عنوان مقاله [English]
Emphasizing the importance of competition and cooperation in supply chains has caused the resurgence of the game theory as a useful tool for the analysis of interactions of the members within a supply chain. Any member of a supply chain can have its own promotion and advertising programs. However, an interactive relationship (i.e. win-win) occurs when any member of the chain is able to convince to its partner to cover a portion of the cost of advertising. This action is named as vertical cooperative advertising also known as co-op advertising. Generally speaking, there are two types of advertising in the relation manufacturer-retailer which are the global and local advertising. Manufacturer is responsible of the global advertising which his purpose is to create a brand image with a nationwide scope. On the other hand, the retailer has under its hands the local advertising that treats on promotion and prices in order to stimulate the consumer demand. In the co-op advertising the costs for locally placing advertising among a retailer or wholesaler and a manufacturer are shared by all members of the chain. Coordination of pricing and marketing policies is one of the main problems in business. An economical way to achieve marketing objectives is cooperation advertising. So the manufacturer undertakes a percentage of the advertisingcosts of retailer. On the other hand, market noise effects are effective in achieving these goals. Using game theory, we consider four strategies including Nash game, Stackelberg-manufacturer, Stackelberg-retailer and cooperative game to optimize the cooperative advertising and pricing problem where market noise effect is considered. In this regard, to obtain optimal values, in each case the convexities of objective functions are proved and a numerical example is presented for each state. Then sensitivity analyses are presented to assess changes and their impact on the decision variables. It is observed that although the noise effects of the market will increase advertising costs, but increase the profits of the chain members, and the entire system.