Some researchers only took manufacturers as an objective. Wang et al. (2018) divided manufacturers into under-emitter manufacturers and over-emitter manufacturers and found conditions under which the over-emitter manufacturers’ decisions were identified. Given carbon emission reduction, Xia et al. (2020) divided manufacturers into low-carbon manufacturers and ordinary product manufacturers and analyzed impacts of the CET on retail prices, sales, and profits. Other researchers took the supply chain consisting of a manufacturer and a retailer as the objective. Wang et al. (2016) designed a wholesale price premium contract and a cost-sharing contract and found that these two contracts could increase the manufacturer’s carbon emission reduction rate and the supply chain’s profit; the cost-sharing contract could increase profits of both the manufacturer and the retailer, and the wholesale price premium contract could increase the profit of the supply chain. Yang et al. (2018) analyzed the effects of the manufacturer’s promotion and the retailer’s promotion through the manufacturer’s channel and a retail channel. However, all these researchers only took CET into account and neglected CEA.

CEA could prompt the supply chain to provide green products (Zhang et al., 2020) and always benefit the manufacturer (Li et al., 2021). Under the three structures, Liu et al. (2012) constructed three models where the manufacturer (manufacturers) decided carbon emission reduction and wholesale prices and the retailer (retailers) decided the retail prices of products separately and analyzed the impacts of CEA on the supply chain players. In a supply chain compromised of a manufacturer and a retailer, Du et al. (2015) found that compared to the wholesale-price contract, both the revenue-sharing contract and the quantity-discount contract could increase the supply chain’s profit, and the carbon emission reductions in the decentralized supply chain could be the same as those in the centralized supply chain. Zhang et al. (2019) found that retailer’s fairness concerns would not change the carbon emission reduction but could influence the wholesale price and retail price. Liu and Li (2020) found that the introduction of CEA could increase the carbon emission reduction of the supply chain, both the carbon emission reduction and profit of the supply chain in the centralized scenario are higher than those in the decentralized scenario, and the bilateral cost-sharing contract could effectively encourage the manufacturer and the retailer to engage in carbon emission reduction. Wang et al. (2021) found that both carbon emission reduction and production in the centralized model are much higher than those in the decentralized model. However, all these researchers only took CEA into account and neglected CET. Xia et al. (2022) found that either with or without a cost-sharing contract, the carbon emission reduction in the decentralized scenario was no more than that in the centralized scenario.

Luo et al. (2016) considered two manufacturers with different carbon reduction efficiencies and constructed two models where manufacturers made decisions cooperatively or non-cooperatively. They found that manufacturers who made decisions cooperatively could increase profit and decrease total carbon emissions. However, they neglected the cooperation in pricing. Cao et al. (2017) analyzed the impacts of CET on the production and carbon emission reduction level of the manufacturer.

In the supply chain consisting of a manufacturer and a retailer, Xia et al. (2018) considered that the manufacturer decided the emission reduction rate and the retailer decided the promotion level and investigated their optimal decisions and profits. Wang et al. (2020) designed several contracts and found that the one-way cost-sharing contract was beneficial for the supply chain, the two-way cost-sharing contract could also achieve this effect if the sharing rate is small, and the joint carbon-emission reduction could be an optimal choice for the supply chain. Liu et al. (2021) provided three carbon emission reduction modes and found that the carbon emission reduction level was the highest in the joint carbon emission reduction, and firms would prefer the single carbon emission reduction or the joint carbon emission reduction under different conditions. However, these studies analyzed the interaction between the manufacturer and the retailer and were not able to investigate the cooperation between manufacturers.

In the two two-echelon supply chains, each of which consists of a manufacturer and a retailer, Yang et al. (2017) found that compared to the structure in which both chains were decentralized, vertical cooperation could increase carbon emission reduction but decrease retail prices and horizontal cooperation could damage retailers’ profit. In the supply chain consisting of a supplier and a manufacturer, Bai et al. (2018) found that compared to the decentralized scenario, the centralized decision scenario could increase the supply chain’s profit and decrease its carbon emission. However, these studies neglected the cooperation in pricing and took initial carbon emission allowances of the government and the price of carbon emission trading as given.

Our key contributions lie in the following aspects. First, this paper designs three strategies of carbon emission reduction and pricing for two manufacturers, which can be better to describe the operation practice. Second, this paper takes the initial carbon emission allowances of the government as one of decision variables, which can extend the existing game models to four-staged ones. Finally, this paper investigates the effects of different strategies and finds strategy selections for manufacturers from a single view and comprehensive views, which contributes to explaining various strategies between manufacturers.

For simplicity, the marginal production cost of each manufacturer is neglected. To reduce carbon emission, the manufacturer m can invest in environmental R&D. The cost of environmental R&D for manufacturer m is C m = x m 2 / 2 (Bai et al., 2018), where x m is the environmental R&D level of manufacturer m . Then, net carbon emission of manufacturer m is e m = q m − x m − β x n ,   m , n = 1,2 , m ≠ n , where β 0 < β < 1 is the environmental R&D spillover rate.

Based on Katsoulacos et al. (2001), consumer surplus is C S = q m + q n 2 / 2 , and we introduce a sensitive parameter θ 0 < θ < 1 to measure consumers’ environmental awareness, and the product is sold to consumers at a retail price p m = 1 − q m − q n − θ e m . Then, consumers’ demand function can be obtained as follows: q m = θ − 1 + θ p m + p n + θ 1 + θ x m + β x n − θ β x m + x n / θ 2 + θ . (1)

Carbon emission damages the environment, and environmental damage caused by carbon emission is D = e m + e n 2 / 2 (Poyago-Theotoky, 2007). The government’s free allocation of carbon allowance for the manufacturer m is e ¯ m . The manufacturer m needs to buy additional allowance from the carbon trading market if e m > e ¯ m ; otherwise, the manufacturer m can sell additional allowance on the carbon trading market, and the clear price of carbon allowance in the carbon trading market is p e .

Therefore, profit functions of the retailer and the manufacturer m are shown as follows: π r = p m − ω m q m + p n − ω n q n , (2) π m = ω m q m − x m 2 / 2 − p e e m − e ¯ m . (3)

The welfare function of the government is W = π m + π n + π r + C S − D , which is as follows after arranging: W = p m q m + p n q n + q m + q n 2 / 2 − x m 2 + x n 2 / 2 − e m + e n 2 / 2 . (4)

In the last stage, the retailer determines retail prices to maximize its profit. Substituting (1) in (2), the problem of optimal retail prices can be described as follows: max p m , p n π r = p m − ω m θ − 1 + θ p m + p n + θ 1 + θ x m + β x n − θ β x m + x n + p n − ω n θ + p m − 1 + θ p n + θ 1 + θ β x m + x n − θ x m + β x n } / θ 2 + θ . (5)

Combining ∂ π r / ∂ p 1 = 0 and ∂ π r / ∂ p 2 = 0 , the optimal retail price for the product of the manufacturer m can be solved as follows: p m * = 1 + ω m + θ x m + β x n / 2 . (6)

Substituting (6) in (2), consumers’ demand function for the product of the manufacturer m can be rewritten as follows: q m * = θ − 1 + θ ω m + ω n + θ 1 + θ x m + β x n − β x m + x n / 2 θ 2 + θ . (7)

In the third stage, the problem of the optimal wholesale price of the product of the manufacturer m under the NC model can be described as follows: max ω m π m = ω m q m * − x m 2 / 2 − p e q m * − x m − β x n − e ¯ m . (8)

Combining ∂ π m / ∂ ω m = 0 with ∂ π n / ∂ ω n = 0 , the optimal wholesale price for the product of the manufacturer m can be solved as follows: ω m * = θ 3 + 2 θ + 1 + θ 3 + 2 θ p e + θ 2 θ 2 + 4 θ + 1 x m + β x n − θ 1 + θ β x m + x n / 1 + 2 θ 3 + 2 θ . (9)

In the second stage, the problem of the optimal environmental R&D level of the manufacturer m under the NC model can be described as follows: max x m π m = ω m * q m * − x m 2 / 2 − p e q m * − x m − β x n − e ¯ m . (10)

Combining ∂ π m / ∂ x m = 0 with ∂ π n / ∂ x n = 0 , the optimal environmental R&D level of the manufacturer m can be solved as follows: x m * = − θ α 1 α 2 − β α 1 + α 3 α 4 + β θ α 1 2 p e / α 5 + β θ 2 α 1 α 6 , (11) where α 1 = 1 + θ , α 2 = 2 θ 2 + 4 θ + 1 , α 3 = 2 θ 2 + 6 θ + 3 , α 4 = 3 θ 2 + 6 θ + 2 , α 5 = 2 θ 5 − 2 θ 4 − 31 θ 3 − 53 θ 2 − 31 θ − 6 , α 6 = 2 θ 2 + 3 θ − α 1 β θ . Taking into account the clear condition of the carbon trading market ( e m − e ¯ m + e n − e ¯ n = 0 ), its clear price is solved as follows: p e * = { α 1 2 θ α 1 β 2 − 2 θ 2 2 α 1 + 1 β − 4 θ 2 α 1 + 3 2 α 1 − 1 + α 5 + β θ 2 α 1 α 6 e ¯ m + e ¯ n } / 2 θ α 1 2 β 2 + 2 α 1 + 1 α 7 β + α 8 , (12) where α 7 = 4 θ 3 + 19 θ 2 + 17 θ + 4 , α 8 = 8 θ 4 + 52 θ 3 + 99 θ 2 + 68 θ + 15 .

In the first stage, the problem of optimal allocation of carbon allowance under the NC model can be described as follows: max e ¯ 1 , e ¯ 2 W = ∑ m = 1 2 p m * q m * + ∑ m = 1 2 q m * 2 / 2 − ∑ m = 1 2 x m * 2 / 2 − ∑ m = 1 2 e m * 2 / 2 . (13)

Combining ∂ W / ∂ e ¯ 1 = 0 and ∂ W / ∂ e ¯ 2 = 0 , the optimal allocation of carbon allowance under the NC model can be solved as follows: e ¯ m n c = − α 1 2 α 1 − 1 2 α 1 + 1 4 θ 2 α 1 2 β 3 + 4 θ α 9 β 2 + α 10 β − α 1 − 2 α 11 / 2 Δ 1 , (14) where Δ 1 = 4 β 4 θ 2 α 1 4 − 2 β 3 θ α 1 2 2 α 1 + 1 α 12 − β 2 α 13 − 2 β α 14 − α 15 , α 9 = 4 θ 4 + 24 θ 3 + 41 θ 2 + 24 θ + 4 , α 10 = 32 θ 5 + 180 θ 4 + 288 θ 3 + 139 θ 2 + 3 θ − 6 , α 11 = 16 θ 4 + 92 θ 3 + 162 θ 2 + 103 θ + 21 , α 12 = 2 θ 4 − 5 θ 3 − 37 θ 2 − 34 θ − 8 , α 13 = 32 θ 9 + 224 θ 8 + 156 θ 7 − 2522 θ 6 − 9281 θ 5 − 14824 θ 4 − 12731 θ 3 − 6038 θ 2 − 1476 θ − 144 , α 14 = 32 θ 9 + 204 θ 8 + 24 θ 7 − 2887 θ 6 − 9921 θ 5 − 15722 θ 4 − 13700 θ 3 − 6706 θ 2 − 1722 θ − 180 , α 15 = 32 θ 9 + 120 θ 8 − 812 θ 7 − 6372 θ 6 − 17839 θ 5 − 26404 θ 4 − 22448 θ 3 − 10964 θ 2 − 2853 θ − 306 . Substituting 14 in 12, 11, 9, 7, and 6, the equilibrium clear price of carbon allowance ( p e n c ), environmental R&D level ( x m n c ), wholesale price ( ω m n c ), production ( q m n c ), and retail price ( p m n c ) under the NC model can be solved. It is easy to find that when β , θ ∈ 0,1 , x m n c > 0 , ω m n c > 0 , q m n c > 0 , p m n c > 0 will always hold, and sign e ¯ m n c = sign − 4 θ 2 α 1 2 β 3 + 4 θ α 9 β 2 + α 10 β − α 1 − 2 α 11 . Figure 2 shows conditions where e ¯ m n c = 0 , e ¯ m n c > 0 , and e ¯ m n c < 0 can satisfy. Let 4 θ 2 α 1 2 β 3 + 4 θ α 9 β 2 + α 10 β − α 1 − 2 α 11 = 0 , we can get the solution θ = g 1 β ; then, we have e ¯ m n c = 0 . If θ < g 1 β , 4 θ 2 α 1 2 β 3 + 4 θ α 9 β 2 + α 10 β − α 1 − 2 α 11 < 0 will hold; then, e ¯ m n c > 0 will hold; otherwise, e ¯ m n c < 0 will hold.

Solutions for the optimal retail price and wholesale price under the SC model are the same as those under the NC model shown in 6 and 9; then, we solve the second stage and the first stage under the SC model.

In the second stage under the SC model, manufacturers determine environmental R&D levels to maximize their joint profit π m n = π m + π n . The problem of the optimal environmental R&D level of the manufacturer m under the SC model can be described as follows: max x m , x n π m n = ω m * q m * + ω n * q n * − x m 2 + x n 2 / 2 . (15)

Combining ∂ π m n / ∂ x m = 0 and ∂ π m n / ∂ x n = 0 , the optimal environmental R&D level of the manufacturer m can be solved as follows: x ∼ m * = − 1 + β θ 2 α 1 + 3 α 1 − 1 δ 1 p e / β 2 + β θ 3 α 1 + δ 2 , (16) where δ 1 = θ 2 + 3 θ + 1 , δ 2 = θ 4 − 3 θ 3 − 12 θ 2 − 9 θ − 2 . The clear price of carbon allowance is solved as follows: p ∼ e * = − α 1 2 θ 2 β 2 + 4 θ 2 β + δ 3 − β 2 + β θ 3 α 1 + δ 2 e ¯ m + e ¯ n / β 2 δ 4 + 2 β δ 4 + δ 5 , (17) where δ 3 = 2 θ 2 − 2 θ − 1 , δ 4 = 4 θ 3 + 19 θ 2 + 17 θ + 4 , δ 5 = 4 θ 3 + 21 θ 2 + 20 θ + 5 .

In the first stage, the problem of optimal allocation of carbon allowance under the SC model can be described as follows: max e ¯ 1 , e ¯ 2 W = ∑ m = 1 2 p m * q m * + ∑ m = 1 2 q m * 2 / 2 − ∑ m = 1 2 x m * 2 / 2 − ∑ m = 1 2 e m * 2 / 2 . (18)

Combining ∂ W ∼ * / ∂ e ¯ 1 = 0 and ∂ W ∼ * / ∂ e ¯ 2 = 0 , the optimal allocation of carbon allowance under the SC model can be solved as follows: e ¯ m s c = α 1 2 α 1 − 1 1 + β 2 θ − 1 2 β 2 δ 6 + 4 β δ 6 + δ 7 / 2 Δ 2 , (19) where Δ 2 = β 4 δ 8 + 4 β 3 δ 8 + 2 β 2 δ 9 + 4 β δ 10 + δ 11 , δ 6 = 4 θ 3 + 17 θ 2 + 14 θ + 3 , δ 7 = 8 θ 3 + 36 θ 2 + 31 θ + 7 , δ 8 = 8 θ 7 + 30 θ 6 − 69 θ 5 − 432 θ 4 − 655 θ 3 − 438 θ 2 − 136 θ − 16 , δ 9 = 24 θ 7 + 79 θ 6 − 296 θ 5 − 1550 θ 4 − 2293 θ 3 − 1525 θ 2 − 474 θ − 56 , δ 10 = 8 θ 7 + 19 θ 6 − 158 θ 5 − 686 θ 4 − 983 θ 3 − 649 θ 2 − 202 θ − 24 , δ 11 = 8 θ 7 + 8 θ 6 − 251 θ 5 − 960 θ 4 − 1348 θ 3 − 892 θ 2 − 281 θ − 34 . Substituting 19 in 17, 16, 9, 7, and 6, the equilibrium clear price of carbon allowance ( p e s c ), environmental R&D level ( x m s c ), wholesale price ( ω m s c ), production ( q m s c ), and retail price ( p m s c ) under the SC model can be solved. It is easy to find that when β , θ ∈ 0,1 , x m s c > 0 , ω m s c > 0 , q m s c > 0 , p m s c > 0 will always hold, and sign e ¯ m s c = sign − 1 + β 2 θ − 1 . Figure 3 shows conditions where e ¯ m s c = 0 , e ¯ m s c > 0 , and e ¯ m s c < 0 can satisfy. Let 1 + β 2 θ − 1 = 0 , we can get the solution θ = 1 / 1 + β 2 = g 2 β ; then, we have e ¯ m s c = 0 . If θ < g 2 β , 1 + β 2 θ − 1 < 0 will hold; then, e ¯ m s c > 0 will hold; otherwise, e ¯ m s c < 0 will hold.

Solutions for the optimal retail price under the CC model are the same as those under the NC model, which is shown in (6); then, we solve the third stage, the second stage, and the first stage under the CC model.

In the third stage under the CC model, manufacturers determine their wholesale prices to maximize their joint profit. This problem under the CC model can be described as follows: max ω m , ω n π m n = ω m q m ∗ + ω n q n ∗ − x m 2 + x n 2 / 2 . (20)

Combining ∂ π m n / ∂ ω m = 0 and ∂ π m n / ∂ ω n = 0 , the optimal wholesale price of the manufacturer m can be solved as follows: ω ∼ m ∗ ∗ = 1 + θ x m + β x n + p e / 2 . (21)

In the second stage under the CC model, manufacturers also determine their environmental R&D levels to maximize their joint profit. The problem of the optimal environmental R&D level of the manufacturer m under the CC model can be described as follows: max x m , x n π m n = ω ∼ m ∗ ∗ q m ∗ + ω ∼ n ∗ ∗ q n ∗ − x m 2 + x n 2 / 2 . (22)

Combining ∂ π m n / ∂ x m = 0 and ∂ π m n / ∂ x n = 0 , the optimal environmental R&D level of the manufacturer m can be solved as follows: x ∼ m ∗ ∗ = − 1 + β θ + 8 + 3 θ p e / θ 2 1 + β 2 − 4 α 1 + 1 . (23)

The clear price of carbon allowance is solved as follows: p ∼ e ∗ ∗ = − 2 θ 1 + β 2 − 1 − θ 2 1 + β 2 − 4 α 1 + 1 e ¯ m + e ¯ n / 2 2 1 + β 2 α 1 + 3 + 1 . (24)

In the first stage, the problem of optimal allocation of carbon allowance under the CC model can be described as follows: max e ¯ 1 , e ¯ 2 W ∼ ∗ ∗ = ∑ m = 1 2 p m ∗ q m ∗ ∗ + ∑ m = 1 2 q m ∗ ∗ 2 / 2 − ∑ m = 1 2 x ∼ m ∗ ∗ 2 / 2 − ∑ m = 1 2 e ∼ m ∗ ∗ 2 / 2 . (25)

Combining ∂ W ∼ ∗ ∗ / ∂ e ¯ 1 = 0 and ∂ W ∼ ∗ ∗ / ∂ e ¯ 2 = 0 , the optimal allocation of carbon allowance under the CC model can be solved as follows: e ¯ m c c = θ 1 + β 2 − 1 2 2 α 1 + 5 1 + β 2 + 1 / Δ 3 , (26) where Δ 3 = 2 4 + β β 3 δ 12 + β 2 δ 13 + 2 β δ 14 + δ 15 , δ 12 = 2 θ 3 + 3 θ 2 − 32 θ − 64 , δ 13 = 24 θ 3 + 25 θ 2 − 452 θ − 864 , δ 14 = 8 θ 3 + θ 2 − 196 θ − 352 , δ 15 = 4 θ 3 − 5 θ 2 − 134 θ − 228 . Substituting 26 in 24, 23, 21, 7, and 6, the equilibrium clear price of carbon allowance ( p e c c ), environmental R&D level ( x m c c ), wholesale price ( ω m c c ), production ( q m c c ), and retail price ( p m c c ) under the CC model can be solved. It is easy to find that when β , θ ∈ 0,1 , x m c c > 0 , ω m c c > 0 , q m c c > 0 , p m c c > 0 will always hold, and sign e ¯ m c c = sign − 1 + β 2 θ − 1 . As under SC, if θ < g 2 β , e ¯ m c c > 0 will hold; otherwise, e ¯ m c c < 0 will hold.

Putting Figures 2, 3 together, we can get Figure 4 to get the condition for a positive solution of free allocation of carbon allowance under each model. Then, we can find g 2 β < g 1 β when 0 < β , θ < 1 . Therefore, if θ < g 2 β , all the equilibrium allocations of carbon allowance under the NC model, SC model, and CC model are positive, meaning that e ¯ m n c > 0 , e ¯ m s c > 0 , e ¯ m c c > 0 will hold.

This paper first compares the environmental R&D level under the three models, and their results are summarized in Proposition 1.

Proposition 1.

When θ < g 2 β , x m c c < x m s c < x m n c will hold if f β < θ < g 2 β , but x m c c < x m n c < x m s c will hold if 0 < θ < min f β , g 2 β .

Proposition 1 indicates that from the view of the environmental R&D level, CC is a dominated strategy and NC and SC may be the optimal strategy or second-best strategy, respectively. The environmental R&D level under CC is always much lower than that under NC and SC, but the environmental R&D level under NC may be much lower or higher than that under SC. Especially, the environmental R&D level under NC is much higher than that under SC if the spillover rate and consumers’ environmental awareness can satisfy f β < θ < g 2 β . Therefore, the environmental R&D level under NC is the highest, that under SC is much higher, and that under CC is the lowest if f β < θ < g 2 β , meaning that NC is the optimal strategy, SC is the second-best strategy, and CC is the dominated strategy at this time. However, the environmental R&D level under SC is much higher than that under NC if the spillover rate and consumers’ environmental awareness can satisfy 0 < θ < min f β , g 2 β . Therefore, the environmental R&D level under SC is the highest, that under NC is much higher, and that under CC is the lowest if 0 < θ < min f β , g 2 β , meaning that SC is the optimal strategy and NC is the second-best strategy, and CC is also the dominated strategy at this time.

This paper then compares the net carbon emission under the three models. Let net carbon emissions under NC, SC, and CC be e m n c = q m n c − x m n c − β x n n c , e m s c = q m s c − x m s c − β x n s c , and e m c c = q m c c − x m c c − β x n c c , respectively, and their comparisons are summarized in Proposition 2.

Proposition 2.

When θ < g 2 β , e m c c < e m s c < e m n c will always hold.

Proposition 2 reveals that from the view of net carbon emission, CC is the optimal strategy, SC is the second-best strategy, and NC is the dominated strategy. Compared to NC, the manufacturer m chooses SC or CC that can decrease net carbon emission and chooses CC that can decrease more net carbon emission than NC can. Therefore, the net carbon emission under NC is the highest, that under SC is much higher, and that under CC is the lowest, meaning that NC is the dominated strategy, SC is the second-best strategy, and CC is the optimal strategy.

This paper next compares profits of each manufacturer and the supply chain under the three models.

Finally, this paper makes a comprehensive comparison of the environmental R&D level, net carbon emission, and profit under the three models, and results are summarized in Proposition 5.

Proposition 5.

When θ < g 2 β , e m n c > e m s c > e m c c will always hold; x m c c < x m s c < x m n c , π m n c < π m s c < π m c c and π c c < π s c < π n c will hold if f β < θ < g 2 β , x m c c < x m n c < x m s c , π m n c < π m s c < π m c c , π c c < π s c < π n c will hold if ρ 1 β < θ < min f β , g 2 β , x m c c < x m n c < x m s c , π m s c < π m n c < π m c c , π c c < π s c < π n c will hold if 0 < θ < min ρ 1 β , ρ 2 β , and x m c c < x m n c < x m s c , π m s c < π m n c < π m c c , π c c < π n c < π s c will hold if ρ 2 β < θ < g 2 β .

Proposition 5 indicates that from the comprehensive comparison of the environmental R&D level, net carbon emission, and profit under the three models, none of the three strategies could be the optimal strategy or dominated strategy, but SC may be the second-best strategy. If f β < θ < g 2 β , compared to NC, the environmental R&D level, net carbon emission of the manufacturer m , and supply chain’s profit are much lower, but profit of the manufacturer m is much higher under SC and CC. Compared to SC, net carbon emission of the manufacturer m and the supply chain’s profit are much lower, but profit of the manufacturer m is much higher under CC. These mean that the environmental R&D level, net carbon emission of the manufacturer m , and supply chain’s profit under NC are the highest, those under SC are much higher, and those under CC are the lowest, but profit of the manufacturer m under NC is the lowest, that under SC is much higher, and that under CC is the highest. Therefore, as a whole, there is no optimal strategy or dominated strategy, but SC can be the second-best strategy if f β < θ < g 2 β . If ρ 1 β < θ < min f β , g 2 β , compared to NC, the environmental R&D level and profit of the manufacturer m are much higher, but net carbon emission of the manufacturer m and the supply chain’s profit are much lower under SC; the environmental R&D level and net carbon emission of the manufacturer m and the supply chain’s profit are much lower, but profit of the manufacturer m is much higher under CC. Compared to SC, the environmental R&D level, net carbon emission of the manufacturer m , and supply chain’s profit are much lower, but profit of the manufacturer m is much higher. These mean that the environmental R&D level of the manufacturer m under SC is the highest, that under NC is much higher, and that under CC is the lowest; net carbon emission of the manufacturer m and the supply chain’s profit under NC are the highest, those under SC are much higher, and those under CC are the lowest; profit of manufacturer m under NC is the lowest, that under SC is much higher, and that under CC is the highest. Therefore, as a whole, there is also no optimal strategy or dominated strategy, but SC can be the second-best strategy if ρ 1 β < θ < min f β , g 2 β . If 0 < θ < min ρ 1 β , ρ 2 β , compared to NC, the environmental R&D level of the manufacturer m is much higher, but net carbon emission and profit of the manufacturer m are much lower under SC. Compared to NC and SC, the environmental R&D level, net carbon emission of the manufacturer m , and supply chain’s profit are much lower, but profit of the manufacturer m is much higher under CC. Therefore, as a whole, there is no optimal strategy, second-best strategy, or dominated strategy if 0 < θ < min ρ 1 β , ρ 2 β . If ρ 2 β < θ < g 2 β , compared to NC, the environmental R&D level of the manufacturer m and supply chain’s profit are much higher, but net carbon emission and profit of the manufacturer m are much lower. Compared to NC and SC, environmental R&D level and net carbon emission of the manufacturer m and supply chain’s profit are much lower, but profit of manufacturer m is much higher. Therefore, as a whole, there is also no optimal strategy, second-best strategy, or dominated strategy if ρ 2 β < θ < g 2 β .