供应链中耐用品的广告投入和零售价策略分析

针对供应链中制造商和零售商关于耐用商品的合作广告和零售价定价问题，本文构建了一个微分博弈模型. 将市场累计销售量作为状态变量，并把广告和价格因素引入到市场累计销售量的动态方程中. 运用汉密尔顿-雅可比-贝尔曼方程，分别得到了零售商的最优定价和广告投入策略以及制造商对零售商广告成本的最优分担比例；发现零售商的最优定价和制造商的分担比例均为常数，而零售商的广告投入随市场累计销售量的增加而递减；并且给出了制造商对零售商进行广告补贴的阈值. 最后，给出了各厂商决策变量的比较静态分析.

Optimal advertising and retail pricing in a durable goods supply chain

Aiming at the problem of optimal advertising and pricing in a dynamic durable goods supply chain, this paper developed a differential games model. The cumulative sales is used as state variable, and we considered the effect of advertising and retail price on the dynamic equation of sales. Using the Hamilton-Jacobi-Bellman equation, we obtained the optimal advertising and pricing of retail and the optimal feedback subsidy rate of the manufacturer, and show how they are influenced by market parameters. An important finding is that the subsidy of manufacturer and optimal pricing of retail are constants. The optimal advertising investment of retail decreased with increasing the cumulative sales. And we gave the subsidy threshold that the manufacturer should support its retailer advertising. At last, we gave the comparatively static analysis of decision variable of the manufacturer and the retail.