Dynamic pricing with waiting and price-anticipating customers

Over the last decades, dynamic pricing has become increasingly popular. To solve pricing problems, however, is particularly challenging if the customers' and competitors' behavior are both strategic and unknown. Reinforcement Learning (RL) methods are promising for solving such dynamic problems with incomplete knowledge. RL algorithms have shown to outperform rule-based competitor heuristics if the underlying Markov decision process is kept simple and customers are myopic. However, the myopic assumption is becoming increasingly unrealistic since technology like price trackers allows customers to act more strategically. To counteract unknown strategic behavior is difficult as pricing policies and consumers buying patterns influence each other and hence, approaches to iteratively update both sides sequentially are time consuming and convergence is unclear. In this work, we show how to use RL algorithms to optimize prices in the presence of different types of strategic customers that may wait and time their buying decisions. We consider strategic customers that (i) compare current prices against past prices and that (ii) anticipate future price developments. To avoid frequently updating pricing policies and consumer price forecasts, we endogenize the impact of current price decisions on the associated changes in forecast-based consumer behaviors. Besides monopoly markets, we further investigate how the interaction with strategic consumers is affected by additional competing vendors in duopoly markets and present managerial insights for all market setups and customer types.