**1. Introduction**

In last two decades, a closed-loop supply chain (CLSC) is gaining increasing attention from both industry practitioners and academics due to alleged benefits for sustainable development and growing environmental awareness among consumers and environmental regulations [1–7]. Government organizations play an impressive role in the development of sustainable product manufacturing and re-manufacturing decisions; they can enforce strict legislation, as well as offer support through various subsidy policies. In Japan, the Ministry of Environment approved 5 billion yen in 2019 as a subsidy for the manufacturer to cover 33% to 50% of their equipment price to produce products with biodegradable bio-plastics (https://bioplasticsnews.com/2018/08/27/japangovernment-bioplastics/). The government of China provides a subsidy in different ways. For example,

a manufacturer in Hunan province receives a one-time subsidy to improve re-manufacturing activities, whereas in Hubei province, Sevalo Construction Machinery Re-manufacturing Co. Ltd. receives 1 million RMB as a research and development (R&D) subsidy to improve re-manufacturing activities [8]. In 2016, the Chinese government introduced the "Guidance on Promoting Green Consumption" program to achieve the long-term goal of stimulating green product consumption. Through the Technology & Quality Up-gradation Support scheme for MSMEs (TEQUP), the government of India provides a subsidy up to 25% of the project cost for implementation of energy efficient technology. The support became one of the key factors influencing growth for the companies like Banyan Nation, Karma Recycling; in fact, the former company received the Dell People's choice award for circular economy entrepreneur at the world economic forum in Davos (www.standupmitra.in/ Home/SubsidySchemesForAll). To encourage the consumer to procure an energy-efficient green vehicle, the United States government provides subsidies up to \$7500 for the purchase of a plug-in electric vehicle [9]. Government organizations in the USA, such as The Ohio Environmental Protection Agency (EPA), has awarded a total of \$1.24 million in recycling market development grant money to upgrade and install new equipment to increase the amount of recyclables (www.recyclingtoday.com/ article/ohio-epa-recycling-grants/). The European Union also put significant efforts to promote green product manufacturing and expedite product reuse, as well as introduce various financial packages to encourage the circular economy (European Commission, 2015). Recently, an innovative and flexible pan-European network of research funding organizations, supported by EU Horizon 2020, proposed a funding of 14.530 million euros (www.era-min.eu/sites/default/files/docs/call\_text\_2018\_0.pdf). The above evidences explain that government subsidy policies are made in different ways.

Therefore, it is imperative to conduct comparative analysis for highlighting the pros and cons among those policies. Despite the necessity to explore the effect of different government subsidy policies in CLSCs under government social welfare (SW) maximization objective, comparative study is relatively sparse. This study considers omnipotence of three subsidy policies under the manufacturer-Stackelberg (MS) and retailer-Stackelberg (RS) games to pinpoint their effects and explores the answers to the following research issues:


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.

#### *1.1. Literature Review*

It is imperative for CLSC members trading with green product to consider the evolving behavior of consumers when making important strategic and operational decisions. Possibly, Ottman [16] first reported the opportunities and the pitfalls in green marketing. The author noted double benefit for the consumer, i.e., 'personal benefit' and 'environmental benefit', in green product procurement. Since then, numerous studies related to green supply chain (GSC) management explored the properties of optimal decision under price-GL sensitive demand in different perspectives [17–19]. We will discuss some recent works focusing on variation of optimal decisions in different games under price-GL sensitive demand. Ghosh and Shah [20] compared optimal decisions obtained for different games and stated that the GL increased in the MS game, but the consumers needs to pay more. Liu and Yi [21] established that pricing and GL changes considerably under various power structures when the manufacturer also invest in knowing consumer preference information in the big data environment, and the manufacturer needs to set the lowest wholesale price under the RS game. Yang and Xiao [22] explored optimal decisions for a GSC under governmental interventions and used triangular fuzzy numbers to describe the imprecise information. The authors found that RS game scenario is the best for all players if governmental interventions are strong enough. Nielsen et al. [23] explored characteristics of the three-level GSC in a two-period setting. The authors found that the manufacturer needs to trade with the product at lower GL if the distributor dominates the GSC. Chen et al. [24] examined pricing, along with the investment effort of both the manufacturer and retailer in a GSC. The authors found that the total GSC profits increased if members share the R&D expenditure but not individual of the manufacturer or retailer simultaneously. Dey et al. [14] found that the manufacturer's decision to produce MIGPs and DIGPs is highly sensitive to the power structure. The authors found that a powerful retailer might want to trade with MIGPs, which leads to less amount of profit for the manufacturer. In this direction, the recent works of Huang et al. [25] and Ranjan and Jha [26] are worthy of mention. The findings of the above cited articles support that the game structures always made an impact on the optimal decisions. However, the above studies explored the characteristics of a forward SC. We extended this stream of research and studied the properties of CLSC under price-GL sensitive demand. CLSC is one of the great interests in both business and academic researchers due to growing consumer awareness on environmental issues and regulations. In existing literature, CLSC models are studied to explore various perspectives. For example, Hong and Yeh [27], Ma et al. [28], and Saha

et al. [29] compared optimal decisions in a CLSC under different collection mode. The authors formulated their models mainly under the MS game framework and explored the consequences where the manufacturer, retailer, or a third party, individually or jointly collects used products. On the other hand, CLSC coordination issues were comprehensively studied by Zhang and Ren [30], He et al. [31], and others. For example, Hong et al. [32], Johari and Motlagh [33], and He et al. [31] discussed effect of two-part tariff contract; Zhao et al. [34] used a commission fee contract, while a revenue-and-expense sharing contract is used by Xie et al. [35], and spanning revenue-cost sharing is used by Choi et al. [36]. On the other hand, the optimal decision under different game structures is discussed by Wang et al. [37], Gao et al. [38], Zheng et al. [39], and others. In those studies, the authors made an effort to highlight how the optimal decision changes according to game structure. We refer to recent review articles [2,40–42] on CLSC for detailed discussion. 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 [43–45] 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. Zhang 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, Hafezalkotob [47], in addition to Sinayi and Rasti-Barzoki [12], explored the optimal decision where the consumer receives a subsidy directly from the government; Chen et al. [48] explored characteristics of optimal decisions when both the manufacturer and retailer receive a subsidy on per unit product; Safarzadeh and Rasti-Barzoki [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.** Comparison of existing studies with the present study. SW = social welfare; GL = greening level; MS = manufacturer-Stackelberg; RS = retailer-Stackelberg.

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 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.

#### **2. Prerequisites and Assumptions**

We considered eight different scenarios, namely Scenarios *ij*, *i* ∈ {*m*,*r*}, which signifies MS and RS games; *j* ∈ {*C*, *RE*, *T*, *N*}, which refers to the models where consumers receive a subsidy (C), the manufacturer receives a subsidy on the investment effort on recycling (RE), and the manufacturer receives a subsidy on the total R&D investment (T); and the benchmark decision model where the government organizations do not provide a subsidy (N), respectively. Therefore, the first index represents the game structure, and the second one represents the subsidy policy. The following notations presented in Table 2 are used to differentiate the decision and auxiliary variables in different scenarios:

**Table 2.** Decision and auxiliary variables.


The following assumptions are made to establish proposed models:


a R&D subsidy on the total investment. As noted by Dey et al. [14], for MIGPs, the variable cost is directly proportional with the product quality, and it might not possible to recover the cost for the manufacturers. For example, installing emission reduction devices or packaging material are directly proportional to the unit product, but it is difficult for the manufacturer to recover the cost of those in the re-manufacturing process.

	- Step 1: The government decides the subsidy rate (*ρ<sup>C</sup> <sup>i</sup>* or *<sup>η</sup>RE <sup>i</sup>* or *<sup>μ</sup><sup>T</sup> <sup>i</sup>* ) by maximizing social welfare;
	- Step 2: In the MS game, the manufacturer decides *w<sup>j</sup> <sup>m</sup>*, *θ j <sup>m</sup>*, and *<sup>τ</sup><sup>j</sup> <sup>m</sup>*. In the RS game, the retailer decides the profit margin *m<sup>j</sup> <sup>r</sup>* = *p j <sup>r</sup>* <sup>−</sup> *<sup>w</sup><sup>j</sup> r*;
	- Step 3: In the MS game, the retailer decides the retail price *p j <sup>m</sup>*. In the RS game, the manufacturer decides *w<sup>j</sup> <sup>r</sup>*, *θ j <sup>r</sup>*, and *<sup>τ</sup><sup>j</sup> r*.

Therefore, the government takes the responses of the CLSC members into consideration, while deciding the subsidy rate [48,59].
