Optimal investment strategy on  advertisement in duopoly

Fengjun  Wang; Qingling Zhang; Bin  Li; Wanquan Liu

doi:10.3934/jimo.2016.12.625

Article Contents

2016, Volume 12, Issue 2: 625-636. Doi: 10.3934/jimo.2016.12.625

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Optimal investment strategy on advertisement in duopoly

1.
Institute of Systems Science, Northeastern University, Shenyang, Liaoning Province, 110819
2.
Institute of Systems Science, Northeastern University, Shenyang, Liaoning, 110819
3.
Department of Mathematics and Statistics, Curtin University, GPO Box U1987, Perth, WA 6845
4.
Department of Computing, Curtin University of Technology, Perth, WA 6102

Received: August 31, 2014

Revised: February 28, 2015

Published: March 2016

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Abstract

In this paper, we will investigate a duopoly competition issue in a commencing period of horizontal expansion. This is an important problem in marketing investment for new products in free market. First, we propose a new market model characterized by nonlinear differential-algebraic equations with continuous inequality constraints, which aims to maximize an enterprise's product market share rather than its profit in the commencing period in an environment of the duopoly market. In order to solve the investment problem numerically based on proposed model, the control parameterization technique together with the constraint transcription method is used by transforming the proposed problem into a sequence of optimal parameter selection problems. Finally, a practical example on beer sales is used to show the effectiveness of proposed model and we present the optimal advertising strategies corresponding to different competition situations.

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Mathematics Subject Classification: Primary: 90-08; Secondary: 49M37.

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