Dynamic Pricing and Learning under The Effect of Inventory Scarcity

Revealing inventory scarcity messages to customers to trigger scarcity effect is an important and widely adopted way to promote sales in online platforms. Under such circumstances, the demand is affected by both price and scarcity messages. In this article, we study the joint dynamic pricing and learning problem under the inventory scarcity effect. Specifically, we consider three popular scarcity messages: partially revealed, fully revealed, and mixedly revealed inventory information, and we design passive learning algorithms with/without forced learning steps to learn unknown parameters in the demand function with a planning horizon consisting of many independent selling seasons. The main challenge is that there is always a strictly positive probability of no learning in one selling season, since the change of inventory status is not fully under control. To balance the learning speed and regret in this setting, we introduce the idea of endogenous and forced learning cycles, and design indices to determine when to conduct forced learning steps. Furthermore, to increase the success learning probability, we design learning steps by grouping two selling seasons together based on the MDP structure for the optimal pricing policy, which is quite different from the scenario without inventory scarcity effect. As a result, our methods have $O(\log^2 T)$ regret bounds in all cases. Moreover, numerical experiments show that ignoring the scarcity effect will cause significant revenue loss. We also provide insights on when the seller should choose pure passive learning method or passive learning methods with forced learning steps. Our work sheds light on the practice of online retailing in the presence of inventory scarcity effect