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

Guillermo Gallego () and Ruxian Wang ()
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Guillermo Gallego: Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027
Ruxian Wang: The Johns Hopkins Carey Business School, Baltimore, Maryland 21202

Operations Research, 2014, vol. 62, issue 2, 450-461

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 decisions sequentially under the nested logit model: they first select a nest of products and subsequently purchase one within the selected nest. We consider the multiproduct 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 the 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 multiproduct 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 we show that similar techniques can be used to significantly simplify the corresponding pricing problems.

Keywords: substitutable products; multiproduct pricing; attraction model; nested logit model; multinomial logit model (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (75)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:62:y:2014:i:2:p:450-461

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