Under a carbon tax, with the constraint of carbon emissions reduction, by establishing game theoretical models for a low-carbon supply chain, the article investigates how the carbon tax rate and risk aversion degree may affect retail price, product carbon emission degree, and profits of the manufacturer, the retailer, and the entire supply chain. The results show that product carbon emission degree and supply chain profit in a centralized supply chain are higher than those in a decentralized supply chain. With a risk-averse manufacturer, the product’s carbon emission degree and supply chain profit will further decrease. With increased risk aversion, the manufacturer's profit and total channel profit will decrease, but the retailer's profit will be affected by the carbon tax rate. Carbon reduction investment cost-sharing contracts can contribute to the implementation of increased demand for low-carbon products and decreased retail prices. Regardless of whether the manufacturer is risk-averse, a carbon reduction investment cost-sharing contract can increase the overall efficiency and profit of the supply chain. Finally, the results are verified by numerical examples.
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