广告竞争模型的最优控制策略研究

考虑了竞争性和信息性两种广告对企业市场份额不同作用,提出一个在两强竞争情况下的动态广告投入模型,运用动态规划的Bellman方程求出模型的闭环Nash均衡解,得到企业应采取的广告最优控制策略,并进一步研究Nash均衡解有经济意义的参数范围以及Nash均衡解收敛的条件.最后用一个数值例子分析了Nash均衡下的广告策略.

Optimal Control Strategies for an Advertising Competing Model

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.