Optimal Control Strategies for an Advertising Competing Model
广告竞争模型的最优控制策略研究

Due to the different effect that predatory and informative advertising act on the market,a dynamic advertising efforts model is considered with both predatory and informative advertising in duopoly.Dynamic programming method is applied to solve this model.Using Bellman equation,we work out the close-loop Nash equilibriums,i.e.,advertising optimal control strategies that firms should adopt.Besides,the parameters range in which Nash equilibriums have economic sense and the condition that Nash equilibrium can converge are obtained.In the end of this paper,we use a numerical instance to analyze the advertising strategies in the Nash equilibrium.