Multi Product Price Optimization And Competition Under The Nested Logit Model With Product Differentiated Price Sensitivities
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Multi-Product Price Optimization and Competition Under the Nested Logit Model with Product-Differentiated Price Sensitivities
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.
Operations Research Proceedings 2017
This book gathers a selection of peer-reviewed papers presented at the International Conference on Operations Research (OR 2017), which was held at Freie Universität Berlin, Germany on September 6-8, 2017. More than 800 scientists, practitioners and students from mathematics, computer science, business/economics and related fields attended the conference and presented more than 500 papers in parallel topic streams, as well as special award sessions. The main theme of the conference and its proceedings was "Decision Analytics for the Digital Economy."
Algorithmic Aspects of Discrete Choice in Convex Optimization
This book develops a framework to analyze algorithmic aspects of discrete choice models in convex optimization. The central aspect is to derive new prox-functions from discrete choice surplus functions, which are then incorporated into convex optimization schemes. The book provides further economic applications of discrete choice prox-functions within the context of convex optimization such as network manipulation based on alternating minimization and dynamic pricing for online marketplaces.