<p>This study examines a two-period green supply chain involving a green manufacturer and a retailer. Two external incentive strategies from the government and two internal incentive contracts from the supply chain are proposed, namely government green-cost subsidy, government per-unit product subsidy, green cost-sharing contract and two-part tariff contract. Considering the cost learning effect, this study applies game theory to explore the impact of incentives on equilibrium outcomes and supply chain coordination. The results show that both external and internal incentives can improve the environmental and economic performance. Only the two-part tariff contract can achieve the perfect coordination. In addition, the external incentive strategy should be combined with the internal incentive contract, especially the combination with the two-part tariff contract can maximize the benefits. Moreover, this study discusses the incentive preferences of supply chain members. It is found that their preferences for the external incentive strategy change with the relationship between the unit subsidy amount and the cost subsidy rate. However, their preferences for the internal incentive contract are definite: the manufacturer favors the two-part tariff contract, whereas the retailer prefers the green cost-sharing contract. This study offers pertinent advice for enterprises and governments.</p>