Evolving remanufacturing strategies in China: an evolutionary game theory perspective

Abstract

Rapid pace of natural resource depletion and environment deterioration is a cause of concern worldwide. Remanufacturing offers a promising option for reduction in the waste and the resources consumption. As a rapidly developing economy, China initiated remanufacturing efforts in the 1990s. While focusing on the evolution of remanufacturing in China, using a game theoretic setup, we analyze manufacturer and retailer's decisions to enter remanufacturing industry. Entry decisions are determined based on evolutionary stable strategies (ESS) for both parties in different phases of remanufacturing in China. The model uses replicator dynamic system to establish ESS. We find that a different ESS is suitable in different phase of evolution. As our model reveals, over time, additional new players have entered the industry. Finally, we conclude that remanufacturing industry in China is well prepared to increase its scale and help alleviate the concerns of waste and environment deterioration. This could be primarily attributed to the government policies, subsidies, and incentives that have played an important role in kick-starting the industry. To verify theoretical results, a case study was conducted involving a prominent manufacturer and retailer. Based on the mathematical findings and case analysis, we make several suggestions for government policymakers, practitioners, and enterprises to enable additional companies enter the market and increase the scale of remanufacturing.

Appendices

Appendix A. Solution of replicator dynamics equations for manufacturers and retailers

Using the strategies and payoffs illustrated in Table 2, the expected profit for manufacturers with remanufacturing and non-remanufacturing are $U_{1Y}$ and $U_{1N}$, where subscript Y and N represent remanufacturing and no remanufacturing, respectively. Let $\overline{U}_{1}$ indicate expected profit for the manufacturer. Based on the expected profit of the manufacturers with different strategies, the expected revenue functions can be formulated as follows: $U_{1Y} = y\pi_{1}^{{{\text{IV}}}} + (1 - y)\pi_{1}^{{{\text{II}}}}$, ${U_{1N}} = y\pi _1^{{\text{III}}} + (1 - y)\pi _1^{\text{I}}$, and ${\bar U_{1Y}}{ = _x}{U_{1Y}} + (1 - x){U_{1N}}$, respectively. Using the replicator dynamics system in Samuelson (1997), Smith (2012), and Xiao et al. (2018), the equation for manufacturers with remanufacturing strategy is expressed as follows:

$${F_1}(x) = \frac{{dx}}{{dt}} = x({U_{1Y}} - {\bar U_1}) = x(1 - x)[({w_R} - {c_R}){q_{R,1}} - kq_{R,1}^2]$$

Similar to above, the expected profit for retailing firms can be formulated as follows: ${U_{2Y}} = x\pi _2^{{\text{IV}}} + (1 - y)\pi _2^{{\text{III}}},$${U_{2N}} = x\pi _2^{{\text{IV}}} + (1 - x)\pi _2^{\text{I}},$ and ${\bar U_2} = y{U_{1Y}} + (1 - y){U_{2N}}$, where U_2Y, U_2N and ${\bar U_2}$ represent remanufacturing, no remanufacturing, and the expected profit for retailers, respectively. Thus, the replicator dynamics equation of the retailing enterprises with the remanufacturing strategy can be presented as follows:

$${F_2}(y) = \frac{{dy}}{{dt}} = y({U_{2Y}} - {\bar U_2}) = y(1 - y)[({p_R} - {c_R}){q_{R,2}} - kq_{R,2}^2 - t{q_{R,2}}]$$

Appendix B. Proofs of Propositions 1–4

In Scenario Ι, substituting potential stable point (0,0) into the Jacobian matrix, we have ${\text{Jacobian}} = \left[ {\begin{array}{*{20}c} {\Delta_{1} } & 0 \\ 0 & {\Delta_{2} } \\ \end{array} } \right]$. It can be seen from the matrix that $\det J = {\Delta _1} \cdot {\Delta _2}$ and$trJ = {\Delta _1} + {\Delta _2}$. The stable equilibrium scenarios are presented in Table

Table 3 Stable equilibrium solutions in point (0,0)

3, from which we get that, when ${\Delta _1} > 0$ and${\Delta _2} > 0$, ESS for manufacturers and retailers is (No remanufacturing, No remanufacturing).

In Scenario II, substituting the stable point (1,0) into the Jacobian matrix, we get the equilibrium solutions shown in Table

Table 4 Stable equilibrium solutions in point (1,0)

4. When both conditions ${\Delta _1} > 0$ and ${\Delta _2} < 0$ are satisfied, the ESS is (Remanufacturing, No remanufacturing) in this scenario.

For Scenario III, by substituting the potential equilibrium point (0,1) into the Jacobian matrix, we can see that $\det J$ and $trJ$ changes to $- {\Delta _1} \cdot {\Delta _2}$ and ${\Delta _1} - {\Delta _2}$, respectively. The new stable equilibrium solutions are shown in Table

Table 5 Stable equilibrium solutions in point (0,1)

5, from which we obtain: In Scenario III, With ${\Delta _1} < 0$ and ${\Delta _2} > 0$, the ESS can be depicted as (No remanufacturing, remanufacturing).

Similar to the three scenarios presented above, we can have another potential stable equilibrium point at (1,1). The Jacobian matrix under Scenario IV is shown in Table

Table 6 Stable equilibrium solutions in point (1,1)

6. With ${\Delta _1} > 0$ and ${\Delta _2} > 0$, in Scenario IV, the ESS set is (Remanufacturing, Remanufacturing).