New Approach of Game Theory for Seller’s Price Selecting Strategies in Bi-Level Programming

The relationships between the members of supply chain were modeled in many researches, such as cooperative and non-cooperative situation. In our paper, the main question is how much and for which price should each seller offer her product to maximize the profit. In the proposed methodology, Bi-level programming is used for modeling and then GAMS (general algebraic modeling system) language for solving the problem. In the presented model, the first level, called upper sub-problem and supposed as leader is trying to maximize each seller profits by obtaining the optimal offered quantity of individual seller. The objective of follower (buyer) is at second level. The lower sub-problem uses the results of the seller’s model and then maximizes its profit. These optimizations are obtained with regard to the some other constraints. Similar the other game theories problems, the Nash equilibrium point(s) is (are) the optimum decision of this seller-buyer supply chain. A numerical example is employed to illustrate the application of the proposed method.