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The influence of τ on the stability of the system; (a, c, d) bifurcation diagrams; (b) the largest Lyapunov exponent diagrams. (a) a=5,α=0.6. (b) a=5,α=0.6. (c) a=5,α=0.65. (d) a=4,α=0.6.
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Taking the carbon emissions per unit product as the standard to measure the low-carbon technology level of the enterprise, this article analyzed how the technology supplier enterprises realize low-carbon production and achieve a win-win situation for both supply and demand through technology sharing through technology research and development. Base...
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... Furthermore, as low-carbon technology advances and the cost of innovation decreases, it is expected that the level of lowcarbon innovation among manufacturing companies will naturally increase. Thus, this study emphasizes the importance of investing in and promoting the advancement of low-carbon technology [54]. (2) This study examines the impact of government low-carbon subsidies on the level of low-carbon innovation achieved by manufacturing companies. ...
Low carbon has become a highly relevant topic in today’s society, particularly for manufacturing enterprises. To gain insight into how manufacturing enterprises embedded in the industrial internet platform make decisions regarding low-carbon technology innovation, this article examines the service quality of the platform, the low-carbon preferences of the manufacturing enterprises, and government subsidy factors. A platform ecological system game model, comprised of a single manufacturing enterprise and an industrial internet platform, is then established. The results indicate that, under the model’s assumptions, the decarbonization of production can only occur when the cost of low-carbon innovation is below a specific threshold. Decentralized decision making is more effective in promoting low-carbon innovation by the manufacturing enterprises when the cost of low-carbon technology innovation is low. The greater the service quality of the industrial internet platform, the stronger the positive influence of the low-carbon preferences of users and government subsidies on the low-carbon innovation level of the manufacturing enterprises. This study offers useful decision-making advice for both the industrial internet platform and the manufacturing enterprises.
... This paper is committed to analyzing the game relationship between cooperative enterprises and clarifying the optimal pricing strategy and sharing technology matching level. The closest article to this paper is Si et al. (2020), but this paper further discusses how to eliminate the unstable state of the system through variable feedback method, Therefore, the main contributions of this paper are as follows: (1) this paper gives the optimal product pricing and capacity matching strategy for the competition and cooperation between two enterprises in the duopoly market. (2) Because the decision-makers are unwilling to change their decisions too quickly, this paper applies the differential game of delayed decision-making, fully considers the limited rational behaviour of the game subject and the long-term stability of the optimal solution, and defines the influence of delayed decision variables, price adjustment speed and decision weight on the stability of the game system. ...
... Combining complex dynamic systems in the supply chain to solve the game problems can be more effective. And existing research has discussed this dynamic model from different perspectives (Aust and Buscher 2012, Dasci and Guler 2019, Hong, Chu, and Zhang 2017, Dhanorkar, Kim, and Linderman 2019, Si et al. 2020. Combined with the issue of carbon emission reduction, Lou and Ma (2018) studied the price game and the complexity of carbon emission reduction in the supply chain of household appliances. ...
... It lacks market competitiveness, making it all the more necessary for the relevant national departments to formulate corresponding policies to promote the innovative development of LCT. Traditional enterprises, universities, and local governments face many issues [20]. Universities provide technology and solutions for enterprises in the process of LCT innovation. ...
... Substituting E 1 , E 2 , E 3 , β 1 , and β 2 into Equations (19), (20), and (22). It can be shown that the optimal linear function of x is the solution of the HJB equation, which is deformed as follows: ...
This paper focuses on developing low-carbon technology (LCT) innovation in traditional enterprises under carbon trading policies. The Hamilton–Jacobi–Berman equation quantitatively investigates the coordination mechanism and optimal strategy of LCT innovation systems in conventional industries. A three-way dynamic differential game model is constructed to analyze three cases: the Nash disequilibrium game; the Stackelberg master–slave game; and the cooperative game with the optimal effort of universities, traditional enterprises, and local government, the optimal benefits of the three parties, the region, and the regional LCT level. The results are as follows: (1) by changing the government subsidy factor, carbon trading price, and carbon trading tax rate, the optimal effort of universities and traditional enterprises can be significantly increased; (2) cost-sharing contracts do not change the level of effort of local government to manage the environment, and the use of cost-sharing agreements can change the status of action of universities and enterprises; (3) the optimal effort, optimal benefit, and total system benefit of the three parties and the level of LCT of the industry in the cooperative game are better than those in the non-cooperative case. The combined game achieves the Pareto optimum of the system. The study will contribute to both sustainable business development and environmental sustainability.
... Hou et al. (2020) used the differential game model to explore the dynamic emission reduction technology investment decision-making problem in the binary supply chain composed of manufacturers and retailers. Si et al. (2020) established a time-lag differential price game model, and analyzed the equilibrium strategy of price competition between technology supply and demand companies and the local asymptotic stability of the game system at the equilibrium point. Yin and Li (2018) used stochastic differential game to analyze the LC technology sharing problem in enterprise collaborative innovation. ...
Knowledge sharing (KS) in the green supply chain (GSC) is jointly determined by the KS efforts of suppliers and manufacturers. This study uses the differential game method to explore the dynamic strategy of KS and the benefits of emission reduction in the process of low carbon (LC) technology in the GSC. The optimal trajectory of the knowledge stock and emission reduction benefits of suppliers and manufacturers under different strategies are obtained. The validity of the model and the results are verified by numerical simulation analysis, and the sensitivity analysis of the main parameters in the case of collaborative sharing is carried out. The results show that in the case of centralized decision-making, the KS efforts of suppliers and manufacturers are the highest, and the knowledge stock and emission reduction benefits of GSC are also the best. The cost-sharing mechanism can realize the Pareto improvement of GSC’s knowledge stock and emission reduction benefits, but the cost-sharing mechanism can only increase the supplier’s KS effort level. In addition, this study found that the price of carbon trading and the rate of knowledge decay have a significant impact on KS. The study provides a theoretical basis for promoting KS in the GSC and LC technology innovation.
We investigate green technology unilateral licensing strategies between two competing manufacturers under carbon cap‐and‐trade policy. We construct Nash game models and compare the optimal strategies in the unilateral licensing situation with the no‐licensing situation. Comprehensive numerical experiments are taken to investigate the influence of some key parameters on optimal decisions. Our findings show that the green technology unilateral licensing strategy may benefit consumers; when green technology improvement is high, manufacturers tend to take the unilateral licensing strategy to obtain more profits; when initial unit carbon emission difference is moderate or large, the optimal strategy is that the manufacturer with lower level of green technology acts as the licensor; green technology unilateral licensing strategy may not necessarily reduce all manufacturers' total carbon emissions; only when green technology improvement is high, the unilateral licensing strategy is beneficial to environmental protection.
Due to information asymmetry, spatial distance will affect the associated credit cooperation relationship among enterprises. This paper employed the real‐world economic data to construct the entropy spatial interaction complex network model, which effectively depicts the associated credit risk among enterprises with the consideration of the influence of spatial distance and regional economic development level. Based on the calculation experiment and the Moran index, this paper reveals the spatial correlation of the credit risk contagion in each region and builds the theoretical model for spatial correlation of credit risk contagion. The research findings indicate the facts as follows. Firstly, enterprises in regions with close spatial proximity or higher level of economic development are more likely to attract enterprises from other regions for cooperation. For instance, due to the close distance between cities and more advanced economy, the eastern coastal region in China presents more intensive enterprise cooperation with other regions. Second, the analysis using the global Moran index reveals a significant spatial credit risk contagion pattern in credit defaults during 2020, attributed to the impact of the COVID‐19 pandemic. Third, the risk contagion effect of long‐distance associated credit is more complex. With the increase of the infection rate of long‐distance linked credit risk, the system will enter a chaotic state, hindering accurate long‐term prediction.
This study constructs a Cournot duopoly model that considers unilateral cross‐ownership and emission‐reduction technology sharing, compares the equilibrium results under different cases, explores the impacts of unilateral cross‐ownership and technology sharing, and analyzes the boundary conditions for realizing technology sharing. The results indicate that unilateral cross‐ownership has complex effects on the equilibrium results. Emission‐reduction technology plays a positive role in improving environmental and social welfare. Furthermore, the boundary conditions of technology sharing were found to be affected by the carbon tax, cost‐reduction effect of emission‐reduction technology, and cross‐ownership.
This study constructs a duopoly model considering technology R&D and technology sharing in carbon emission reduction, analyzes the market equilibrium results and the impacts of product differentiation, R&D costs and sharing charges in four cases, and analyzes firms' emission reduction technologies R&D decisions and technology sharing decisions by comparing. The results show that, in most cases, an increase in product differentiation can increase the two firms' profits. However, under price competition, the increase in product differentiation reduces Firm 2's profit; one firm's technology R&D decision is affected by the other, and it is also affected by R&D marginal cost and R&D fixed costs; sharing charges affect the achievement of technology-sharing agreements. When sharing charges are within a certain range, both firms achieve win-win results. Sharing emission reduction technology can improve social welfare and reduce environmental damage, which depends on sharing charges.
Based on the carbon emission policy and low-carbon capacity sharing, this paper studies the optimal product pricing and capacity matching strategies of competition and cooperation between two companies in a duopoly market. And the optimal strategies with or without capacity sharing are discussed. In addition, a differential game model based on carbon emission constraints, low-carbon capacity sharing, and delayed decision-making is established. We also study the evolution of duopoly enterprises from the initial state to the equilibrium state. Besides, the influence of delayed decision variables, price adjustment speed and decision weights on the stability of the game system is analyzed. The results show that the government can effectively intervene and guide the enterprises’ low-carbon production strategy through carbon emission restriction policy. Low-carbon capacity sharing is beneficial to both enterprises, and the demand side benefits more than the supply side. We discuss the impact of stable and unstable systems on enterprises’ decisions. When the system is stable, enterprises can converge from different initial game states to equilibrium states. The adoption of a delay strategy will not affect the tendency of convergence to the equilibrium. Furthermore, the system using the variable feedback control method is of higher stability.
