Capacity rationing with strategic customers

Dynamic pricing offers the potential to increase revenues. At the same time, varying prices creates an incentive for customers to strategize over the timing of their purchases. How should a firm account for customer strategic behavior and profitably influence such behavior when making pricing and capacity decisions? One approach is to create rationing risk by deliberately understocking products. Then the resulting threat of shortages creates an incentive for customers to purchase early at higher prices. We develop a stylized capacity rationing model in which customers have heterogeneous valuations for the firm’s product and face declining prices over two periods. Customers behave strategically and weigh the payoff of immediate purchases against the expected payoff of delaying their purchases. Via its capacity choice, the firm is able to influence the fill rate and hence the rationing risk faced by customers. We analyze the firm’s optimal capacity choice in two different scenarios. In one case, customers can perfectly anticipate fill rates; in the other case, customers do not have fully rational expectations and they learn about availability through experience. We investigate, for both cases, when the rationing is optimal; if it is optimal, how it is affected by market characteristics and risk aversion of customers, etc. We also relate the results for each case together when the firm’s discount factor approaches 1.