## 1 Introduction
### Literature Review
The environmental and operational measures of a CLSC network is another important aspect, where how to reduce number of vehicles to be used and the resulting carbon emissions, as well as the impact of re-manufacturing on environment, are studied extensively under an integer programming framework. We refer to the work by [43; 44; 45] for the detailed discussion in this direction. However, as mentioned earlier, it is difficult to ignore the influence of government organizations on the optimal decision in a CLSC, but literature is scanty in that direction. [PERSON] et al. [46] measured the supply-chain green efficiency (SCGE) of thirty-seven different industrial sectors in China and found that environmental policy management and innovation capacity of the manufacturer are important factors affecting SCGE. Researchers mostly explored the influence of a government subsidy in a forward SC. For example, [PERSON] [47], in addition to [PERSON] and [PERSON] [12], explored the optimal decision where the consumer receives a subsidy directly from the government; [PERSON] et al. [48] explored characteristics of optimal decisions when both the manufacturer and retailer receive a subsidy on per unit product; [PERSON] and [PERSON] [49] discussed the optimal decision for a two-echelon SC when the manufacturer receives a subsidy on the R&D investment. To establish the position of the present study, we outline existing work on CLSCs under influence of a subsidy in Table 1.  
Table 1 demonstrates that most of the articles focused on the behavior of participants under a single subsidy policy, mostly under the MS game setting. The effect of joint influence of price-GL is also ignored. With growing awareness about green products, the influence of GL needs to be considered to obtain a pragmatic CLSC decision. Comparative study to explore preferences of the \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Study** & **Games** & **Effect of GL** & **Nature of Subsidy** & **SW Maximization** \\ \hline Mitra and [PERSON] [50] & MS & No & To the manufacturer to increase re-manufacturing & No \\  & & & activity & \\ [PERSON] et al. [51] & MS & No & To consumers to procure new products & No \\ [PERSON] et al. [52] & MS & No & To the manufacturer for re-manufacturing & No \\ [PERSON] et al. [53] & MS & No & To the manufacturer and consumer jointly & Yes \\ [PERSON] et al. [54] & MS & No & To the manufacturer and retailer for re-manufacturing & No \\ [PERSON] et al. [55] & MS & No & Replacement subsidy to the customer and manufacturer & Yes \\ [PERSON] et al. [56] & MS & No & To the manufacturer for re-manufacturing & No \\ [PERSON] et al. [3] & MS & No & To the manufacturer for re-manufacturing & No \\ [PERSON] and [PERSON] [57] & MS & No & To the manufacturer for re-manufacturing and retailer & No \\  & & & for recycling & \\ [PERSON] et al. [58] & MS & No & To the manufacturer and to consumer based on the & No \\  & & & greening level & \\ [PERSON] et al. [59] & MS & No & Directly to consumers & Yes \\ Present study & MS and & Yes & Directly to consumers, to the manufacturer for & Yes \\  & RS & & improving quality and to the manufacturer for & \\  & & & re-manufacturing & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of existing studies with the present study. SW = social welfare; GL = greening level; MS = manufacturer-Stackelberg; RS = retailer-Stackelberg. CLSC members, consumers, and government organizations are not examined in the previous literature. In this study, the investment and pricing decisions of a CLSC members are explored by correlating the optimal decision of the government organization. This study can help practitioners to understand the pricing and investment patterns for the manufacturer under the MS and RS games in a CLSC setting. Comparative analysis conducted in this study on the efficiency of investment and consumer preference can help government organizations to cultivate a pragmatic subsidy policy.