Multiproduct Price Optimization Under the Multilevel Nested Logit Model

34 Pages Posted: 2 Nov 2014

See all articles by Hai Jiang

Hai Jiang

Tsinghua University - Department of Industrial Engineering; Tsinghua University

Rui Chen

Tsinghua University - Department of Industrial Engineering

He Sun

Tsinghua University

Date Written: October 30, 2014

Abstract

We study the multiproduct price optimization problem under the multilevel nested logit model, which includes the multinomial logit and the two-level nested logit models as special cases. When the price sensitivities are identical within each primary nest, that is, within each nest at level 1, we prove that the profit function is concave with respect to the market share variables. We proceed to show that the markup, defined as price minus cost, is constant across products within each primary nest, and that the adjusted markup, defined as price minus cost minus the reciprocal of the product between the scale parameter of the root nest and the price-sensitivity parameter of the primary nest, is constant across primary nests at optimality. This allows us to reduce this multidimensional pricing problem to an equivalent single-variable maximization problem involving a unimodal function. Based on these findings, we investigate the oligopolistic game and characterize the Nash equilibrium. We also develop a dimension reduction technique which can simplify price optimization problems with flexible price-sensitivity structures.

Keywords: differentiated products, multiproduct pricing, multilevel nested logit, oligopolistic competition

Suggested Citation

Jiang, Hai and Chen, Rui and Sun, He, Multiproduct Price Optimization Under the Multilevel Nested Logit Model (October 30, 2014). Available at SSRN: https://ssrn.com/abstract=2516848 or http://dx.doi.org/10.2139/ssrn.2516848

Hai Jiang (Contact Author)

Tsinghua University - Department of Industrial Engineering ( email )

Beijing, 100084
China

Tsinghua University ( email )

Rui Chen

Tsinghua University - Department of Industrial Engineering ( email )

Beijing
China

He Sun

Tsinghua University ( email )

Beijing, 100084
China

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