Retail Supply Chain Management pp 293-307 | Cite as

# Markdown Competition

## Abstract

We present a stylized model of markdown competition. We consider two retailers who compete in a market with a fixed level of initial inventory. The initial inventory level is only known to the retailer, and not to the other. To maximize the profit, each retailer would mark down at a time of his individual choice. The model assumes deterministic demands, a single chance of price change, and a prefixed set of prices. We consider a two-parameter strategy set where a retailer chooses the timing of markdown as a function of the current time, his inventory level and the other’s move so far. We characterize the equilibrium of the game and derive managerial insights.

## Keywords

Inventory Level Equilibrium Strategy Reservation Price Expected Profit Demand Rate## References

- Aviv, W. and A. Pazgal (2003), “Optimal Pricing of Seasonal Products in the Presence of Forward-Looking Consumers,” Working Paper, Olin School of Business, Washington University, St. Louis, MO 63141.Google Scholar
- Belobaba, P.P. (1987), “Airline Yield Management: An Overview of Seat Inventory Control,”
*Transportation Science*29(3), 63–73.CrossRefGoogle Scholar - Bitran R. and R. Caldency (2003), “Pricing Models for Revenue Management,”
*Manufacturing and Service Operations Management*5(3), 203–229.CrossRefGoogle Scholar - Dudey, M. (1992), “Dynamic Edgeworth-Bertrand Competition,”
*The Quarterly Journal of Economics*107(4), 1461–1477.CrossRefGoogle Scholar - Evers, J. “Microsoft announces Xbox Price Cut,”
*PCWorld,*May 15, 2002, http://www.pcworld.com/news/article/0,aid,99524,00.asp. - Feng, Y. and G. Gallego (1995), “Optimal Starting Times for End-of-Season Sales and Optimal Stopping Times for Promotional Fares,”
*Management Science*41(98), 1371–1391.CrossRefGoogle Scholar - Feng, Y. and B. Xiao (2000), “Optimal Policies of Yield Management with Multiple Predetermined Prices,”
*Operations Research*48(2), 332–343.CrossRefGoogle Scholar - Gallego, G. and G. van Ryzin, (1993), “Optimal Dynamic Pricing of Inventories with Stochastic Demand over Finite Horizons,”
*Management Science*40, 999–1020.CrossRefGoogle Scholar - Gul, F. and R. Lundholm (1995), “Endogenous Timing and the Clustering of Agents’ Decisions,”
*Journal of Political Economy*103(5), 1039–1066.CrossRefGoogle Scholar - Hayek, F. (1945), “The Use of Knowledge in Society,”
*American Economic Review*35, 519–530.Google Scholar - Kreps, D. (1990),
*A Course in Microeconomic Theory*, Princeton Book Company.Google Scholar - Lal, R. (1990), “Price Promotions: Limiting Competitive Encroachment,”
*Marketing Science*9(3), 247–262.CrossRefGoogle Scholar - Lazear, E., (1986), “Retail Pricing and Clearance Sales,”
*The American Economic Review*76(1), 14–32.Google Scholar - Luenberger, D. G. (1969),
*Optimization by Vector Space Methods,*John Wiley & Sons, Inc., New York.Google Scholar - Netessine, S. and R. Shumsky (2004), “Revenue Management Games: Horizontal and Vertical Competition,” Working Paper, Wharton School, The University of Pennsylvania.Google Scholar
- Rao, R. (1991) “Pricing and Promotions in Asymmetric Duopolies,”
*Marketing Science*, 10 (2), pp. 131–144.CrossRefGoogle Scholar - Talluri, K. and G. van Ryzin (2004),
*Theory and Practice of Revenue Management*, Springer-Verlag, New York.Google Scholar - Varian H., (1980), “A Model of Sales,”
*American Economic Review,*70(4), 651–659.Google Scholar - Varian H., (1981), “Errata: A Model of Sales,”
*American Economic Review*71(3), 517.Google Scholar