基于随机微分对策的纵向合作广告模型  

Vertical Cooperative Advertising Model with Stochastic Differential Game

作　　者：聂佳佳[1,2] 熊中楷[1] 

机构地区：[1]重庆大学经济与工商管理学院,重庆400030 [2]西南交通大学经济管理学院,四川成都610031

出　　处：《管理工程学报》2010年第3期136-143,131,共9页Journal of Industrial Engineering and Engineering Management

基　　金：国家自然科学基金资助项目(70571088)

摘　　要：本文利用随机微分对策理论研究了供应链中的纵向合作广告问题,建立了一个随机微分对策模型。运用汉密尔顿-雅可比-贝尔曼方程分别求得了Stackelberg博弈和合作博弈下均衡的全国性广告投入、地方性广告投入、制造商商誉的期望值、方差和商誉的概率分布函数以及Stackelberg博弈下均衡的广告分担比例,并对此两种博弈进行了比较。结果发现,合作博弈下制造商和零售商的广告投入分别高于Stackelberg博弈下的广告投入,而且在一定条件下,合作博弈下供应链的总利润高于Stackelberg博弈下的总利润。同时,合作博弈下制造商的商誉期望值高于Stackelberg博弈下的期望值,但其方差也高于Stackelberg博弈下商誉的方差。而且研究发现在一定条件下制造商具有一致渐进稳定的商誉概率分布函数。最后,运用效用理论对系统增量利润进行了划分。This paper studies the vertical cooperative advertising in supply chain with stochastic differential game and the stochastic differential game model is developed. The equilibrium national advertising, local advertising, expected goodwill and deviation of manufacturer, probability distribution function are obtained in Stackelberg game and cooperative game. And the equilibrium advertising sharing rate is obtained in Stackelberg game. This paper compares the results between in Stackelberg game and cooperative game and finds the optimal advertising of manufacturer and retailer are higher than in Stackelberg game respectively. Furthermore, the optimal profit in cooperative game is higher than in Stackelberg game in certain condition. At the same time, the expected goodwill of the manufacturer is higher than in Stackelberg game, but the deviation is higher in cooperative game. The probability distribution function of goodwill is evolutionary stability in certain condition. At last, the increment profit is divided between the retailer and the manufacturer with utility theory.

关 键 词：供应链 合作广告 随机微分对策 STACKELBERG博弈 合作博弈 

分 类 号：F270.5[经济管理—企业管理]