Pricing under the Generalized Markov Chain Choice Model : Learning through Large-scale Click Behaviors

Motivated by the large-scale click behaviors on the online platform, we present three new click models for different applicable scenarios, namely, the local-browsing click model and global-browsing click model with recurrent/nonrecurrent customers. These three click models are developed based on the generalized Markov chain choice model (GMCCM). We propose a data-driven framework to learn customers' browsing and purchasing behaviors, and analyze the optimal pricing policy. By utilizing the low-rank structure of the transition matrix in the GMCCM, we are able to reduce the sample complexity and improve the computational efficiency. We further analyze the relations between the optimal pricing policy and the transition matrix in the GMCCM. Our results show that a higher click rate does not necessarily lead to higher optimal prices. Instead, the change of optimal prices depends on the optimal stationary revenue. For the dynamic pricing problem in the online setting, we design an exploration-free online algorithm and prove a regret bound which is significantly lower than that in the case without considering the low-rank structure of the transition matrix. Lastly, our numerical study on real-world data verifies the low-rank structure of the empirical transition matrix. We further evaluate the performance of our algorithms using the synthetic and real-world datasets, and both show promising numerical results