Manufacturers provide products that have distinct green levels (i.e. higher degree of environmental friendliness) to satisfy consumer demands with different green preferences. A product with a higher green level generate fewer emissions but have higher costs. To encourage those manufacturers to produce environmentally friendly products, a government can implement subsidy policies. This paper focuses on the decision-making problem faced by manufacturers to determine which levels of green products to produce and production quantities at each green level. We develop an optimization model under oligopolistic competition considering green preferences and subsidies, with the objective of profit maximization for the manufacturers. We prove the existence and uniqueness of equilibrium and propose a converged algorithm with theory of finite dimensional variational inequality. Numerical results show that an increase of consumer environmental awareness will incentivize manufacturers to produce more green products with higher green levels, but this does not necessarily lead to higher profits for the manufacturers. Moreover, a well-designed subsidy policy can not only generate more profits for manufacturers, but also save subsidy investment for the government. In addition, with the changes of consumer environmental awareness or/and subsidy policy, manufacturers may obtain more profits even if the competition is more fierce.

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This study proposes a supply chain system model containing Nash game companies that compete in a common market. Each company adopts a vertical integration strategy and runs offline and online selling channels. To maximise profits, the companies determine optimal production quantities and prices. Using theory of finite-dimensional variational inequality, we prove the existence and uniqueness of the equilibrium pattern and develop a converged algorithm. Numerically, we compute the equilibrium production quantities and prices, and subsequently generate three findings through sensitivity analyses. By changing the transportation cost, we demonstrate that the offline price is conditionally higher than the online price with different transportation and processing costs. All equilibrium prices and profits decrease when substitution intensity is increased, and thus companies should differentiate their products. Altering consumer preference for online purchasing shows that consumer preference significantly influences the production quantities and profits. Online selling is not positively affected by consumer preference for online purchasing but is affected by the complex relationship between consumer preference and its variable cost.