Dynamic price competition with discrete customer choices

For many years, dynamic pricing has proven to be an effective tool to increase revenue in the airline and other service industries. Most studies, however, focused on monopolistic models and ignored the fact that nowadays consumers can easily compare prices on the Internet. In this paper, we develop a game-theoretic model to describe real-time dynamic price competition between firms that sell substitutable products. By assuming the real-time inventory levels of all firms are public information, we show the existence of Nash equilibrium. We then discuss how a firm can adapt if it knows only the initial - but not the real-time - inventory levels of its competitors. We compare a firm's expected revenue under different information structures through numerical experiments.

[1]  Gabriel R. Bitran,et al.  An Application of Yield Management to the Hotel Industry Considering Multiple Day Stays , 1995, Oper. Res..

[2]  Kevin F. McCardle,et al.  The Competitive Newsboy , 1997, Oper. Res..

[3]  L. Herk.  Consumer choice and Cournot behavior in capacity- constrained duopoly competition , 1993 .

[4]  X. Vives.  Oligopoly Pricing: Old Ideas and New Tools , 1999 .

[5]  Garrett J. van Ryzin,et al.  A Multiproduct Dynamic Pricing Problem and Its Applications to Network Yield Management , 1997, Oper. Res..

[6]  Pinar Keskinocak,et al.  Dynamic pricing in the presence of inventory considerations: research overview, current practices, and future directions , 2003, IEEE Engineering Management Review.

[7]  W. M. Kincaid,et al.  An inventory pricing problem , 1963 .

[8]  Marc Dudey.  Dynamic Edgeworth-Bertrand Competition , 1992 .

[9]  Garrett J. van Ryzin,et al.  Inventory Competition Under Dynamic Consumer Choice , 2001, Oper. Res..

[10]  Jeffrey I. McGill,et al.  Revenue Management: Research Overview and Prospects , 1999, Transp. Sci..

[11]  G. Ryzin,et al.  Optimal dynamic pricing of inventories with stochastic demand over finite horizons , 1994 .

[12]  Peng-Sheng You,et al.  Dynamic Pricing in Airline Seat Management for Flights with Multiple Flight Legs , 1999, Transp. Sci..

[13]  Gerard Debreu,et al.  A Social Equilibrium Existence Theorem* , 1952, Proceedings of the National Academy of Sciences.

[14]  M. J. Sobel,et al.  DYNAMIC OLIGOPOLY WITH INVENTORIES , 1974 .

[15]  Paul H. Zipkin,et al.  Competitive and Cooperative Inventory Policies in a Two-Stage Supply Chain , 1999 .

[16]  Fernando Bernstein,et al.  Pricing and Replenishment Strategies in a Distribution System with Competing Retailers , 2003, Oper. Res..

[17]  Wenjiao Zhao,et al.  Optimal Dynamic Pricing for Perishable Assets with Nonhomogeneous Demand , 2000 .

[18]  Shaul P. Ladany,et al.  Optimal cruise-liner passenger cabin pricing policy , 1991 .

[19]  V. Krishna,et al.  Dynamic Duopoly: Prices and Quantities , 1987 .

[20]  Shaler Stidham,et al.  The Underlying Markov Decision Process in the Single-Leg Airline Yield-Management Problem , 1999, Transp. Sci..

[21]  Philip Hans Franses,et al.  Quantitative Models in Marketing Research , 2001 .

[22]  Nils Rudi,et al.  Centralized and Competitive Inventory Models with Demand Substitution , 2002, Oper. Res..

[23]  Georgia Perakis,et al.  Competitive Multi-period Pricing with Fixed Inventories , 2004 .

[24]  Moshe Ben-Akiva,et al.  Discrete Choice Analysis: Theory and Application to Travel Demand , 1985 .

[25]  A. Federgruen,et al.  Dynamic inventory and pricing models for competing retailers , 2004 .

[26]  Janakiram Subramanian,et al.  Airline Yield Management with Overbooking, Cancellations, and No-Shows , 1999, Transp. Sci..

[27]  Youyi Feng,et al.  A Continuous-Time Yield Management Model with Multiple Prices and Reversible Price Changes , 2000 .

[28]  Serguei Netessine,et al.  Revenue Management Games: Horizontal and Vertical Competition , 2005, Manag. Sci..

[29]  Richard E. Chatwin,et al.  Optimal dynamic pricing of perishable products with stochastic demand and a finite set of prices , 2000, Eur. J. Oper. Res..

[30]  Kyle Y. Lin.  A sequential dynamic pricing model and its applications , 2004 .

[31]  Samuel E. Bodily,et al.  A Taxonomy and Research Overview of Perishable-Asset Revenue Management: Yield Management, Overbooking, and Pricing , 1992, Oper. Res..