## 1 Introduction
In an attempt to answer the above questions and provide insights, we examined outcomes of eight scenarios and compared corresponding optimal decisions. For tractability, and in line with the CLSC configuration considered by previous studies [10], we mainly focused on single period optimal decision. However, product collection and network design [11] is an important aspect, we limited this study on the manufacturer collection mode only to keep our focus on the assessment of three subsidy policies under a three-stage game framework. In Policy C, the government provides a subsidy directly to the consumer [12] to stimulate a green product purchase. In Policy RE, the government shares a fraction of manufacturer investment effort to encourage used product return. In Policy T, the manufacturer receives a fraction of R&D investment from the government as a subsidy to improve the greening level (GL) [13]. To compare outcomes of subsidy policies, we derived an optimal decision under no subsidy as the benchmark, called Policy N. To explore the influence of a powerful retailer, models were formulated under both the MS and RS game frameworks; and results are compared. This study contributes to the present literature as follows: First, comparative analysis will help practitioners to understand the behavior of pricing, investment decision for the manufacturer in used product return,and R&D to improve GL in a CLSC. Second, the government sets the SW optimization goal and decides the amount of the subsidy. Therefore, results can provide a guideline for them before implementing subsidy policies. Third, according to the investment decision, green products can be categorized as development intensive green products (DIGPs); marginal cost-intensive green products (MIGPs); and marginal-development cost-intensive green products (MDIGPs) [14,15]. Examples belonging to the first categories are developing LED bulbs; integrating an adaptive product business model, energy star home appliances, technology for product-life extension, and high-speed electric cars. All of these require a substantial amount of R&D investments. On the other hand, there is installing lithium-ion car batteries or emission control devices, using biodegradable plastics for FMCG packaging, and the manufacturing cost increasing with per unit product, all of which belong to second category. To the best of the authors' knowledge, the effect of MDIGPs on CLSCs has not been explored yet. Therefore, this study provides a complete overview for the manufacturer on the investment decision to produce MDIGPs. Finally, comparative study in the perspective of participating members can assist to formulate a framework to design a subsidy policy for green product manufacturing and re-manufacturing. This study is organized as follows. The following subsection a brief literature review is reported to highlight the position of our research in the literature. Assumptions and background of the models are presented in Section 2. CLSC decisions under subsidy policies are discussed in Section 3. In Section 4, managerial insights are drawn with numerical illustration. Finally, conclusions, limitations, and future research are presented in Section 5.