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Dynamic Pricing of Perishable Assets under Competition

Management Science, Forthcoming

45 Pages Posted: 2 Dec 2008 Last revised: 10 Aug 2013

Guillermo Gallego

Columbia University

Ming Hu

University of Toronto - Rotman School of Management

Date Written: August 9, 2013


We study dynamic price competition in an oligopolistic market with a mix of substitutable and complementary perishable assets. Each firm has a fixed initial stock of items and competes in setting prices to sell them over a finite sales horizon. Customers sequentially arrive at the market, make a purchase choice and then leave immediately with some likelihood of no-purchase. The purchase likelihood depends on the time of purchase, the product attributes and the current prices. The demand structure includes time-variant linear and MultiNomial Logit demand models as special cases. Assuming deterministic customer arrival rates, we show that any equilibrium strategy has a simple structure, involving a finite set of shadow prices measuring capacity externalities that firms exert on each other: equilibrium prices can be resolved from a one-shot price competition game under the current-time demand structure, taking into account capacity externalities through the time-invariant shadow prices. The former reflects the transient demand side at every moment and the latter captures the aggregate supply constraint over the sales horizon. This simple structure sheds light on dynamic revenue management problems under competition, which helps capture the essence of the problems under demand uncertainty. We show that the equilibrium solutions from the deterministic game provide pre-committed and contingent heuristic policies that are asymptotic equilibria for its stochastic counterpart, when demand and supply are sufficiently large.

Keywords: oligopoly pricing, dynamic pricing, perishable asset, finite horizon, Nash equilibrium, supermodular game, revenue management

Suggested Citation

Gallego, Guillermo and Hu, Ming, Dynamic Pricing of Perishable Assets under Competition (August 9, 2013). Management Science, Forthcoming. Available at SSRN: or

Guillermo Gallego

Columbia University ( email )

3022 Broadway
New York, NY 10027
United States

Ming Hu (Contact Author)

University of Toronto - Rotman School of Management ( email )

105 St. George st
Toronto, ON M5S 3E6
416-946-5207 (Phone)


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