Increasing consumption of the natural resources to produce goods and services on the one hand and the world's population growth on the other hand reveal the necessity of the energy-resource management such as fossil fuels more than ever. Therefore, in recent decades, different countries have been seeking to increase the energy-efficiency of energy-consuming products and processes, besides the improvement of the public awareness of the efficiency side-effects, e.g. rebound effects. The present research intends to investigate the status of energy-efficiency improvement and rebound effects in a sustainable supply chain of energy consuming products and processes, consisting of manufacturers, an energy supplier, and end-users as a multi-agent problem using game-theoretic approach. Also, the government intervention policies, decision-making structures, and the behavioral aspects of end-users are analyzed according to the real-world assumptions under some scenarios. In this regard, the formulation and solving process of subproblems is discussed in three sections after the explanation of concepts and literature review.