To study the cooperation of upstream and downstream enterprises of a supply chain in energy saving and emissions reduction, we establish a Stackelberg game model. The retailer moves first to decide a cost-sharing contract, then the manufacturer determines the energy-saving level, carbon-emission level, and wholesale price successively. In the end, the retailer determines the retail price. As a regulation, the government provides subsidies for energy-saving products, while imposing a carbon tax on the carbon emitted. The results show that (1) both the energy-saving cost-sharing (ECS) and the carbon emissions reduction cost-sharing (CCS) contracts are not the dominant strategy of the two parties by which they can facilitate energy savings and emissions reductions; (2) compared with single cost-sharing contracts, the bivariate cost-sharing (BCS) contract for energy saving and emissions reduction is superior, although it still cannot realise prefect coordination of the supply chain; (3) government subsidy and carbon tax policies can promote the cooperation of both the upstream and downstream enterprises of the supply chain—a subsidy policy can always drive energy saving and emissions reductions, while a carbon tax policy does not always exert positive effects, as it depends on the initial level of pollution and the level of carbon tax; and (4) the subsidy policy reduces the coordination efficiency of the supply chain, while the influences of carbon tax policy upon the coordination efficiency relies on the initial carbon-emission level.
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