中文摘要：

针对一个制造商与多个竞争性零售商组成的供应链系统，研究了需求不确定的情况下，处于主方的制造商的最优品牌广告投入水平、地方性广告投入补贴费用，以及作为从方的多个具有关联性（竞争）的零售商的最佳地方性广告投入和订货问题。建立了合作广告的主从对策模型，证明了均衡解的存在，并给出了优化模型的求解算法。最后以一个制造商和两个零售商为例进行了数值实验，分析了参数变化对最优策略的影响。

英文摘要：

For a supply chain system formed by one manufacturer and a number of competitive multi-retailers, the problems about the optimal brand advertising investment and local advertising allowance of the manufacturer as a leader, and the optimal local advertising investment and ordering policy of numerous competitive retailers as followers were studied when the demand was uncertain. The Stackelberg game model about cooperative advertising was given, and the existence of equilibrium solution was proved, and then the algorithm for solving the optimization model was put forward. Finally, a numerical exemplification was carded out based on one manufacture and two retailers, and influence caused by parameter variances on the optimal strategy was analyzed.