Dynamic Pricing in e-Services under Demand Uncertainty

High volatility of the e-services market, due to increasing competition, low life cycle of products, and easy availability of information about competing service offerings to customers, makes the demand for service offerings quite uncertain. Revenue management in such markets calls for real-time techniques to learn the demand and its dependence on both the price and the service level associated with the service offering. We assume firms reply on exploratory approaches for demand estimation, in which firms experiment with different service offerings in order to simultaneously learn the demand while doing business. Such exploration and learning process can be costly without supervision. As reported by Rothschild (Journal of Economic Theory, 9 185-202, 1974), traditional Bayesian dynamic control approaches may conclude with suboptimal offerings. We propose a novel demand learning approach that is guaranteed to converge to the optimal offering. The approach combines simulated annealing algorithm with Bayesian learning. We further present intelligent techniques that adaptively reduce the effort of exploration on suboptimal service offerings so as to improve the long-run average profit.

[1]  A. Alchian Uncertainty, Evolution, and Economic Theory , 1950, Journal of Political Economy.

[2]  D. Berry A Bernoulli Two-armed Bandit , 1972 .

[3]  M. Rothschild A two-armed bandit theory of market pricing , 1974 .

[4]  U. Rieder Bayesian dynamic programming , 1975, Advances in Applied Probability.

[5]  Y. Rinott On two-stage selection procedures and related probability-inequalities , 1978 .

[6]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[7]  R. Wilcox A Table for Rinott's Selection Procedure , 1984 .

[8]  A. McLennan Price dispersion and incomplete learning in the long run , 1984 .

[9]  V. Cerný Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm , 1985 .

[10]  Bruce E. Hajek,et al.  Cooling Schedules for Optimal Annealing , 1988, Math. Oper. Res..

[11]  N. Kiefer,et al.  Controlling a Stochastic Process with Unknown Parameters , 1988 .

[12]  S. Mitter,et al.  Simulated annealing with noisy or imprecise energy measurements , 1989 .

[13]  John N. Tsitsiklis,et al.  Markov Chains with Rare Transitions and Simulated Annealing , 1989, Math. Oper. Res..

[14]  B. Jullien,et al.  OPTIMAL LEARNING BY EXPERIMENTATION , 1991 .

[15]  Sandjai Bhulai,et al.  On the value of learning for Bernoulli bandits with unknown parameters , 2000, IEEE Trans. Autom. Control..

[16]  Patrick T. Harker,et al.  Competition and Outsourcing with Scale Economies , 2002, Manag. Sci..

[17]  Giuseppe A. Paleologo Price-at-Risk: A methodology for pricing utility computing services , 2004, IBM Syst. J..

[18]  Parijat Dube,et al.  Competitive equilibrium in e-commerce: Pricing and outsourcing , 2007, Comput. Oper. Res..