Optimizing Queues When Customers Commit the Sunk Cost Fallacy

We study a service system in which customers make a join-or-balk decision upon arrival and make a purchase-quantity decision when they are served. Empirical evidence shows that customers in this setting tend to consume more to amortize their sunk waiting costs. We model this sunk cost fallacy and study how it affects a firm's optimal operations strategies. We model the system using an unobservable M/M/1 queue. Customers form references of the waiting times and are influenced when making their purchasing decisions by the resulting reference effect of the average waiting cost per unit purchase. We characterize customers' decisions in equilibrium and analyze how the firm's sales and profit change with the service rate, the waiting environment (captured by the unit-time waiting cost), and the product price. We find that under certain conditions the firm's sales decrease as the service rate increases or as the unit-time waiting cost decreases because of alleviated sunk cost effect and lower per-capita sales. This implies that in the presence of customers' sunk cost fallacy the firm should carefully consider the managerial levers for improving service. Furthermore, we examine how the firm should optimally set prices to complement the sunk cost fallacy. We find that the rate at which the marginal consumption benefit diminishes determines whether a firm should price lower or higher in the presence of customers' sunk cost fallacy. Interestingly, our analysis shows that the sunk-cost effect can reduce deadweight losses caused by a firm's price markup. Social welfare increases with the sunk cost effect if the effect is small but decreases if the effect is large. Specifically, a social planner will refer a mild sunk-cost effect to no such effect, as the former helps to reduce deadweight losses in consumption; in contrast, a social planner will prefer no sunk-cost effect to a severe effect because the latter results in inefficient over-consumption