Price and capacity decisions of service systems with boundedly rational customers

We consider price and capacity decisions for a profit-maximizing service provider in a single server queueing system, in which customers are boundedly rational and decide whether to join the service according to a multinomial logit model. We find two potential price-capacity pair solutions for the first-order condition of the profit-maximizing problem. Profit is maximized at the solution with a larger capacity, but minimized at the smaller one. We then consider a dynamically adjusting capacity system to mimic a real-life situation and find that the maximum can be reached only when the initial service rate is larger than a certain threshold; otherwise, the system capacity and demand shrink to zero. We also find that a higher level of customers' bounded rationality does not necessarily benefit a firm, nor does it necessarily allow service to be sustained. We extend our analysis to a setting in which customers' bounded rationality level is related to historical demand and find that such a setting makes service easier to sustain. Finally we find that bounded rationality always harms social welfare.