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Optimal Markdown Pricing: Implications of Inventory Display Formats in the Presence of Strategic Customers

W. P. Carey School of Business, Arizona State University, Tempe, Arizona 85287
Olin Business School, Washington University in St. Louis, St. Louis, Missouri 63130
Jesse H. Jones Graduate School of Management, Rice University, Houston, Texas 77252
Anderson School of Management, University of California, Los Angeles, Los Angeles, California 90095
rui.yin{at}asu.edu
aviv{at}olin.wustl.edu
amit.pazgal{at}rice.edu
chris.tang{at}anderson.ucla.edu

We propose a game-theoretical model of a retailer who sells a limited inventory of a product over a finite selling season by using one of two inventory display formats: display all (DA) and display one (DO). Under DA, the retailer displays all available units so that each arriving customer has perfect information about the actual inventory level. Under DO, the retailer displays only one unit at a time so that each customer knows about product availability but not the actual inventory level. Recent research suggests that when faced with strategic consumers, the retailer could increase expected profits by making an upfront commitment to a price path. We focus on such pricing strategies in this paper, and study the potential benefit of DO compared to DA, and its effectiveness in mitigating the adverse impact of strategic consumer behavior. We find support for our hypothesis that the DO format could potentially create an increased sense of shortage risk, and hence it is better than the DA format. However, although potentially beneficial, a move from DA to DO is typically very far from eliminating the adverse impact of strategic consumer behavior. We observe that, generally, it is not important for a retailer to modify the level of inventory when moving from a DA to a DO format; a change in the display format, along with an appropriate price modification, is typically sufficient. Interestingly, across all scenarios in which a change in inventory is significantly beneficial, we observed that only one of the following two actions takes place: either the premium price is increased along with a reduction in inventory, or inventory is increased along with premium price reduction. We find that the marginal benefit of DO can vary dramatically as a function of the per-unit cost to the retailer. In particular, when the retailer's per-unit cost is relatively high, but not too high to make sales unprofitable or to justify exclusive sales to high-valuation customers only, the benefits of DO appear to be at their highest level, and could reach up to 20% increase in profit. Finally, we demonstrate that by moving from DA to DO, while keeping the price path unchanged, the volatility of the retailer's profit decreases.

Key Words: retailing; dynamic pricing; game-theory applications; marketing-operations interface; strategic customers; revenue management; inventory display
History: Received: June 2, 2007; accepted: March 22, 2009.

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