Non-cooperative competition among revenue maximizing service providers with demand learning
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.
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- 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.
- I. V. Konnov & Sangho Kum & Gue Myung Lee, 2002. "On convergence of descent methods for variational inequalities in a Hilbert space," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 55(3), pages 371-382, June.
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- 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.
- 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. Full references (including those not matched with items on IDEAS)
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