Joint Information and Mechanism Design for Queues with Heterogeneous Users

Abstract: We consider a queue with an unobservable backlog by the incoming users. There is an information designer that observes the queue backlog and makes recommendations to the users arriving at the queue whether to join or not to join the queue. The arriving users have payoff relevant private types. The users, upon arrival, send a message, that is supposed to be their type, to the information designer if they are willing to hear a recommendation. The information designer then creates a recommendation for that specific type of user. The users have to pay a tax in exchange for the information they receive. In this setting, the information designer has two types of commitments. The first commitment is the recommendation policy and the second commitment is the tax function. We combine mechanism design and information design to study a queuing system with heterogeneous users. In this setting, the information designer is a sender of the information in the information design aspect and a receiver in the mechanism design aspect of the model. We formulate an optimization problem that characterizes the solution of the joint design problem. We characterize the tax functions and provide structural results for the recommendation policy of the information designer.