# Study on Low-Carbon Technology Innovation Strategies through Government–University–Enterprise Cooperation under Carbon Trading Policy

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Basic Assumptions of the Model

**Hypothesis**

**1.**

**Hypothesis**

**2.**

**Hypothesis**

**3.**

**Hypothesis**

**4.**

**Hypothesis**

**5.**

## 4. Model Development and Solution

#### 4.1. Costless Decentralised Decision Making (Nash Non-Cooperative Game)

**Proposition**

**1.**

- (1)
- The optimal decision for each university, the traditional enterprise, and the local government are:

- (2)
- The optimal trajectory of the optimal LCT stock for this system is ${x}^{N}\left(t\right)=\frac{{A}^{N}}{\delta}+\left({x}_{0}-\frac{{A}^{N}}{\delta}\right){e}^{-\delta t}$, where:

- (3)
- The respective profit optimality functions of universities, traditional enterprises, and local government are ${V}_{1}^{N}={k}_{1}^{N}{x}^{N}+{b}_{1}^{N}{V}_{2}^{N}={k}_{2}^{N}{x}^{N}+{b}_{2}^{N}{V}_{3}^{N}={k}_{3}^{N}{x}^{N}+{b}_{3}^{N}$, where${k}_{1}^{N}=\frac{{\omega}_{1}\left(\theta +\tau {P}_{cq}\right)}{\rho +\delta},{k}_{2}^{N}=\frac{{\omega}_{2}\left(\theta +\tau {P}_{cq}\right)}{\rho +\delta},{k}_{3}^{N}=\frac{\left(1-{\omega}_{1}-{\omega}_{2}\right)\left(\theta +\tau {P}_{cq}\right)}{\rho +\delta}$,

**Proof.**

#### 4.2. Stackelberg Master–Slave Game

**Proposition**

**2.**

- (1)
- The optimal decision and cost-sharing ratio for each university, traditional enterprise, and local government are:

- (2)
- The optimal trajectory of the optimal LCT stock for this system is ${x}^{Y}\left(t\right)=\frac{{A}^{Y}}{\delta}+\left({x}_{0}-\frac{{A}^{Y}}{\delta}\right){e}^{-\delta t}$, where

- (3)
- The respective profit optimal value functions of universities, traditional enterprises, and local government are ${V}_{1}^{Y}={k}_{1}^{Y}{x}^{Y}+{b}_{1}^{Y}{V}_{2}^{Y}={k}_{2}^{Y}{x}^{Y}+{b}_{2}^{Y}{V}_{3}^{Y}={k}_{3}^{Y}{x}^{Y}+{b}_{3}^{Y}$, where${k}_{1}^{Y}=\frac{{\omega}_{1}\left(\theta +\tau {P}_{cq}\right)}{\rho +\delta},{k}_{2}^{Y}=\frac{{\omega}_{2}\left(\theta +\tau {P}_{cq}\right)}{\rho +\delta},{k}_{3}^{Y}=\frac{\left(1-{\omega}_{1}-{\omega}_{2}\right)\left(\theta +\tau {P}_{cq}\right)}{\rho +\delta}$:

**Proof.**

#### 4.3. Centralised Decision Making (Collaborative, Cooperative Game)

**Proposition**

**3.**

- (1)
- The optimal decision of each university, the traditional enterprise. and the local government is:$${E}_{1}^{C}=\frac{{\epsilon}_{1}\left(\rho +\delta \right)+{r}_{1}\left(\theta +\tau {P}_{cq}\right)}{{\eta}_{1}\left(\rho +\delta \right)}{E}_{2}^{C}=\frac{{\epsilon}_{2}\left(\rho +\delta \right)+{r}_{2}\left(\theta +\tau {P}_{cq}\right)}{{\eta}_{2}\left(\rho +\delta \right)}{E}_{3}^{C}=\frac{{\epsilon}_{3}\left(\rho +\delta \right)+{r}_{3}\left(\theta +\tau {P}_{cq}\right)}{{\eta}_{3}\left(\rho +\delta \right)}$$
- (2)
- The optimal trajectory of the optimal stock of LCT for this system is ${x}^{C}\left(t\right)=\frac{{A}^{C}}{\delta}+\left({x}_{0}-\frac{{A}^{C}}{\delta}\right){e}^{-\delta t}$where${A}^{C}=\frac{{r}_{1}[{\epsilon}_{1}\left(\rho +\delta \right)+{r}_{1}\left(\theta +\tau {P}_{cq}\right)]}{{\eta}_{1}\left(\rho +\delta \right)}+\frac{{r}_{2}\left[{\epsilon}_{2}\left(\rho +\delta \right)+{r}_{2}\left(\theta +\tau {P}_{cq}\right)\right]}{{\eta}_{2}\left(\rho +\delta \right)}+\frac{{r}_{3}\left[{\epsilon}_{3}\left(\rho +\delta \right)+{r}_{3}\left(\theta +\tau {P}_{cq}\right)\right]}{{\eta}_{3}\left(\rho +\delta \right)}$.
- (3)
- The respective profit optimality functions of universities, traditional firms, and local government are ${V}^{C}={k}^{C}{x}^{C}+{b}^{C}$, where ${k}^{C}=\frac{\theta +\tau {P}_{cq}}{\rho +\delta}$,${b}^{C}=\frac{\mu {P}_{cq}}{\rho}+\frac{{\left[{\epsilon}_{1}\left(\rho +\delta \right)+{r}_{1}\left(\theta +\tau {P}_{cq}\right)\right]}^{2}}{2\rho {\eta}_{1}{\left(\rho +\delta \right)}^{2}}+\frac{{\left[{\epsilon}_{2}\left(\rho +\delta \right)+{r}_{2}\left(\theta +\tau {P}_{cq}\right)\right]}^{2}}{2\rho {\eta}_{2}{\left(\rho +\delta \right)}^{2}}+\frac{{\left[{\epsilon}_{3}\left(\rho +\delta \right)+{r}_{3}\left(\theta +\tau {P}_{cq}\right)\right]}^{2}}{2\rho {\eta}_{3}{\left(\rho +\delta \right)}^{2}}$.

**Proof.**

#### 4.4. Comparative Analysis

**Proposition**

**4.**

- (1)
- The best effort level of universities ${E}_{1}^{C}\ge {E}_{1}^{Y}>{E}_{1}^{N}$;
- (2)
- The best effort level of traditional enterprises ${E}_{2}^{C}\ge {E}_{2}^{Y}>{E}_{2}^{N}$;
- (3)
- The best effort level of local government ${E}_{3}^{C}\ge {E}_{3}^{Y}={E}_{3}^{N}$;
- (4)
- The optimal subsidy coefficient of local government to universities and traditional enterprises is ${\beta}_{1}=\frac{{E}_{1}^{Y}-{E}_{1}^{N}}{{E}_{1}^{Y}}$, ${\beta}_{2}=\frac{{E}_{2}^{Y}-{E}_{2}^{N}}{{E}_{2}^{Y}}$.

**Proof.**

**Proof.**

**Proof.**

**Inference**

**1.**

**Inference**

**2.**

**Proposition**

**5.**

**Proof.**

**Inference**

**3.**

**Proposition**

**6.**

- (1)
- The best interests of colleges and universities${V}_{1}^{Y}>{V}_{1}^{N}$;
- (2)
- The best interests of traditional enterprises ${V}_{2}^{Y}>{V}_{2}^{N}$;
- (3)
- The best interest of local government${V}_{3}^{Y}>{V}_{3}^{N}$;
- (4)
- Comparison of the optimal total benefit of the tripartite cooperation low-carbon system ${V}^{C}>{V}^{Y}>{V}^{N}$.

**Proof.**

**Inference**

**4.**

**Inference**

**5.**

## 5. Simulation Analysis

#### 5.1. Comprehensive Analysis

#### 5.2. Sensitivity Analysis in Decentralized Decision Making

#### 5.3. Sensitivity Analysis in Centralized Decision Making

## 6. Research Findings and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Schematic diagram of LCT cooperation innovation between government, schools, and enterprises.

**Figure 2.**Comparison of regional total low carbon innovation technology stocks under different decision scenarios.

**Figure 5.**${P}_{cq}-{\omega}_{2}$ impact on the extent of government efforts to govern the environment.

**Figure 6.**${P}_{cq}-{\omega}_{2}$ impact on the extent of low carbon innovation efforts by traditional firms.

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## Share and Cite

**MDPI and ACS Style**

Wang, J.; Song, Y.; Li, M.; Yuan, C.; Guo, F.
Study on Low-Carbon Technology Innovation Strategies through Government–University–Enterprise Cooperation under Carbon Trading Policy. *Sustainability* **2022**, *14*, 9381.
https://doi.org/10.3390/su14159381

**AMA Style**

Wang J, Song Y, Li M, Yuan C, Guo F.
Study on Low-Carbon Technology Innovation Strategies through Government–University–Enterprise Cooperation under Carbon Trading Policy. *Sustainability*. 2022; 14(15):9381.
https://doi.org/10.3390/su14159381

**Chicago/Turabian Style**

Wang, Junwu, Yinghui Song, Mao Li, Cong Yuan, and Feng Guo.
2022. "Study on Low-Carbon Technology Innovation Strategies through Government–University–Enterprise Cooperation under Carbon Trading Policy" *Sustainability* 14, no. 15: 9381.
https://doi.org/10.3390/su14159381