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

54 Pages Posted: 22 Jul 2022

See all articles by Mo Liu

Mo Liu

University of California, Berkeley - Department of Industrial Engineering and Operations Research

Junyu Cao

University of Texas at Austin - Red McCombs School of Business

Zuo-Jun Max Shen

University of California, Berkeley - Department of Industrial Engineering & Operations Research (IEOR)

Date Written: July 8, 2022

Abstract

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.

Keywords: generalized Markov chain choice model, optimal pricing policy, click model, low-rank model

Suggested Citation

Liu, Mo and Cao, Junyu and Shen, Zuo-Jun Max, Pricing under the Generalized Markov Chain Choice Model: Learning through Large-scale Click Behaviors (July 8, 2022). Available at SSRN: https://ssrn.com/abstract=4158054 or http://dx.doi.org/10.2139/ssrn.4158054

Mo Liu

University of California, Berkeley - Department of Industrial Engineering and Operations Research ( email )

4141 Etcheverry Hall
Berkeley, CA 94720-1777
United States

Junyu Cao (Contact Author)

University of Texas at Austin - Red McCombs School of Business ( email )

Austin, TX
United States

Zuo-Jun Max Shen

University of California, Berkeley - Department of Industrial Engineering & Operations Research (IEOR) ( email )

IEOR Department
4135 Etcheverry Hall
Berkeley, CA 94720
United States

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