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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.
In this paper, a differential game model is constructed for manufacturers and retailers of manufacturers and retailers on the pricing of advertising and retail price of durable goods. The cumulative sales of the market as a state variable, and the advertising and price factors introduced to the market cumulative sales The dynamic equation of Hamilton retailer is obtained by using the Hamilton-Jacobian-Bellman equation, and the optimal retailer’s optimal pricing and advertising investment strategy and the optimal share of the retailer’s advertising cost are obtained respectively. The share of manufacturer is constant, while the retailer’s advertising investment decreases with the increase of accumulated market sales, and the threshold of manufacturer subsidies for retailers is given.Finally, Compare static analysis.