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This study examines the role of power relationship and coordination in sustainable supply chain management. We investigate a two-echelon supply chain that consists of a manufacturer and a retailer whose Customer demand is carbon emission sensitive. Using the game-theoretic approach, we compare the equilibrium solutions under three supply chain power structures to analyse the effects of power relationship on supply chain decisions and sustainability performance. A two-part tariff contract is designed to coordinate the supply chain. The findings provide important managerial insights that can help firms develop a better understanding of power relationship and coordination in achieving sustainability goals.