Joint service and price competitions facing naive customers

Abstract

In this paper, we consider a system consisting of two service providers each with its queue. Customers are unaware of the service rates and are pragmatic in service selections. They each choose a queue to enter based on prices and actual queue lengths upon arrival and can in real time change queues before entering service. Under such customer behavior assumptions, we first characterize the steady state distributions for the queue lengths, for given service rates and prices at the two service providers, and then investigate a game in which the two service providers competitively select service rates and prices. The results underlie our exploration of the interplay between the two competition modes. We also compare system performance with those in existing literature that model customer behaviors in a different way than that in this paper, and find that the service providers tend to select lower service rates but earn higher profits when the customers are unaware of service rates than when they are aware of such information; but the uninformed customers are expected to spend more time waiting in line. Customers' state-dependent service selection upon arrival and jockeying between the queues aggravate service providers' capacity under investment and further lengthen customers' duration of stay.