Game theoretic approach for coordinating unlimited multi echelon supply chains

In order to achieve the overall objectives of the supply chain (SC), there have been seen many contradictions between the components and different levels, and these disorders may result in decreased strength and competitiveness. The main contradictions that are considered in this paper comprise inventory, pricing and marketing costs in an unlimited three echelon supply chain. The basics of the game theory make it a suitable and reliable tool for solving contradiction situations by considering all the levels and players' goals. Initially, an unlimited three echelon supply chain, including S suppliers, M manufacturers, and K retailers, is considered in order to solve the aforementioned problem. Further on, a nonlinear mathematical cooperative model based on specific assumptions, game theory approach, Nash equilibrium definition, Pareto efficiency, and revenue sharing contract is proposed Subsequently, the proposed model is employed in a numerical example, and the results are illustrated according to the genetic algorithm. Furthermore, the sensitivity of the proposed model is analysed using the design of experiment. Ultimately, the validation of the proposed cooperative model is assessed by the simulation.