This paper researches the relationships between seller and buyer with regard to game theory. The research continues by assuming an indirectly managing by an Intermediation. The intermediation is considered as third party who tried to decrease the distance between seller and buyer willing. In our proposed methodology, Bi-level programming is used for modeling the decision making between seller and buyer in supply chain, and then extend the model in Multi-level decision making. In the presented solution, the third part offers a price to each of the seller and buyer individually and supposed as leader. Final answers of described algorithms are Nash equilibrium point for supply chain. The object of seller and buyer are considered as a follower in each stage. Profits maximization for sellers and buyer are calculated by considering their own constraints.
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