An explicit Nash equilibrium for a market share attraction game. (2021)

• Record Type: Journal Article
• Authors: Schuur, Peter; Badur, Bertan; Sencer, Asli
• Is Part Of: Operations research perspectives. Volume 8(2021)
• Publication Date: 2021
• Subjects: Marketing management tool -- Market share attraction models -- Competitive models -- Non-cooperative games -- Nash equilibrium; Operations research -- Periodicals; Management science -- Periodicals; 658.403405
• DOI: 10.1016/j.orp.2021.100188
• Languages: English
• ISSNs: 2214-7160

Abstract

Highlights: We design price-demand relations by a market share model based on linear attraction. We show that the model parameters are estimated effortlessly. For multiple substitute products, we derive explicit best-response functions. For two substitute products, we obtain the unique Nash equilibrium in closed form. We provide managerial insights on finding an effective competitive strategy. Abstract: In competitive marketing, the speed of generating the best price has become as critical as its reliability. In this study, we aim to design a practical marketing management tool. We consider a non-cooperative marketing environment with multiple substitute products, where total market size is moderately price-sensitive. The price-demand relations are determined by a market share attraction model, where the attraction of each product is a linear function of its price. The product's brand image is reflected in the parameters of this linear function. For the general case of multiple substitute products, we derive explicit expressions for the best-response functions. For the specific case of two substitute products, we derive closed form expressions for the prices at Nash equilibrium. These expressions help managers in changing their marketing instruments other than price, so as to obtain substantial individual profits. We show how our closed form Nash equilibrium enables the examination of the profit loss due to competition. Relevant for practice is the fact that our model can be easily calibrated. We provide a simple procedure for estimating the model parameters.