Dynamic Price Competition with Fixed Capacities

• 成果类型: Article
• 署名作者: Martinez-de-Albeniz, Victor; Talluri, Kalyan
• 署名单位: University of Navarra; IESE Business School; ICREA; Pompeu Fabra University
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.1110.1337
• 发表日期: 2011
• 页码: 1078-1093
• 关键词: revenue management; bid prices; subgame-perfect equilibrium

摘要

In this paper, we study price competition for an oligopoly in a dynamic setting, where each of the sellers has a fixed number of units available for sale over a fixed number of periods. Demand is stochastic, and depending on how it evolves, sellers may change their prices at any time. This reflects the fact that firms constantly, and almost costlessly, change their prices, reacting to updates in their estimates of market demand, competitor prices, or inventory levels. In a setting with demand uncertainty, we show that there is a unique subgame-perfect equilibrium for a duopoly, in which all states sellers engage in Bertrand competition and the seller with the lower equilibrium reservation value sells a unit at a price equal to the competitor's equilibrium reservation value. This structure therefore extends the marginal-value concept of bid-price control, used in many revenue management implementations, to a competitive model. We give a closed-form solution to the equilibrium price paths for a duopoly and extend all the results to an n-firm oligopoly. We then study extensions to multiple customer types, uncertain valuations, and differentiated products.