A chaotic model for advertising diffusion problem with competition

Abstract

In this article, the author extends Dawid and Feichtinger's chaotic advertising diffusion model into the duopoly case. A computer simulation system is used to test this enhanced model. Based on the analysis of simulation results, it is found that the best advertising strategy in duopoly is to increase the advertising investment to reach the best Win–Win situation where the oscillation of market portion will not occur. In order to effectively arrive at the best situation, we define a synthetic index and two thresholds. An estimation method for the parameters of the index and thresholds is proposed in this research. We can reach the Win–Win situation by simply selecting the control parameters to make the synthetic index close to the threshold of min-oscillation state. The numerical example and computational results indicated that the proposed chaotic model is useful to describe and analyse advertising diffusion process in duopoly, it is an efficient tool for the selection and optimisation of advertising strategy.

Keywords:

• advertising diffusion
• competition
• chaotic model
• control strategy
• simulation
• parameter estimation

Acknowledgements

The research was partly supported by the grant (G-YF56, G-YG81) of Hong Kong Polytechnic University and partly by the National Natural Science Foundation (70931001, 70771021, 60821063) of People's Republic China.