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The application of game theory to supply chain is a novel approach and it has been captured many researchers' attention, due to the theory of game provides essential tools for analysing supply chain members' behaviours in competitive and cooperative environment. The interaction among supply chain members will have significant impact on their strategies and profits. Therefore, in this work, we conducted several comprehensive studies of supply chain related problems, based on mathematical game theory concepts, by considering real life situations such as competition and cooperation, role of leadership position and availability of prior information among supply chain members. We have also considered the situation where the consumer is a strategic player in a supply chain, and incorporated his/her preference and purchasing behaviour to reflect demand. The analysis of this study should provide better understanding of complex working of a real supply chain and its members' behaviour to the researchers and practitioners in the discipline, and should also assist practitioners for decision making in order to improve supply chain members' performance.