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Non-cooperative competition among revenue maximizing service providers with demand learning

Author

Listed:
  • Kwon, Changhyun
  • Friesz, Terry L.
  • Mookherjee, Reetabrata
  • Yao, Tao
  • Feng, Baichun

Abstract

This paper recognizes that in many decision environments in which revenue optimization is attempted, an actual demand curve and its parameters are generally unobservable. Herein, we describe the dynamics of demand as a continuous time differential equation based on an evolutionary game theory perspective. We then observe realized sales data to obtain estimates of parameters that govern the evolution of demand; these are refined on a discrete time scale. The resulting model takes the form of a differential variational inequality. We present an algorithm based on a gap function for the differential variational inequality and report its numerical performance for an example revenue optimization problem.

Suggested Citation

  • Kwon, Changhyun & Friesz, Terry L. & Mookherjee, Reetabrata & Yao, Tao & Feng, Baichun, 2009. "Non-cooperative competition among revenue maximizing service providers with demand learning," European Journal of Operational Research, Elsevier, vol. 197(3), pages 981-996, September.
  • Handle: RePEc:eee:ejores:v:197:y:2009:i:3:p:981-996
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    References listed on IDEAS

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    1. I. V. Konnov & Sangho Kum & Gue Myung Lee, 2002. "On convergence of descent methods for variational inequalities in a Hilbert space," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(3), pages 371-382, June.
    2. Youyi Feng & Guillermo Gallego, 1995. "Optimal Starting Times for End-of-Season Sales and Optimal Stopping Times for Promotional Fares," Management Science, INFORMS, vol. 41(8), pages 1371-1391, August.
    3. Guillermo Gallego & Garrett van Ryzin, 1994. "Optimal Dynamic Pricing of Inventories with Stochastic Demand over Finite Horizons," Management Science, INFORMS, vol. 40(8), pages 999-1020, August.
    4. Lin, Kyle Y., 2006. "Dynamic pricing with real-time demand learning," European Journal of Operational Research, Elsevier, vol. 174(1), pages 522-538, October.
    5. George R. Murray, Jr. & Edward A. Silver, 1966. "A Bayesian Analysis of the Style Goods Inventory Problem," Management Science, INFORMS, vol. 12(11), pages 785-797, July.
    6. Friesz, Terry L. & Rigdon, Matthew A. & Mookherjee, Reetabrata, 2006. "Differential variational inequalities and shipper dynamic oligopolistic network competition," Transportation Research Part B: Methodological, Elsevier, vol. 40(6), pages 480-503, July.
    7. Balvers, Ronald J & Cosimano, Thomas F, 1990. "Actively Learning about Demand and the Dynamics of Price Adjustment," Economic Journal, Royal Economic Society, vol. 100(402), pages 882-898, September.
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    Cited by:

    1. Chung, Sung H. & Weaver, Robert D. & Friesz, Terry L., 2012. "Oligopolies in pollution permit markets: A dynamic game approach," International Journal of Production Economics, Elsevier, vol. 140(1), pages 48-56.

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