Study of Signalling Game in Queueing Systems
DescriptionWhen service quality is unknown to some customers, they can sometimes infer quality through observing the length of queues. For example, tourists can infer that a restaurant's quality is good if they observe a long queue in front of the restaurant; patients can infer that a doctor's quality is high if the appointment takes a long time. Study on customers' queueing strategy with information updating based on queues has been conducted by many researchers. However, such literature ignores a key issue that the server's queue hiding /revealing action itself also serves as a device for conveying their quality. For example, for a low quality server, it may decide to hide its queue if the potential arrival rate is less than 5 and reveal it when it is larger than 5; and a high quality server may set such a threshold at 10. Then when the arrival rate falls into the range of 5 and 10, high- and low-quality servers have different incentives to reveal/hide the queue and customers can directly infer their quality by observing their action (hiding/revealing queue). Knowing customers' behavior, the low-quality server may try to mimic the high-quality server's behavior and the high-quality one may try to differentiate from the low-quality's behavior. Hence, this is a signalling game problem. This project aims to study such a signalling game between a server and customers. We plan to start with the simplest setting where customers are homogeneous on both service reward and delay sensitivity and they have no information on the service quality initially. The server can choose to reveal or conceal its queue length. We have conducted some initial studies with pure strategies of servers, and we show that there exist both separating equilibrium (high- and low-quality servers choose different signals) and pooling equilibrium (both high- and low-quality servers choose the same signal). We also identify some cases where no equilibrium exists for the signalling game. We plan to further investigate the signalling game along three dimensions. One, consider mixed strategy for servers where each type of server chooses to reveal/hide its queue in a probability. Two, consider more complex composition of customers with some being informed with the quality and some uninformed. Both the server's action and and the queue length convey quality information. Third, consider both selfish and collective customers, where collective customers make their queueing decision to maximize their overall utility.
|Effective start/end date||1/01/21 → …|