize users into two groups: (1) high-needusers who have no feasible outside option and (2) low-needusers who have a viable alternative. Both types incur higher waiting costs upon joining a longer queue. A high-need user always joins as she does not have any other choice whereas a low-need user makes a joinor leavedecision to maximize her expected utility. Since an arriving user does not observe the queue, her decision relies on her belief about the queue size based on the information shared by the service provider. The service provider has complete information about the status of the queue and can commit to a signaling mechanism, as in the Bayesian persuasion framework of Kamenica and Gentzkow (2011). Because high-need users always join the queue, the service provider does not need to know user types to implement a signaling mechanism. The main contribution of this paper is the characterization of the Pareto-optimal signaling mechanisms and the comparison of their welfare against key benchmarks: full-information and no-information mechanisms, and centralized admission policies. To ensure welfare improvement for bothtypes, we focus on the notion of Pareto-dominance, and we show that under mild assumptions, any such signaling mechanism has a threshold structure. The welfare comparison establishes the following: if the user population is mainly composed of a single type, information design does not provide much improvement over full-information or no-information, whereas if the population has sufficient heterogeneity, information design can lead to substantial Pareto improvement in welfare; and with enough high-need users, the Pareto frontier of information design coincides with that of the strongest "first-best" benchmark, i.e, the Pareto-optimal centralized admission policy with knowledge of users' types and no incentive constraints. In other words, in such settings, information design plays the role of a coordination device to achieve first-best welfare.