**Theorem 1.** *In Policy C*


We refer to Appendix C for the details of Theorem 1. Lemma 1,2 indicate that if the manufacturer is not efficient enough, then it is difficult to produce greener product. Per unit subsidy and the collection rate decreases with respect to *λ*<sup>1</sup> and *λ*2, and as a result, SW decreased. Additionally, the manufacturer needs to reduce the total investment effort in improving used product collection if the manufacturing cost is high. Therefore, results are sensible. Except profits of CLSC members, game structures do no have any effect on the optimal decision. The manufacturer charges a higher wholesale price, and the retailer sets a higher retail price in the MS game because *w<sup>C</sup> <sup>m</sup>* − *<sup>w</sup><sup>C</sup> <sup>r</sup>* <sup>=</sup> <sup>2</sup>(*a*−*cm*)*κλ*<sup>2</sup> <sup>Δ</sup><sup>1</sup> > 0 and *pC <sup>m</sup>* − *<sup>p</sup><sup>C</sup> <sup>r</sup>* <sup>=</sup> (*a*−*cm*)(*κ*(*β*−*λ*1)2+*X*2*λ*2) <sup>Δ</sup><sup>1</sup> > 0, respectively. Due to more bargaining power, the subsidy rate is always higher in the MS game, but the consumer needs to pay the same price under the MS and RS games because (*p<sup>C</sup> <sup>m</sup>* − *<sup>ρ</sup><sup>C</sup> <sup>m</sup>*) − (*p<sup>C</sup> <sup>r</sup>* − *<sup>ρ</sup><sup>C</sup> <sup>r</sup>* ) = 0. Overall, consumers remain unaffected, and the government needs to provide a higher per unit subsidy under the MS game, which does not ensure higher quality.

### *3.2. Optimal Decisions in Policy RE*

The profit structure of CLSC members and the SW of government remain similar to the previous subsection, but the demand function converts to *DRE <sup>i</sup>* = *<sup>a</sup>* − *<sup>p</sup>RE <sup>i</sup>* + *βθRE <sup>i</sup>* . For example, in China, manufacturers and government organizations, such as China's National Development and Reform Commission in 2010, collaborated to promote the program "Comments on Boosting the Re-manufacturing Development" to encourage product reuse [52]. As discussed in Section 3.1, the profit functions for the retailer and manufacturer, and SW in Scenarios MRE and RRE are obtained as follows:

$$
\pi\_{ri}^{RE}(p\_i^{RE}) = (p\_i^{RE} - w\_i^{RE}) D\_i^{RE} \,\prime \tag{4}
$$

$$
\pi\_{\rm mi}^{RE}(w\_{\rm i}^{RE}, \theta\_{\rm i}^{RE}, \tau\_{\rm i}^{RE}) = (w\_{\rm i}^{RE} - \lambda\_1 \theta\_{\rm i}^{RE} + X \tau\_{\rm i}^{RE}) D\_{\rm i}^{RE} - (1 - \eta\_{\rm i}^{RE}) \kappa \tau\_{\rm i}^{RE} - \lambda \theta\_{\rm i}^{RE} \tag{5}
$$

$$
\pi\_{gi}^{RE}(\eta\_i^{RE}) = \pi\_{ri}^{RE} + \pi\_{mi}^{RE} + \frac{D\_i^{RE^2}}{2} - \kappa \eta\_i^{RE} \pi\_i^{RE^2}.\tag{6}
$$

Derivations of optimal decisions are similar to Policy C, hence omitted. The concavity of profit functions for CLSC members and SW for the government in Scenarios MRE and RRE is ensured by condition Δ2*<sup>m</sup>* > 0 and Δ2*<sup>r</sup>* > 0, respectively. Optimal decisions under the MS and RS games are presented in Lemma 3,4, respectively.

**Lemma 3.** *Optimal decision in Scenario MRE are obtained as follows:*

*ηRE <sup>m</sup>* = <sup>6</sup>*λ*<sup>2</sup> *<sup>M</sup>*<sup>4</sup> *; <sup>w</sup>RE <sup>m</sup>* <sup>=</sup> (*a*(4*M*3*κ*−*M*4*X*2)+4*cmM*3*κ*)*λ*<sup>2</sup> <sup>Δ</sup>2*<sup>m</sup> ; <sup>p</sup>RE <sup>m</sup>* <sup>=</sup> <sup>4</sup>(8(3*a*+*cm*)*κ*−7*aX*2)*λ*<sup>2</sup> <sup>2</sup>−2*Z*2(*a*(6*κ*−*X*2)+2*cmκ*)*λ*2+2*M*3*YZ<sup>κ</sup>* <sup>Δ</sup>2*<sup>m</sup> ; θRE <sup>m</sup>* <sup>=</sup> (*a*−*cm*)*M*3*Z<sup>κ</sup>* <sup>Δ</sup>2*<sup>m</sup> ; <sup>τ</sup>RE <sup>m</sup>* <sup>=</sup> (*a*−*cm*)*M*4*Xλ*<sup>2</sup> <sup>Δ</sup>2*<sup>m</sup> ; <sup>π</sup>RE mm* <sup>=</sup> (*a*−*cm*)2*M*3*κλ*<sup>2</sup> <sup>Δ</sup>2*<sup>m</sup> ; <sup>π</sup>RE rm* <sup>=</sup> <sup>4</sup>(*a*−*cm*)2*M*3*κ*2*λ*<sup>2</sup> 2 <sup>Δ</sup>2*m*<sup>2</sup> *; <sup>π</sup>RE gm* = (*a*−*cm*)2*M*4*κλ*<sup>2</sup> <sup>Δ</sup>2*<sup>m</sup> ; QRE <sup>m</sup>* <sup>=</sup> <sup>2</sup>(*a*−*cm*)*M*4*κλ*<sup>2</sup> <sup>Δ</sup>2*<sup>m</sup> , where* <sup>Δ</sup>2*<sup>m</sup>* = *<sup>M</sup>*<sup>3</sup> <sup>2</sup>*<sup>κ</sup>* <sup>−</sup> *<sup>M</sup>*4*X*2*λ*2*.*

$$\begin{array}{llll}\textbf{lemma}\ \textbf{4.}\ \textit{Optimal decision in Secncia RRE are obtained as follows:}\\\eta\_{r}^{\textrm{RE}} =&\frac{\mathsf{N}\_{3}\lambda\_{2}-\mathsf{Z}^{2}\mathsf{x}}{2\kappa(\mathsf{M}\_{2}+\lambda\_{2})};\ \textbf{w}\_{r}^{\textrm{RE}} =&\frac{\mathsf{M}\_{2}(2(a+c\_{m})(\mathsf{x}-\mathsf{X}^{2})\lambda\_{2}+(c\_{m}\mathsf{M}\_{2}+\mathsf{Y}\mathsf{Z})\mathsf{x})+\mathsf{X}^{2}(c\_{m}\mathsf{M}\_{2}+\mathsf{Y}\mathsf{Z})\lambda\_{2}}{2\Delta\_{2}};\ \textbf{p}^{\textrm{RE}}=&\frac{\mathsf{x}\,\mathsf{Z}^{3}}{2\mathsf{x}}\\\mathtt{x}\,\mathrm{Z}^{3}((a-c\_{m})\boldsymbol{\theta}-2\boldsymbol{\lambda})+\mathsf{Z}((a-c\_{m})(2\mathsf{x}\mathsf{Z}+(4\mathsf{x}^{2})\boldsymbol{\theta})-2\mathrm{M}\_{4}\mathsf{Z})\lambda\_{2}+2(a(7\mathsf{M}\_{1}-\mathsf{X}^{2})+\mathsf{c}\_{m}(4\mathsf{x}+\mathsf{X}^{2})\lambda\_{2}^{2}}{2\Delta\_{2}};\ \boldsymbol{\theta}^{\textrm{RE}}\_{r}=&\frac{(a-c\_{m})\mathcal{Z}(4\mathsf{x}\mathsf{z}+\mathcal{X}^{2}\lambda\_{2})}{2\Delta\_{2}};\ \boldsymbol{\theta}^{\textrm{RE}}\_{r}=&\frac{(a-c\_{m})\mathcal{Z}(4\mathsf{x}\mathsf{z}+\mathcal{X}^{2}\lambda\_{2})}{2\Delta\_{2}};\ \textbf{p}^{\textrm{RE}}\_{r}=&\frac{(a-c\_{m})\mathcal{Z}(4\mathsf{x}\mathsf{z}+\mathcal{X}^{2}\lambda\_{2})}{2\Delta\_{2}};\ \textbf{\$$

Recall that optimal subsidy rates in Policy C are directly proportional with market potential, and different results are obtained in Policy RE. Although the demand increases with market potential, it does not directly affect the subsidy rate. However, the government may have to spend more because the collection rates *τRE <sup>m</sup>* and *τRE <sup>r</sup>* , or overall demand *Q<sup>C</sup> <sup>m</sup>* and *Q<sup>C</sup> <sup>r</sup>* , increase with market potential. The following theorem highlights the characteristics of the optimal decision.

### **Theorem 2.** *In Policy RE,*


We refer to Appendix D for the details of Theorem 2. The outcome of Theorem 2 differs from the previous one. A powerful retailer can enforce that the manufacturer produce and trade with greener product. The product collection rate is also higher under the RS game. Similar to Policy C, the subsidy rate is higher under the MS game. Therefore, one can find an indication that the sustainability goal can be achieved under the RS game in the presence of a subsidy.
