Competition modeling in coordinating a three level supply chain

This paper concerns studying a three-level supply chain and coordinating price and inventory decisions using game theory. In the retailing level, competing exist between retailers and they compete each other to gain higher demand. Demand is deterministic. The main challenge is modeling a multi-level supply chain and formulating the game between players to determine price and replenishment period. Integer multiplier method adopted as replenishment mechanism and three-level nested Stackelberg-Nash game used to formulate the optimization problem that produces a three-level programming model. Retailers formulate the bottom-level Nash game, the whole retailers play the middle-level Stackelberg game with manufacturer, and both levels as a group formulate the top-level Stackelberg game with supplier. Questions that answered at the end are for supplier; (1) what is the optimal price for raw material sold to manufacturer? In addition (2) how frequent should the raw material procurement take place? For manufacturer: (1) what is the optimal product wholesale price? In addition (2) how frequent should the production process take place? For each retailer: (1) what is the optimal price for products sold to market? and (2) how frequent should the product procurement take place?