In this research, I systematically investigate the decision optimization problem of high-voltage battery recycling under government reward-punishment mechanisms and blockchain technology empowerment. The rapid growth of the electric vehicle market has created an impending wave of retired high-voltage batteries, which presents both environmental threats and resource recovery opportunities. In my analysis, I combine evolutionary game theory and Stackelberg game models to characterize the behavioral dynamics of governments, manufacturers, and consumers, as well as the economic consequences of adopting blockchain technology in different recycling channel structures.
1. Problem Setting and Research Framework
My study addresses two fundamental questions: (1) How should the government design dynamic versus static reward-punishment policies to steer the recycling system toward an ideal equilibrium? (2) How does blockchain technology reshape pricing, profits, and recycling rates under four mainstream recycling modes for high-voltage batteries? I first develop a tripartite evolutionary game model involving the government, electric vehicle manufacturers, and consumers. Then, I construct a closed-loop supply chain model with three tiers: a high-voltage battery manufacturer, an electric vehicle manufacturer, and consumers. The models allow me to compare decentralized, mixed, and alliance-based recycling structures with and without blockchain support.
The core analytical framework follows the logic of “institutional incentives – baseline optimization – technological empowerment – comparative verification.” The policy mechanism resolves the willingness problem of recycling participants, while blockchain technology addresses information friction, transparency, and trust deficiency. Both forces jointly improve the scale and standardization of high-voltage battery recycling.
2. Tripartite Evolutionary Game under Static and Dynamic Reward-Punishment
2.1 Model Construction
I model three bounded-rational populations with the following strategy spaces: the manufacturer chooses between “active recycling” with probability \(x\) and “passive recycling” with probability \(1-x\); the consumer chooses between “formal channel transaction” with probability \(y\) and “informal channel transaction” with probability \(1-y\); the government chooses between “strict supervision” with probability \(z\) and “loose supervision” with probability \(1-z\). The key parameters are summarized in Table 1.
| Notation | Meaning |
|---|---|
| \(C_m\) | Manufacturer’s active recycling cost |
| \(I_m\) | Intangible benefit from active recycling |
| \(\alpha_1, \alpha_2\) | Recovery technology level under active/passive recycling |
| \(I_{c1}, I_{c2}\) | Consumer income via formal/informal channel |
| \(C_{c1}, C_{c2}\) | Consumer transaction cost via formal/informal channel |
| \(\mu\) | Consumer environmental preference coefficient |
| \(L\) | Maximum environmental benefit from formal recycling |
| \(C_g\) | Government strict supervision cost |
| \(R_m\) | Government reward for active manufacturer |
| \(F_m\) | Government penalty for passive manufacturer |
| \(\beta\) | Profit reduction ratio of informal channel due to government crackdown |
| \(\theta\) | Share of reward transferred to consumers |
The payoff matrix is shown below. From this matrix, I derive the replicated dynamic equations using standard evolutionary game analysis. In the static mechanism, the reward \(R_m\) and penalty \(F_m\) are fixed. In the dynamic mechanism, I set the penalty as \(F_m^d = v / z\) where \(v\) is a dynamic adjustment coefficient, meaning that when government supervision probability is low, the penalty is high; and the reward as \(R_m^d = R_m x\), linearly increasing with the manufacturer’s active recycling probability.
| Manufacturer | Consumer | Government (Strict \(z\)) | Government (Loose \(1-z\)) |
|---|---|---|---|
| Active \(x\) | Formal \(y\) | \(I_m + \alpha_1 I_{mc} + \theta R_m – C_m\), \(I_{c1} + \mu L – C_{c1} + \theta R_m\), \(R_e – C_g – R_m\) | \(I_m + \alpha_1 I_{mc} – C_m\), \(I_{c1} – C_{c1}\), \(R_e\) |
| Informal \(1-y\) | \(I_m + R_m – C_m\), \(I_{c2} – \beta I_{c2} – C_{c2}\), \(-C_g – C_{e2} + R_m\) | \(I_m – C_m\), \(I_{c2} – C_{c2}\), \(-C_{e2}\) | |
| Passive \(1-x\) | Formal \(y\) | \(\alpha_2 I_{mc} – F_m\), \(I_{c1} – C_{c1}\), \(F_m – C_g – C_{e1}\) | \(\alpha_2 I_{mc}\), \(I_{c1} – C_{c1}\), \(-C_{e1}\) |
| Informal \(1-y\) | \(-F_m\), \(I_{c2} – \beta I_{c2} – C_{c2}\), \(F_m – C_g – C_{e2}\) | \(0\), \(I_{c2} – C_{c2}\), \(-C_{e2}\) |
The replicated dynamic equations for the three groups are as follows:
\[
\begin{aligned}
F(x) &= x(1-x)\left[ z(R_m + F_m) + y\theta R_m + \alpha_1 I_{mc} – I_m – C_m \right], \\
F(y) &= y(1-y)\left[ \mu L + x\theta R_m + \beta z(1-x) I_{c2} + I_{c1} – C_{c1} – I_{c2} + C_{c2} \right], \\
F(z) &= z(1-z)\left[ x(R_m + F_m) – C_g – F_m \right].
\end{aligned}
\]
2.2 Stability Analysis and Equilibria
Using the Jacobian matrix and Lyapunov stability theory, I obtain eight pure-strategy equilibria under the static mechanism. After eliminating points with non-negative eigenvalues, I focus on three meaningful equilibrium states. Under condition \(C_g > F_m\), the system converges to \((0,0,0)\), meaning passive recycling, informal transactions, and loose supervision. Under \(C_g < F_m\) and \(I_{c1} – C_{c1} < (1-\beta)I_{c2} – C_{c2}\), the system converges to \((1,0,0)\). Finally, when \(\mu L + I_{c1} – C_{c1} > I_{c2} – C_{c2}\) and \(\alpha_1 I_{mc} – I_m – C_m > \alpha_2 I_{mc}\), the system reaches the ideal state \((1,1,0)\) or \((1,1,1)\) depending on the government’s cost-benefit trade-off.
| Equilibrium | Eigenvalues |
|---|---|
| \(E_1(0,0,0)\) | \(F_m – C_g\), \(I_{c2}-C_{c2}-I_{c1}+C_{c1}\), \(I_m – C_m – C_{ti}-C_{tr}\) |
| \(E_4(1,0,0)\) | \(C_g – F_m\), \(I_{c2}(1-\beta)-C_{c2}-I_{c1}+C_{c1}\), \(R_m+F_m+I_m-C_m\) |
| \(E_5(0,1,1)\) | \(R_m – C_g\), \(\mu L – I_{c2}+C_{c2}+I_{c1}-C_{c1}\), \(\alpha_1 I_{mc} – I_m – C_m – \alpha_2 I_{mc} + R_m\) |
In the dynamic mechanism, I find six pure equilibria, and four are potentially stable. The dynamic design can eliminate some unstable mixed equilibria and improve the convergence speed and stability of the ideal strategy. Equations below show the dynamic adjustment:
\[
F_m^d = \frac{v}{z}, \quad R_m^d = R_m x.
\]
2.3 Numerical Simulations and Policy Insights
I set initial values \(x=y=z=0.5\) and use MATLAB to simulate the system under three scenarios. Key results are shown in Figures 3–6 (not reproduced here). The simulations confirm that the static mechanism converges to the predicted equilibria. More importantly, when I compare the dynamic and static mechanisms under the same parameter set, the dynamic mechanism significantly shortens the convergence time from about \(t=12.5\) to \(t=5\), representing a roughly 60% improvement in evolutionary speed.
My simulations demonstrate the following crucial policy effects:
- Government penalty \(F_m\) has a clear threshold effect: below a critical value in the range \([2,3]\), the system falls into the trap \((0,0,0)\); above this threshold, the manufacturer shifts to active recycling. The reward \(R_m\) only affects convergence speed, not the final equilibrium direction.
- Manufacturer recovery technology level \(\alpha_1\) is a key intrinsic driver. There exists a threshold near \(0.6\). Above the threshold, the ideal state is reached; below it, the system may even fail to converge within a finite time horizon.
- Consumer environmental preference \(\mu\) is another decisive factor. When \(\mu\) is too low (e.g., \(0.1\)), the system cannot escape the passive recycling trap. Increasing \(\mu\) accelerates convergence to the ideal state.
- The profit reduction ratio \(\beta\) acts as a speed regulator rather than a directional switch: a larger \(\beta\) speeds up active strategies but does not change the final equilibrium.
These findings inform the government that dynamic reward-punishment policies should be integrated with technology support and environmental awareness campaigns.
3. Closed-Loop Supply Chain Model without Blockchain
3.1 Model Design
I then examine a three-tier closed-loop supply chain consisting of a high-voltage battery manufacturer, an electric vehicle manufacturer, and consumers. The market demand is \(D = \phi(1+g) – \theta p\), where \(\phi\) is the potential demand, \(g\) is the recovery-driven demand gain coefficient, and \(\theta\) is the price sensitivity. The total recycling quantity for channel \(j\) is \(q_{rj} = a + b r_{j} + \delta r_{k}\), where \(a\) is the voluntary return volume, \(b\) is the recycling-price sensitivity, and \(\delta\) is the competition coefficient between channels.
I consider four recycling modes without blockchain:
- Mode N\(_B\): high-voltage battery manufacturer recycling only.
- Mode N\(_V\): electric vehicle manufacturer recycling only.
- Mode N\(_{BV}\): both parties recycle independently, forming a dual-channel competitive structure.
- Mode N\(_{(B+V)}\): both parties form an alliance and recycle jointly.
Table 4 lists the extended parameters.
| Symbol | Definition |
|---|---|
| \(w\) | Wholesale price of the battery |
| \(p\) | Retail price of the vehicle |
| \(r_B, r_V\) | Recycling price offered by battery maker / vehicle maker |
| \(r_{BV}\) | Alliance recycling price |
| \(c_o\) | Unit cost using virgin materials |
| \(c\) | Unit cost using recycled materials |
| \(r_b\) | Echelon utilization benefit per unit |
| \(r\) | Net unit recycling revenue, \(r = c_o – c + r_b\) |
| \(c_r\) | Fixed unit recycling cost |
| \(\delta_B, \delta_V\) | Channel competition coefficients |
| \(g_r\) | Government subsidy per unit recycled |
3.2 Equilibrium Solutions under Four Modes
Using backward induction, I solve the Stackelberg game where the battery manufacturer acts as the leader and the vehicle manufacturer as the follower. In Mode N\(_B\), the profit functions are as follows:
\[
\begin{aligned}
\pi_B^{N_B} &= (w – c + g)(\phi(1+g)-\theta p) + (r + E_r \zeta + g_r)(a + b r_B), \\
\pi_V^{N_B} &= (p – w)(\phi(1+g)-\theta p).
\end{aligned}
\]
The optimal wholesale price and recycling price are derived from the Hessian matrix:
\[
w^{N_B} = \frac{\phi(1+g)+\theta c}{2\theta}, \quad r_B^{N_B} = \frac{a + b(r+c_o-c+r_b+E_r\zeta+g_r)}{2b}.
\]
Similarly, I derive the equilibria for Mode N\(_V\), Mode N\(_{BV}\), and Mode N\(_{(B+V)}\). The retail price in the alliance mode is the lowest, while the wholesale price remains identical across non-alliance modes because it is independent of the recycling structure. Table 5 compares the key performance indicators using a baseline parameter set with \(\phi=300000, \theta=1.6, r=29349, b=1.1, c_{rB}=400, c_{rV}=300, c_{r(B+V)}=250\).
| Mode | Supply Chain Profit (CNY) | Sales Volume | Recycling Volume | Recycling Rate (%) |
|---|---|---|---|---|
| N\(_B\) | 4,933,474,747 | 49,700 | 18,228 | 36.68 |
| N\(_V\) | 4,859,473,348 | 49,700 | 9,150 | 18.41 |
| N\(_{BV}\) | 5,000,859,104 | 49,700 | 19,225 | 38.68 |
| N\(_{(B+V)}\) | 6,540,679,996 | 99,400 | 20,050 | 20.17 |
Two structural findings stand out. First, the alliance mode N\(_{(B+V)}\) yields the highest total supply chain profit because it eliminates double marginalization and duplicates fixed costs. Second, the mixed mode N\(_{BV}\) achieves the highest recycling rate (38.68%) because channel competition induces higher recycling prices, which motivates consumers to return more retired high-voltage batteries.
4. Blockchain-Enabled Recycling Models
4.1 Additional Assumptions and Parameters
I now augment the closed-loop supply chain model by incorporating blockchain technology. Let \(\lambda\) denote the blockchain technology investment level and \(k\) denote the consumer trust coefficient toward blockchain. The demand function becomes:
\[
D = \phi(1+g) + k\lambda – \theta p.
\]
The recycling quantity becomes:
\[
q_{rj} = a + b r_j + \delta r_k + k\lambda.
\]
Blockchain investment incurs a quadratic cost \(C_\lambda = \frac{1}{2}A\lambda^2\), where \(A\) is the cost coefficient. The manufacturer bears a proportion \(t\) of this cost, and the vehicle manufacturer bears \(1-t\). Table 6 lists the additional parameters.
| Symbol | Meaning |
|---|---|
| \(\lambda\) | Blockchain technology investment level |
| \(k\) | Consumer trust in blockchain |
| \(A\) | Blockchain cost coefficient |
| \(t\) | Cost-sharing ratio of blockchain borne by battery maker |
4.2 Optimal Decisions under Blockchain-Enabled Modes
I derive closed-form solutions for four corresponding modes: Y\(_B\), Y\(_V\), Y\(_{BV}\), and Y\(_{(B+V)}\). In Mode Y\(_B\), the profit functions are:
\[
\begin{aligned}
\pi_B^{Y_B} &= (w – c + g)(\phi(1+g)+k\lambda – \theta p) + (r+E_r\zeta+g_r)(a+b r_B+k\lambda) – \frac{t A \lambda^2}{2}, \\
\pi_V^{Y_B} &= (p-w)(\phi(1+g)+k\lambda – \theta p) – \frac{(1-t) A \lambda^2}{2}.
\end{aligned}
\]
The equilibrium wholesale price, retail price, recycling price, and blockchain investment level are, respectively:
\[
w^{Y_B} = \frac{2(c+g)\theta^2 + \theta \phi(1+g)(4\theta – A t(2\theta-b)) + A t \theta^2 k^2 + …}{2(4\theta^2 – A t(2\theta-b))},
\]
with the full expressions available through symbolic computation. A representative solution for the blockchain investment level in the alliance mode Y\(_{(B+V)}\) is:
\[
\lambda^{Y_{(B+V)}} = \frac{k \left[ r+g_r + c_o – c + r_b + A t (c+g) – … \right]}{2(4\theta – k^2)^2}.
\]
4.3 Comparative Results
Using the same baseline parameters plus \(A=500, k=4, t=0.7\), I obtain the results in Table 7.
| Mode | Supply Chain Profit (CNY) | Sales Volume | Recycling Volume | Recycling Rate (%) |
|---|---|---|---|---|
| Y\(_B\) | 4,998,974,780 | 50,260 | 19,367 | 38.53 |
| Y\(_V\) | 4,916,297,388 | 50,158 | 9,608 | 19.15 |
| Y\(_{BV}\) | 5,108,024,171 | 50,456 | 21,906 | 43.42 |
| Y\(_{(B+V)}\) | 6,684,186,668 | 100,068 | 23,037 | 23.02 |
Blockchain consistently improves both profit and recycling rate. The highest absolute profit increase occurs in the alliance mode: from 6.5407 billion to 6.6842 billion, an increase of about 2.2%. However, the largest relative improvement in recycling rate appears in Mode Y\(_{BV}\): the recycling rate rises from 38.68% to 43.42%, an increase of more than 4.7 percentage points. The mechanism is that blockchain eliminates information asymmetry in the dual-channel competition and prevents underpricing based on hidden battery-quality information, thereby encouraging consumers to sell their retired high-voltage batteries to the formal channels.
My analysis also reveals that the retail price in every blockchain-enabled mode is higher than in the corresponding no-blockchain mode, while the optimal recycling price is lower. This is a novel insight: because blockchain enables transparent valuation of battery health and residual value, consumers no longer need a high monetary reward to compensate for information risk. They are willing to return their high-voltage battery even if the recycling price is lower, as long as the price is justified by credible data. Conversely, blockchain enhances consumer willingness to pay for a new electric vehicle equipped with a traceable battery, enabling manufacturers to raise the retail price without sacrificing demand.
5. Sensitivity Analysis and Mechanism Discussion
5.1 Blockchain Cost-Sharing Ratio
I examine how the cost-sharing ratio \(t\) affects the profits of the battery manufacturer and the vehicle manufacturer. Figure 7 shows that regardless of \(t\), both parties earn higher profits when blockchain is adopted than when it is absent. The cost-sharing ratio only redistributes the surplus between the two parties. This result provides a robust economic rationale for collaborative blockchain investment.
5.2 Consumer Price Sensitivity Coefficients
Consumers’ sensitivity to the retail price \(\theta\) and to the recycling price \(b\) strongly influence aggregate performance. The total supply chain profit declines as \(\theta\) increases because higher retail-price sensitivity suppresses demand. Managers should monitor \(\theta\) through market research and adjust their retail strategies accordingly. Conversely, increasing the recycling-price sensitivity \(b\) positively stimulates recycling rates: when consumers respond strongly to recycling price, even a small upward adjustment attracts many returns of high-voltage batteries. These patterns remain consistent with and without blockchain.
5.3 Consumer Trust in Blockchain: The Critical Moderator
I perform a sensitivity analysis of the consumer trust coefficient \(k\) across all blockchain-enabled modes. Table 8 displays key results for Mode Y\(_{BV}\) as \(k\) increases from 2 to 6.
| \(k\) | \(\lambda_{BV}\) | Retail Price \(p_{BV}\) | Recycling Rate (%) | Supply Chain Profit |
|---|---|---|---|---|
| 2 | 357.0 | 175,522 | 39.94 | 5,013,479,192 |
| 4 | 756.2 | 176,605 | 43.42 | 5,108,024,171 |
| 6 | 1,253 | 178,711 | 50.19 | 5,263,076,544 |
A clear monotonic pattern emerges: as consumer trust rises, the optimal blockchain investment level rises, the retail price rises, and the recycling rate improves substantially even without increasing the nominal recycling price. This confirms that trust itself becomes a form of incentive for consumers to return used high-voltage batteries. Therefore, blockchain technology cannot fully deliver its value without market-level trust. Governments and enterprises should invest not only in the technology infrastructure but also in consumer education, accreditation systems, and demonstration projects that increase public confidence in blockchain-based tracing of high-voltage battery life cycles.
5.4 Differential Empowerment Mechanisms across Recycling Modes
I identify three distinct structural mechanisms through which blockchain improves recycling performance:
- Single-actor recycling modes (Y\(_B\), Y\(_V\)): Blockchain mainly improves consumer trust in the transaction, lowering negotiation frictions, but its impact is constrained because there is no channel competition to amplify the effect.
- Mixed recycling mode (Y\(_{BV}\)): Blockchain curbs opportunistic behavior such as undervaluing battery residual value. In the competitive dual-channel setting, both recyclers are forced to base prices on objective, tamper-proof data. This prevents a race-to-the-bottom and increases consumers’ perceived fairness, thereby raising the recovery rate sharply.
- Alliance recycling mode (Y\(_{(B+V)}\)): Blockchain reduces internal coordination and verification costs between the cooperating parties. Because the alliance already eliminates double marginalization, the incremental benefit is less dramatic but still positive in both total profit and recycling volume.
The numerical results in Table 7 and Table 8 strongly support these mechanisms. For instance, the recycling-rate improvement in the mixed mode is roughly \(43.42\% – 38.68\% = 4.74\) percentage points, which is larger than the corresponding improvement in the single-actor mode Y\(_B\) (from 36.68% to 38.53%, an increase of 1.85 points). The alliance mode shows a more modest percentage-point increase (from 20.17% to 23.02%), but because the alliance mode starts from a lower recovery rate, the relative improvement is still visible.
6. Policy and Management Implications
6.1 Implications for Government Policy
My results suggest that the government should move from static, fixed penalties and subsidies toward adaptive, real-time regulation. A dynamic reward-punishment mechanism that automatically adjusts penalties with supervision intensity, and rewards with measured performance, can accelerate the convergence of manufacturers and consumers to desirable recycling behaviors by about 60% in evolutionary speed. The government should also prioritize setting an effective penalty threshold that is sufficiently high to make passive recycling more costly than active recycling. At the same time, because manufacturer technology level and consumer environmental consciousness are key internal drivers, government support programs should co-finance recycling-technology R&D and run public campaigns that raise environmental awareness.
For high-voltage battery recycling, governments must also define and enforce data standards and interoperability rules for blockchain platforms. A public blockchain infrastructure, jointly developed with manufacturers, can ease the private cost burden and accelerate nationwide adoption. Table 9 summarizes a set of recommended policy combinations.
| Policy Dimension | Static/Current Approach | Dynamic/Recommended Approach |
|---|---|---|
| Penalty design | Fixed fines | Penalty tied to supervision probability; threshold-based enforcement |
| Reward design | Fixed subsidies | Rewards proportional to actual recycling volume or tech level |
| Technology | Manufacturer internal | Public-private R&D consortium; tax credits for recycling-tech investment |
| Blockchain | Firm-specific pilots | National interoperable blockchain for battery tracing with standard APIs |
| Consumer engagement | Passive information disclosure | Interactive trust-building campaigns; visible traceability QR codes |
6.2 Implications for Enterprises
Enterprises should select recycling modes based on their objectives. If the primary goal is total supply chain profit, alliance recycling (e.g., a joint venture between the high-voltage battery maker and the electric vehicle maker) is the best structure. If the goal is to maximize recovery quantity and comply with stricter future producer-responsibility regulations, mixed-channel recycling creates healthy competition that effectively draws retired batteries back from informal channels. I recommend the following strategic actions:
- Negotiate a blockchain cost-sharing contract before committing to technology investment. My analysis shows that any \(t \in (0,1)\) yields profit improvements over no-blockchain scenarios, so the main concern is the bargaining over surplus allocation, not the feasibility of cooperation.
- Integrate blockchain traceability with consumer-facing communication. Publish battery health data, recycling pricing formulas, and subsequent echelon utilization information in an accessible format. This raises consumer trust \(k\), which is the most powerful internal amplifier of the technology’s economic benefit.
- Build flexible pricing algorithms that exploit the fact that higher trust leads to lower recycling prices and higher retail prices. Blockchain-enabled firms can strategically lower recycling compensation while improving service transparency, thereby increasing both margin and recovery volumes.
7. Conclusion and Future Research
In this study, I have offered an integrated analytical perspective on two complementary levers for improving high-voltage battery recycling performance: dynamic government reward-punishment policies and blockchain-enabled information authentication. My tripartite evolutionary game shows that a DRS-like adaptive mechanism outperforms static instruments in evolutionary speed and resilience. My closed-loop supply chain analysis, spanning four recycling channels with and without blockchain, shows that alliance modes dominate in profit terms, mixed modes dominate in recycling intensity, and blockchain consistently improves both dimensions, yet its effect is strongly moderated by consumer trust.
These conclusions suggest that policy and technology should be deployed jointly. Dynamic policies give entities the motivation to recycle; blockchain provides the trusted data infrastructure that reduces transaction costs and enables informed participation. The combination forms an effective “institutional incentive + digital trust” governance path. Future research can extend my models by adding carbon taxes or cap-and-trade constraints, introducing a third-party recycler competing with formal channels, and empirically calibrating the trust coefficient using choice experiments or field evidence. I believe such extensions will enhance the practical accuracy of the results and provide further guidance for the global transition toward sustainable management of high-voltage batteries.