Dynamic Pricing for Customers with Time-Sensitive Valuations

Dynamic pricing has becoming increasingly prevalent in many industries. One of the main advantages of dynamic pricing is that it helps mitigate the risk associated with demand uncertainty (see, for instance, Aviv and Pazgal 2008 and Cachon and Swinney 2011). In this paper, we show that dynamic pricing can play an important role in differentiating between customers over time even in the absence of demand uncertainty. In many settings, especially in fashion and electronic gadget retail, a customer’s willingness-to-pay (or valuation) for the product is time-sensitive and decreases over time. In these situations, customers are not only different in terms of their initial willingnessto-pay for these items when they are first introduced to the market, but they are also different in terms of how rapidly they lose their interest in these products. So, we may have customers who initially value the product at a high level, but then as time progresses, they lose interest in the product completely. And, we may also have customers who initially value the product at a low level, but still remain interested in the product as time progresses. That is, the willingness-to-pay of the lower valuation customers diminishes at a lower rate relative to that of the higher valuation customers. This phenomenon is illustrated in Figure 1. In this paper, we show that when a firm sells to customers who have heterogeneously decreasing valuations, the firm can achieve significant benefits by incorporating dynamic pricing even in the absence of demand uncertainty. This is not the case if customers were homogeneous in their valuation decay rate. In that case, in the absence of demand uncertainty, the firm’s optimal pricing strategy would be to post a fixed price, and dynamic pricing would have no benefit. When customer valuations decrease at different rates, the ranking of customers (in terms of their valuations)