## 4 Analysis and Discussions
### Retailer and Manufacturer Perspectives  
The following theorem is proposed to highlight the pros and cons for three policies in the perspective of CLSC members.  
**Theorem 5**.: _Under both games, the collection rate of used product and profits for each member are always higher in Policy C._  
We refer to Appendix G for the details of Theorem 5. The outcomes of Theorem 5 are consistent with Theorem 4. GL and sales volume are both higher in Policy C; consequently, CLSC members receive a higher profit in a green-sensitive market. Flexibility of investment for the manufacturer in improving GL and used product return is increased with market demand. In such a scenario, the retailer can also get benefited. The results demonstrate that fact. Graphical representation of the profits for the retailer and manufacturer, collection rate, total investment for the manufacturer to produce product (MI) (\(M_{i}^{C}=\lambda_{1}\theta_{i}^{C}D_{i}^{C}+\lambda_{2}\theta_{i}^{C^{2}}\); \(M_{i}^{RE}=\lambda_{1}\theta_{i}^{R}ED_{i}^{RE}+\lambda_{2}\theta_{i}^{RE^{2}}\); and \(M_{i}^{T}=\lambda_{1}\theta_{i}^{T}D_{i}^{T}+(1-\mu_{i}^{T})\lambda_{2}\theta_ {i}^{T^{2}}\)), investment for the manufacturer in encouraging usehold return (RI) (\(R_{i}^{C}=\alpha\tau_{i}^{C}D_{i}^{C}+\kappa\tau_{i}^{C2}\); \(R_{i}^{RE}=\alpha\tau_{i}^{RE}D_{i}^{RE}+(1-\eta_{i}^{RE})\kappa\tau_{i}^{RE 2}\); and \(R_{i}^{T}=\alpha\tau_{i}^{T}D_{i}^{T}+\kappa\tau_{i}^{T2}\)), ratios of relative change of GL with investment to produce products (\(\Delta\theta M_{i}^{j}=\frac{\theta_{i}^{j}-\theta^{N}}{M_{i}^{j}-M_{i}^{N}}\)), and ratios of relative change of the collection rate with the investment effort to stimulate used product return (\(\triangle\tau R_{i}^{j}=\frac{\tau_{i}^{j}-\tau_{i}^{N}}{R_{i}^{j}-R_{i}^{j}}\)) in six scenarios is presented in Figure 2a-g.  
Figure 2a-g support the statement of Theorem 5. In Policy RE, the manufacturer receives a subsidy to encourage the product collection, but it does not yield a higher return compared to Policy C. Note that the used product collection rates are less in Policy T compared to other two. Figure 2e demonstrates that the investment effort to stimulate used product return for the manufacturer is less in Policy RE; however, due to the government support, collection rate improved. In Policy T, the manufacturer has more flexibility in the R&D investment until the manufacturer can invest more in  
Figure 1: Graphical representation of (**a**) greening levels, (**b**) sales volumes, (**c**) effective retail prices, and (**d**) ratio of greening levels with effective retail prices in Scenarios MC, RC, MRE, RRE, MT, and RT.  
Policy C. However, Figure 2f exhibits some doubts about the efficiency of Policy C. In Policy C, the total amount of investment for the manufacturer to improve GL is maximum, but the ratio of relative change in GL improvement is less. Therefore, higher investment does not ensure higher GL, especially in Policy C. Figure 2g demonstrates a noteworthy outcome in the perspective of designing subsidy policy. It demonstrates that the power of CLSC members should be considered before implementation of the subsidy policy. Interestingly, the manufacturer reduces the investment effort considerably under the RS game, but a reverse trend is observed under the MS game. Overall, investment efficiency in producing greener product and used product return reduced in Policy C.  
Figure 2: Graphical representation of **(a)** profit of manufacturer, **(b)** profit of retailer, (c)** used product return, (d) manufacturer’s R&D investment to produce product, **(e)** investment effort in encouraging used product collection, **(f)** ratios of relative change of greening levels with investment to produce greener product, and **(g)** ratios of relative change of return rate with investment effort to stimulate product return for the manufacturer in Scenarios MC, RC, MRE, RRE, MT, and RT.