As a researcher focused on sustainable energy transitions, I explore how the best solar panel company can thrive through cooperative innovation under China’s dual carbon goals. The urgency to reduce emissions and address energy crises has propelled renewable energy systems to the forefront, with solar power playing a pivotal role. In this context, understanding the strategic interactions between photovoltaic enterprises and the government is crucial. This study employs an evolutionary game model, integrating the Hoteling framework, to analyze how factors like participation willingness, carbon emission reduction gains, and free-riding behaviors influence system stability. By simulating these dynamics, I aim to provide insights that guide the best solar panel company in fostering collaboration and achieving long-term sustainability without excessive reliance on subsidies.
The dual carbon targets—carbon peaking and carbon neutrality—have reshaped China’s energy landscape, emphasizing the need for clean energy adoption. Photovoltaic enterprises, as key players, must navigate innovation strategies that balance individual and collective benefits. My analysis begins with the Hoteling model, which conceptualizes market competition between two solar panel companies. Assume a linear city of length 1, where consumers are uniformly distributed between 0 and 1. The best solar panel company A is located at one end, and company B at the other. A consumer at position m incurs a travel cost t per unit distance. The utility for a consumer choosing company i is given by $U – P_i – t \cdot d_i$, where $P_i$ is the electricity price and $d_i$ is the distance. For companies A and B, the demand functions are derived as:
$$D_A = \frac{P_B – P_A + t}{2t}, \quad D_B = \frac{P_A – P_B + t}{2t}$$
These demand functions form the basis for calculating发电收益 (power generation revenue). For instance, the发电收益 for company A is $\pi_{A1} = D_A (P_A – c_A)$, where $c_A$ is the generation cost. Additionally, carbon emission reduction gains are incorporated through China Certified Emission Reduction (CCER) mechanisms. The carbon reduction revenue for company A is $M_A = D_A \theta P_C$, where $\theta$ is the grid emission factor and $P_C$ is the CCER price. Thus, the total revenue for company A becomes:
$$\pi_A = \pi_{A1} + M_A = \frac{P_B – P_A + t}{2t} (P_A – c_A + \theta P_C)$$
Similarly, for company B, $\pi_B = \frac{P_A – P_B + t}{2t} (P_B – c_B + \theta P_C)$. When both companies cooperate on innovation, they gain additional benefits: extra power generation revenue $P$ and carbon reduction revenue $M$. If the government provides subsidies, an additional gain $M_G$ is included. The cooperative benefits are distributed with a coefficient $\alpha$ for company A and $(1-\alpha)$ for company B. The government also gains a share $\beta$ of these benefits. However, if one company free-rides by opting for solo innovation while the other cooperates, the free-rider gains $G_i$, and the cooperating company experiences an increase in generation $D_{i1}$. This setup leads to a tripartite evolutionary game involving companies A, B, and the government, with strategies of cooperation/solo innovation and subsidy/no subsidy.
To model this, I define the probabilities: $x$ for company A cooperating, $y$ for company B cooperating, and $z$ for the government subsidizing. The replication dynamics equations are derived based on expected payoffs. For company A, the expected payoff for cooperation is:
$$U_{A1} = z \mu S + \pi_A + D_{A1}(P_A – c_A + \theta P_C) + y[\alpha(P + M + M_G) – D_{A1}(P_A – c_A + \theta P_C)]$$
For solo innovation, it is $U_{A2} = z \mu S + y G_A + \pi_A$. The average payoff is $\bar{U}_A = x U_{A1} + (1-x) U_{A2}$. The replication dynamic equation for company A is:
$$F(X) = \frac{dx}{dt} = x(1-x) \left\{ D_{A1}(P_A – c_A + \theta P_C) + y[\alpha(P + M + M_G) – D_{A1}(P_A – c_A + \theta P_C)] – y G_A \right\}$$
Similarly, for company B:
$$F(Y) = \frac{dy}{dt} = y(1-y) \left\{ D_{B1}(P_B – c_B + \theta P_C) + x[(1-\alpha)(P + M + M_G) – D_{B1}(P_B – c_B + \theta P_C)] – x G_B \right\}$$
For the government:
$$F(Z) = \frac{dz}{dt} = z(1-z) [x y \beta (P + M + M_G) + R_2 – S – C_G]$$
Here, $S$ is the subsidy, $C_G$ is government supervision cost, and $R_2$ is additional revenue from subsidizing. The system has eight equilibrium points, and stability analysis using Jacobian matrices reveals four scenarios where evolutionary stable strategies (ESS) emerge. For instance, if $\alpha(P + M + M_G) – G_A – D_{B1}(P_B – c_B + \theta P_C) + R_2 – S – C_G < 0$, the ESS is $(0,1,0)$, meaning company A solos, company B cooperates, and the government does not subsidize. This highlights the sensitivity of outcomes to parameters, guiding the best solar panel company in strategy formulation.
To simulate these dynamics, I assign parameter values based on industry data, as shown in Table 1. These values are illustrative and can be adjusted for different scenarios. The focus is on trends rather than exact figures, ensuring relevance for the best solar panel company seeking to optimize innovation partnerships.
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| $P_A$ | 0.4 | $\alpha$ | 0.5 |
| $P_B$ | 0.5 | $\beta$ | 0.2 |
| $c_A$ | 0.26 | $R_2$ | 60 |
| $c_B$ | 0.37 | $C_G$ | 30 |
| $\theta$ | 0.57 | $S$ | 60 |
| $P_C$ | 60 | $G_A$ | 35 |
| $P$ | 120 | $G_B$ | 40 |
| $M$ | 50 | $D_{A1}$ | 24 |
| $M_G$ | 30 | $D_{B1}$ | 24 |
Numerical simulations using MATLAB analyze how initial willingness, CCER price, profit distribution, and free-riding gains affect system evolution. First, varying initial willingness levels (e.g., 0.1, 0.2, 0.5, 0.9) for all parties shows that companies converge faster to cooperation as initial willingness increases, while the government is more sensitive, slowing its shift to no subsidy. This implies that the best solar panel company can accelerate collaboration by boosting initial engagement, but government policies should adapt dynamically. For example, if company A’s initial willingness rises, company B’s convergence to cooperation slows, and the government’s response time changes non-linearly. However, the final steady state remains unchanged, emphasizing the path dependence of innovation strategies.
Second, CCER price variations ($P_C = 20, 60, 100, 160$) reveal that higher prices encourage companies to cooperate faster, as carbon gains enhance overall收益. The government’s transition to no subsidy slows with rising $P_C$, indicating that carbon markets can partially replace subsidies. For the best solar panel company, this underscores the importance of engaging in carbon trading to sustain innovation without heavy reliance on government support. The system’s stability is not altered, but convergence speeds are affected, as summarized in Table 2.
| CCER Price ($P_C$) | Company A Cooperation Speed | Company B Cooperation Speed | Government Subsidy Reduction Speed |
|---|---|---|---|
| 20 | Slow | Slow | Fast |
| 60 | Moderate | Moderate | Moderate |
| 100 | Fast | Fast | Slow |
| 160 | Very Fast | Very Fast | Very Slow |
Third, the profit distribution coefficient $\alpha$ significantly influences cooperation. When $\alpha$ is in [0.1, 0.3], companies shift from solo to cooperative innovation; for $\alpha \geq 0.3$, cooperation becomes dominant. This threshold effect suggests that the best solar panel company should negotiate fair profit-sharing agreements to stabilize partnerships. Similarly, the government’s收益分配系数 $\beta$ affects its subsidy behavior: if $\beta \geq 0.5$, subsidies are more likely, as the government gains sufficiently from corporate innovation. This aligns with the idea that the best solar panel company can leverage government incentives when mutual benefits are clear.
Fourth, free-riding gains $G_i$ pose a risk to cooperation. For company A, if $G_A \leq 80$, cooperation is preferred; if $G_A > 80$, solo innovation becomes attractive. The same applies to company B with $G_B$. This threshold highlights the need for mechanisms to mitigate free-riding, such as contracts or monitoring, ensuring that the best solar panel company can maintain collaborative integrity. Excessive free-riding收益 destabilize innovation networks, urging companies to focus on long-term collective gains over short-term individual benefits.
In conclusion, my analysis demonstrates that the best solar panel company can achieve sustainable innovation through strategic cooperation, guided by evolutionary game insights. Key findings include: (1) Initial willingness accelerates cooperation but requires adaptive government policies; (2) CCER price hikes foster cooperation, reducing subsidy dependence; (3) Profit distribution must exceed a threshold to incentivize collaboration; and (4) Free-riding gains must be controlled to prevent instability. For practitioners, I recommend that the best solar panel company engage in market-driven partnerships, utilize carbon trading, and advocate for balanced government policies that phase out subsidies as cooperation matures. This approach not only supports dual carbon goals but also positions the best solar panel company as a leader in the renewable energy transition.