Joint Learning and Optimization for Multi-Product Pricing (and Ranking) Under a General Cascade Click Model

We consider joint learning and optimization problems under a general Cascade Click model. Under this model, customers examine the products in a decreasing order of display, from the top to (potentially) the bottom of the list. At each step, customers can decide to either purchase the current product, forego the current product and continue examining the next product, or simply terminate the search without purchasing any product. We first consider the core pricing problem, where the display position (ranking) of each product is fixed and the only decision that the firm needs to make is pricing. We then consider an extension to the problem of joint ranking and pricing in the presence of filtering options, which the customers can use to filter out some undesirable products. For both problems, we develop Upper Confidence Bound (UCB)-based joint learning and optimization algorithms with theoretical performance guarantees. The key challenge here is in constructing a UCB algorithm that exploits the structure of the Cascade Click model while at the same time taking into account all of the historical click and purchase information. Our numerical results yield three key insights. First, naively applying a standard black box UCB algorithm without adapting it to the Cascade structure is very inefficient and results in a huge loss in total revenues during a finite horizon. Second, applying a learning algorithm by assuming a mis-specified model that ignores the Cascade behavior may result in a highly suboptimal solution. Third, jointly optimizing ranking and pricing can significantly improve performance. Thus, although in practice these decisions are sometimes made separately due to organizational structure, our results suggest that a significant benefit can be realized when the two decisions are more closely coordinated.