Multi-Product Price Optimization and Competition Under the Nested Logit Model with Product-Differentiated Price Sensitivities

Operations Research, 62 (2) 450 - 461

26 Pages Posted: 31 Jan 2012 Last revised: 30 Sep 2014

See all articles by Guillermo Gallego

Guillermo Gallego

Columbia University

Ruxian Wang

Johns Hopkins University - Carey Business School

Date Written: September 1, 2013

Abstract

We study firms that sell multiple substitutable products and customers whose purchase behavior follows a Nested Logit model, of which the Multinomial Logit model is a special case. Customers make purchasing decision sequentially under the Nested Logit model: they first select a nest of products and subsequently purchase one within the selected nest. We consider the multi-product pricing problem under the general Nested Logit model with product-differentiated price sensitivities and arbitrary nest coefficients. We show that the adjusted markup, defined as price minus cost minus the reciprocal of price sensitivity, is constant for all products within a nest at optimality. This reduces the problem’s dimension to a single variable per nest. We also show that the adjusted nest-level markup is nest-invariant for all the nests, which further reduces the problem to maximizing a single-variable unimodal function under mild conditions. We also use this result to simplify the oligopolistic multi-product price competition and characterize the Nash equilibrium. We also consider more general attraction functions that include the linear utility and the multiplicative competitive interaction models as special cases, and show that similar techniques can be used to significantly simplify the corresponding pricing problems.

Keywords: multi-product pricing, Attraction model, Nested Logit model, Multinomial Logit model, product-differentiated price sensitivity, substitutable products

Suggested Citation

Gallego, Guillermo and Wang, Ruxian, Multi-Product Price Optimization and Competition Under the Nested Logit Model with Product-Differentiated Price Sensitivities (September 1, 2013). Operations Research, 62 (2) 450 - 461. Available at SSRN: https://ssrn.com/abstract=1995648 or http://dx.doi.org/10.2139/ssrn.1995648

Guillermo Gallego

Columbia University ( email )

3022 Broadway
New York, NY 10027
United States

Ruxian Wang (Contact Author)

Johns Hopkins University - Carey Business School ( email )

100 International Drive
Baltimore, MD 21202
United States

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