Demand Learning and Dynamic Pricing under Competition in a State-Space Framework

In this paper, we propose a revenue optimization framework integrating demand learning and dynamic pricing for firms in monopoly or oligopoly markets. We introduce a state-space model for this revenue management problem, which incorporates game-theoretic demand dynamics and nonparametric techniques for estimating the evolution of underlying state variables. Under this framework, stringent model assumptions are removed. We develop a new demand learning algorithm using Markov chain Monte Carlo methods to estimate model parameters, unobserved state variables, and functional coefficients in the nonparametric part. Based on these estimates, future price sensitivities can be predicted, and the optimal pricing policy for the next planning period is obtained. To test the performance of demand learning strategies, we solve a monopoly firm's revenue maximizing problem in simulation studies. We then extend this paradigm to dynamic competition, where the problem is formulated as a differential variational inequality. Numerical examples show that our demand learning algorithm is efficient and robust.