双寡头价格与广告博弈研究

Research on Duopoly Price and Advertising Game

运用博弈论讨论双寡头在广告与产品价格上的两维竞争关系,通过建立数学模型,得出双寡头在稳定状态下各自最优的广告投入与产品价格,并进行了灵敏性分析和算例分析。研究结果表明:竞争的制造商,若广告成本因子相同时,市场基数越大的制造商,其产品价格就越高,广告投入量、市场需求就越大,市场基数处于劣势的制造商在需求量与利润均处于劣势。加强广告竞争对市场基数大的制造商有利,加强价格竞争对市场基数小的制造商有利。

In this paper, by using game theory, the two-dimensional relationship between advertisement and product price in duopoly competition is discussed. A mathematical model is developed and solved to optimize advertising cost and price at the steady state. With the model and examples, sensitivity analysis is conducted. Results show that, for competing manufacturers with the same advertising cost, the greater the market base a manufacturer has, the higher product price and advertising investment, and greater market demands are. The manufacturers who have small market base are in a disadvantage position in both demands and profits. Thus, strengthening the advertising competition is beneficial to manufacturers with a large market base, while enhancing price competition is beneficial to manufacturers with a small market base.