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

41 Pages Posted: 5 Nov 2018 Last revised: 14 Sep 2019

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

University of Michigan, Stephen M. Ross School of Business

Huanan Zhang

The Pennsylvania State University - The Harold and Inge Marcus Department of Industrial and Manufacturing Engineering

Date Written: October 8, 2018

Abstract

We consider a pricing problem for a set of products displayed on a list. We assume a general cascade click model, in which 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. The objective of the firm is to optimally price the products to maximize its expected total revenues. We first study the case where the firm knows all problem parameters and derive a relatively explicit expression for the optimal prices of the products, for some cases. This is useful for uncovering some interesting managerial insights regarding the properties of the optimal prices when customers behave in the manner prescribed by the general cascade click model. We then study the case where the parameters are unknown and need to be learned/estimated from the data. For this case, we develop online algorithms that jointly learn the unknown parameters and optimize the prices of the products. We provide theoretical performance guarantees for the algorithms and test their empirical performance using numerical experiments. Finally, we also extend our algorithms to the setting with filtering options. To the best of our knowledge, our paper is the first in the literature to study multi-product pricing problem under a general cascade click model.

Suggested Citation

Gao, Xiangyu and Jasin, Stefanus and Najafi, Sajjad and Zhang, Huanan, Joint Learning and Optimization for Multi-product Pricing 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

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

701 Tappan Ave
Ann Arbor, MI 48109
United States

Huanan Zhang

The Pennsylvania State University - The Harold and Inge Marcus Department of Industrial and Manufacturing Engineering ( email )

University Park
State College, PA 16802
United States

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