Semi-explicit Optimal Pricing for Consumer Choice Models with Network Effects

25 Pages Posted: 27 Dec 2016 Last revised: 30 Oct 2019

See all articles by Zhenyu Cui

Zhenyu Cui

Stevens Institute of Technology - School of Business

Lingjiong Zhu

University of Minnesota - Minneapolis

Date Written: December 25, 2016

Abstract

We obtain exact semi-explicit solutions to the optimal pricing problem for the multinomial logit (MNL) consumer choice model with network effects, through a novel conditioning argument and the use of the Lambert W function. Then we manage to characterize the exact optimal solution in the presence of negative, positive and weak or positive and strong network effects, and also in the setting of heterogeneous market parameters. Furthermore, we provide a semi-explicit expression of equilibrium sales quantities in terms of equilibrium prices, based on which we establish sufficient conditions for the uniqueness of market equilibria. In addition, we provide an exact semi-explicit expression for the steady-state choice probability, based on which we discuss the uniqueness of the steady-state choice probability.

Keywords: Pricing, Choice Models, Multinomial Logit Choice, Network Effects, Revenue Management

Suggested Citation

Cui, Zhenyu and Zhu, Lingjiong, Semi-explicit Optimal Pricing for Consumer Choice Models with Network Effects (December 25, 2016). Stevens Institute of Technology School of Business Research Paper. Available at SSRN: https://ssrn.com/abstract=2889978 or http://dx.doi.org/10.2139/ssrn.2889978

Zhenyu Cui (Contact Author)

Stevens Institute of Technology - School of Business ( email )

Hoboken, NJ 07030
United States

HOME PAGE: http://sites.google.com/site/zhenyucui86/publications

Lingjiong Zhu

University of Minnesota - Minneapolis ( email )

206 Church Street SE
Minneapolis, MN 55455
United States

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