When Should We Offer a Discount? Randomized Discount Timing with Strategic Customers

Retailers increasingly use randomized discount timing, such as unannounced flash sales, to influence strategic customer behavior, yet its advantages over traditional pricing strategies remain unclear. We develop a model with high and low valuation customers who strategically choose when to purchase, and compare three policies: single pricing, fixed discount timing, and randomized discount timing. We show that the retailer’s expected profit is independent of the discount time distribution and fully characterize the optimal high and low prices under randomized discount timing. The optimal low price always equals the valuation of low valuation customers. Interestingly, the optimal high price may increase in the total amount of inventory, which is not observed under fixed discount timing. We also show that randomized discount timing can outperform fixed discount timing when the customer segments are similar in size, their valuations are significantly different, and the inventory is about the size of the low valuation segment. Under these conditions, discount uncertainty induces high valuation customers to buy at a higher price, which improves revenue. However, when the retailer is not required to offer a discount, single pricing combined with fixed discount timing dominates randomized discount timing: randomness in discount timing encourages excessive waiting, reduces high price sales, and leads to more sales at the low price. Similar results hold when we consider salvage costs/values. These findings clarify when retailers should use or avoid randomized discount timing.