Designing Optimal Preannounced Markdowns in the Presence of Rational Customers with Multiunit Demands

We analyze the optimal design of a markdown pricing mechanism with pre-announced prices. In the presence of limited supply, buyers who choose to purchase at a lower price may face a scarcity in supply. Our focus is on the structure of the optimal markdown mechanisms in the presence of rational or “strategic” buyers who demand multiple units. We first examine a complete information setting where the set of customer valuations is known but the seller does not know the valuation of each individual customer (i.e., cannot exercise perfect price discrimination). We then generalize our analysis to an incomplete valuation information setting where customer valuations are drawn from known distributions. For both settings, we compare the seller’s profit resulting from the optimal markdown mechanism and the optimal single price. We provide a number of managerial insights into designing profitable markdown mechanisms.