# American Institute of Mathematical Sciences

April  2016, 12(2): 625-636. doi: 10.3934/jimo.2016.12.625

## Optimal investment strategy on advertisement in duopoly

 1 Institute of Systems Science, Northeastern University, Shenyang, Liaoning Province, 110819, China 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  September 2014 Revised  March 2015 Published  June 2015

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.
Citation: Fengjun Wang, Qingling Zhang, Bin Li, Wanquan Liu. Optimal investment strategy on advertisement in duopoly. Journal of Industrial & Management Optimization, 2016, 12 (2) : 625-636. doi: 10.3934/jimo.2016.12.625
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