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

43 Pages Posted: 5 Nov 2018 Last revised: 2 Mar 2021

See all articles by Xiangyu Gao

Xiangyu Gao

The Chinese University of Hong Kong (CUHK) - CUHK Business School

Stefanus Jasin

University of Michigan, Stephen M. Ross School of Business

Sajjad Najafi

HEC Paris

Huanan Zhang

University of Colorado at Boulder - Leeds School of Business

Date Written: October 8, 2018

Abstract

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 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 sub-optimal 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.

Keywords: pricing, cascade click model, nonparametric algorithms, asymptotic analysis, online learning

Suggested Citation

Gao, Xiangyu and Jasin, Stefanus and Najafi, Sajjad and Zhang, Huanan, Joint Learning and Optimization for Multi-product Pricing (and Ranking) under a General Cascade Click Model (October 8, 2018). Available at SSRN: https://ssrn.com/abstract=3262808 or http://dx.doi.org/10.2139/ssrn.3262808

Xiangyu Gao

The Chinese University of Hong Kong (CUHK) - CUHK Business School ( email )

Cheng Yu Tung Building
12 Chak Cheung Street
Shatin, N.T.
Hong Kong

Stefanus Jasin (Contact Author)

University of Michigan, Stephen M. Ross School of Business ( email )

701 Tappan Street
Ann Arbor, MI MI 48109
United States

Sajjad Najafi

HEC Paris ( email )

1, Rue de la Liberation
Jouy en Josas, 78351
France

Huanan Zhang

University of Colorado at Boulder - Leeds School of Business ( email )

Boulder, CO 80309-0419
United States

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