This paper provides an approach in the context of green supply chain management, using game theory to analyze the strategies selected by manufacturers to reduce life cycle environmental risk of materials and carbon emissions. Through the application of the 'tolerability of risk' concept, a basis for determining the extent of environmental risk and carbon emissions reduction has been established. Currently, scant attention is given to holistic supervision of the supply chain with respect to carbon emissions by governments, and thus the starting hypothesis here is that the default strategy that manufacturers will adopt is only to reduce carbon emissions, and thereby environmental risk, in so far as this is compatible with the aim of increasing revenue. Moreover, we further hypothesize that, once necessary governmental policy has been established in the supply chain management, the strategic choices of the manufacturers would be influenced by government penalties or incentives. A case example is provided to demonstrate the insight that indicates the application of game theory. The limitations of the game model and analysis are discussed, laying a foundation for further work. (C) 2012 Elsevier Ltd. All rights reserved.