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

Abstract

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.

Optimal divestment time in supply chain redesign under oligopoly: evidence from shale oil production plants

“…This has been applied by a number of researchers to model monopolistic behaviors in supply chains, for example, the game‐theoretic model of Do Chung et al. (), the application in consumer lending by Boot and Thakor (), and the application in electronic retail market by Raju et al. (), among others.…”

Dealing with the dimensionality curse in dynamic pricing competition: Using frequent repricing to compensate imperfect market anticipations

“…In most existing models, the demand intensity is assumed to be known. Dynamic pricing competition models with limited demand information are analyzed by Tsai, Hung (2009), Adida, Perakis (2010), Chung et al (2012, and Den Boer (2015b) using robust optimization and learning approaches. For a more comprehensive review, we refer to Chen, Chen (2015).…”

Dynamic pricing and learning: Historical origins, current research, and new directions

“…Machine-learning techniques that have been applied to dynamic pricing problems include evolutionary algorithms (Ramezani et al, 2011), particle swarm optimization (Mullen et al, 2006), reinforcement learning and Q-learning (Kutschinski et al, 2003, Raju et al, 2006, Könönen, 2006, Chinthalapati et al, 2006, Schwind, 2007, Cheng, 2008, Han et al, Vengerov, 2008, Cheng, 2009, Jintian and Lei, 2009, Han, 2010, Collins and Thomas, 2012, simulated annealing (Xia and Dube, 2007), Markov chain Monte Carlo methods (Chung et al, 2012), the aggregating algorithm (Levina et al, 2009) by Vovk (1990), goal-directed and derivative-following strategies in simulation (DiMicco et al, 2003), neural networks (Brooks et al, 1999, Kong, 2004, Ghose and Tran, 2009, Liu and Wang, 2013, and direct search methods (Brooks et al, 1999, Brooks et al, 2002.…”

“…The authors propose an algorithm to solve the resulting differential variational inequalities, and illustrate their method by a numerical example. Related to the set-up of Kwon et al (2009) is the recent study by Chung et al (2012), who consider a state-space model for dynamic pricing and learning in an oligopoly. They also assume that expected demand depends on the difference between a posted price and a reference price, which is computed as a weighted moving average of historical prices.…”