Modeling the Transient Nature of Dynamic Pricing with Demand Learning in a Competitive Environment

  • Soulaymane Kachani
  • Georgia Perakis
  • Carine Simon
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 102)

Abstract

This paper focuses on joint dynamic pricing and demand learning in an oligopolistic market. Each firm seeks to learn the price-demand relationship for itself and its competitors, and to set optimal prices, taking into account its competitors’ likely moves. We follow a closed-loop approach to capture the transient aspect of the problem, that is, pricing decisions are updated dynamically over time, using the data acquired thus far.

We formulate the problem faced at each time period by each firm as a Mathematical Program with Equilibrium Constraints (MPEC). We utilize variational inequalities to capture the game-theoretic aspect of the problem. We present computational results that provide insights on the model and illustrate the pricing policies this model gives rise to.

Keywords

dynamic pricing demand learning variational inequalities game theory 

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References

  1. Achabal, D.D. and Smith, S.A. Clearance Pricing and Inventory Policies for Retail Chains. Management Science, 44(3): 285–300, 1998. MATHGoogle Scholar
  2. Adida, E. and Perakis, G. A Nonlinear Fluid Model of Dynamic Pricing and Inventory Control with no Backorders. To Appear in Operations Research, 2005. Google Scholar
  3. Aviv, Y. and Pazgal, A. A Partially observed Markov decision process for dynamic pricing. April, 2004. Google Scholar
  4. Aviv, Y. and Pazgal, A. Pricing of short life-cycle products through active learning. April, 2004. Google Scholar
  5. Balvers, R.J. and Cosimano, T.F. Actively learning about Demand and the Dynamics of Price Adjustment. Econom. Journal, 100: 882–898, 1990. Google Scholar
  6. Barto, A. and Sutton, R. Reinforcement Learning: An Introduction. MIT Press, Cambridge, 1998. Google Scholar
  7. Bernstein, F. and Federgruen, A. Pricing and Replenishment Strategies in a Distribution System with Competing Retailers. Working Paper, 1999. Google Scholar
  8. Bertsimas, D.J. and Perakis, G. Dynamic Pricing: A Learning Approach. In Lawphongpanish, S., Hearn, D.W., and Smith, M.J. (Eds.), Mathematical and Regional Models for Congestion Charging, Vol. 101 of Applied Optimization. Springer, Regionalwissenschaften, 2006. CrossRefGoogle Scholar
  9. Bitran, G. and Caldentey, R. An Overview of Pricing Models for Revenue Management. Manufacturing and Service Operations Management, (to appear), 2002. Google Scholar
  10. Bitran, G., Caldentey, R. and Mondschein, S. Coordinating Clearance Markdown sale of Seasonal Products in Retail Chains. Operations Research, 46: 609–624, 1998. MATHGoogle Scholar
  11. Bitran, G. and Mondschein, S. Periodic Pricing of Seasonal Products in Retailing. Management Science, 43, (1): 64–79, 1997. MATHGoogle Scholar
  12. Boyd, S. and Lobo, M. Pricing and Learning under Uncertain Demand. Working Paper, Fuqua School of Business, Duke University, 2003. Google Scholar
  13. Carvalho, A. and Puterman, M. How Should a Manager Set Prices When the Demand Function is Unknown. Technical Report, Sauder School of Business, University of British Columbia, Vancouver, Canada, 2004. Google Scholar
  14. Dada, M. and Petruzzi, N.C. Dynamic Pricing and Inventory control with Learning. Naval Research Logistics, 49: 303–325, 2002. MATHCrossRefMathSciNetGoogle Scholar
  15. Dafermos, S. Traffic Equilibrium and Variational Inequalities. Transportation Science, 14: 42–54, 1980. MathSciNetGoogle Scholar
  16. Dockner, E. and Jørgensen, S. Optimal Pricing Strategies for New Products in Dynamic Oligopolies. Marketing Science, 7 (4): 315–334, 1988. Google Scholar
  17. Easley, D. and Kiefer, N. Controlling a stochastic process with unknown parameters. Econometrica, 56: 1045–64, 1988. MATHCrossRefMathSciNetGoogle Scholar
  18. Elmaghraby, W., Guleu, A. and Keskinocak, P. Optimal Markdown Mechanisms in the Presence of Rational Customers with Multi-unit Demand. Working Paper, Georgia Institute of Technology, 2002. Google Scholar
  19. Elmaghraby, W. and Keskinocak, P. Dynamic Pricing in the Presence of Inventory Considerations: Research Overview, Current Practices and Future Directions. Management Science, 49 (10): 1287–1309, 2003. CrossRefGoogle Scholar
  20. Federgruen, A. and Heching, A. Combined Pricing and Inventory Control under Uncertainty. Operations Research, 47 (3): 454–475, 1999. MATHMathSciNetGoogle Scholar
  21. Feng, Y. and Gallego, G. Optimal Starting Times for End-of-season Sales and Optimal Stopping Times for Promotional Fares. Management Science, 41: 1371–1391, 1995. MATHGoogle Scholar
  22. Feng, Y. and Xiao, B. Optimal Policies of Yield Management with Multipled Predetermined Prices. Management Science, 48: 332–343, 2000. Google Scholar
  23. Friedman, J. Oligopoly Theory. Cambridge University Press, 1983. Google Scholar
  24. Fudenberg, D. and Tirole, J. Dynamic models of oligopoly. Harwood Academic Publishers, New York, 1986. Google Scholar
  25. Gallego, G. and Ryzin, van G. A Multiproduct Dynamic Pricing Problem and Its Applications to Network Yield Management. Operations Research, 45 (1): 24–41, 1997. MATHGoogle Scholar
  26. Kachani, S. and Perakis, G. A Fluid Dynamics Model of Dynamic Pricing and Inventory Control for Make-to-Stock Manufacturing Systems. Working Paper, Operations Research Center, MIT, 2002. Google Scholar
  27. Kalyanam, K. Pricing Decision under Uncertainty: A Bayesian Mixure Model Approach. Marketing Science, 15 (3): 207–221, 1996. Google Scholar
  28. Lazear, E.P. Retail Pricing and Clearance Sales. The American Economic Review, 76 (1): 14–32, 1986. Google Scholar
  29. Maglaras, C. and Meissner, J. Dynamic Pricing Strategies for Multiproduct Revenue Management Problems. Working Paper, Columbia University, New York, NY, 2004. Google Scholar
  30. Maskin, E. and Tirole, J. A Theory of Dynamic Oligopoly II: Price Competition, kinked demand curves, Edgeworth cycles. Econometrica, 56: 571–99, 1988. MATHCrossRefMathSciNetGoogle Scholar
  31. McGill, J.I. and Ryzin, van G. Revenue Management: Research Overview and Prospects. Transportation Science: Focused Issue on Yield Management in Transportation, 33 (2), 1999. Google Scholar
  32. Mirman, L., Samuelson, L. and Urbano, A. Monopoly Experimentation. International Economic Review, 34 (3): 549–63, August 1995. CrossRefGoogle Scholar
  33. Perakis, G. and Sood, A. Competitive multi-period pricing for perishable products; a robust optimization approach. To appear in Mathematical Programming, 2005. Google Scholar
  34. Popescu, Y. and Wu, Y. Dynamic Pricing Strategies Under Repeated Interactions. Working Paper, INSEAD, Fontainebleau, France, 2005. Google Scholar
  35. Rajan, A., Rakash and Steinberg, R. Dynamic Pricing and Ordering Decisions by a Monopolist. Management Science, 48: 240–262, 1992. CrossRefGoogle Scholar
  36. Rice, J. Mathematical Statistics and Data Analysis. Duxbury Press, Belmont, California, 1995. MATHGoogle Scholar
  37. Rustichini, A. and Wolinsky, A. Learning About Variable Demand in the Long Run. Journal of Economic Dynamics and Control, 19: 1283–92, 1995. MATHCrossRefGoogle Scholar
  38. Stigler, G.J. The Kinky Oligopoly Demand Curve and Rigid Prices. The Journal of Political Economy, 55 (5): 432–449, 1947. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Soulaymane Kachani
    • 1
  • Georgia Perakis
    • 2
  • Carine Simon
    • 3
  1. 1.IEOR DepartmentColumbia UniversityNew York
  2. 2.MIT Sloan School of ManagementCambridge
  3. 3.MIT Operations Research CenterCambridge

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