The sharing economy is a new economic model that can promote the optimal allocation of resources. Distributed energy sharing in the industrial cluster is of great significance for cluster enterprises to improve energy utilization efficiency and reduce carbon emissions. In this paper, we establish a differential game model for energy sharing in the industrial cluster under the cap-and-trade mechanism analyze the equilibrium strategies of core and supporting enterprises in the industrial cluster under three different decision scenarios. We then conduct a comparative analysis of the results, and the effect of the carbon cap and carbon trading prices on energy sharing in the industrial cluster is discussed in detail. Finally, the results of the theoretical analysis were verified through numerical simulations. The conclusions are as follows: (1) The energy sharing synergy, profit for both parties, and total system profit are the highest under the centralized decision, the Stackelberg game is better than the decentralized decision, and the cost-sharing contract can achieve the overall coordination of interests; (2) A higher carbon trading price can increase the low-carbon level of energy consumption, but interestingly, when the carbon cap is below a certain limit, the increase in carbon trading price within a certain time and interval will lead to a decrease in profits for both parties and total system profit; (3) In the Stackelberg game scenario where cost-sharing contracts are introduced, the cost-sharing ratio of core enterprises will increase as the proportion of benefits to core enterprises increases and government subsidies to supporting enterprises decrease.

Distributed energy sharing is an important means for enterprises to improve energy efficiency and reduce carbon emissions. However, the uncertainty of benefits under the carbon tax policy triggers the disappointment aversion behavior of decision makers, which has an important impact on the energy sharing decision of industrial clusters. This paper adopts the differential game approach to study the dynamic coordination problem of distributed energy sharing in industrial clusters, explores the optimal equilibrium strategies under different decision-making models, analyzes the impacts of carbon tax rate and disappointment aversion behavior on decision-making, and finally conducts numerical simulations. The results show that the equilibrium results of centralized decision-making are better than those of decentralized decision-making, and the cost-sharing contract can achieve the coordination of decentralized decision-making. The higher the degree of disappointment aversion of industrial cluster members, the lower the motivation of energy sharing. Increasing the carbon tax rate is conducive to improving the energy low carbon level and energy sharing synergy effect of enterprises. However, when the initial carbon emissions of enterprises are high, it will lead to a decline in their profits. Therefore, the government should choose an appropriate carbon tax rate according to the initial carbon emissions of enterprises.

In order to study how the production network, energy network, and carbon trading network interact with each other in the process of distributed energy sharing in industrial parks under the carbon emissions trading mechanism, this paper constructs a supernetwork model of distributed energy sharing in industrial parks by using variational inequality, analyzes the behavioral patterns of each participant in the pursuit of their own interests and their impact on the equilibrium state of the network, and obtains the conditions for the network to reach an equilibrium state. Then, the projection correction algorithm is applied to solve the model in equilibrium, and the optimal decisions of product trading volume, distributed energy low carbon level, and carbon trading are obtained. Finally, through numerical examples, the influence of the carbon cap and carbon trading price on the network equilibrium decision is analyzed. The results show that the government’s elevation of the carbon emission cap for enterprises will reduce the enthusiasm for distributed energy sharing in industrial parks and expand the polarization of enterprise profits. A higher carbon trading price will increase the carbon trading cost of enterprises, which has a negative impact on distributed energy sharing in industrial parks.

Against the background of carbon neutrality, the government’s carbon regulations have had a profound impact on the distributed energy sharing behavior of industrial parks. To deeply explore the interactive relationship between distributed energy sharing in industrial parks and government regulation, this paper constructs a three-party evolutionary game model composed of the government, core enterprises and supporting enterprises; endogenizes government behavior; and integrates inter-enterprise contractual mechanisms into the evolutionary framework. By establishing a revenue payment matrix and a replication dynamic equation, the stability conditions and system evolution paths of the strategy choices of each subject are analyzed, and numerical simulations are conducted. The results show that there are multiple evolutionary stable equilibria in the system, among which the equilibrium where core enterprises actively share, supporting enterprises actively share, and the government actively regulates carbon is the ideal state. Cost-sharing contracts and cooperative penalty contracts play a significant role in promoting the participation of supporting enterprises in sharing and curbing “free-riding” behavior, respectively. The changes in government subsidy rates and carbon tax rates have a crucial impact on the evolution of corporate strategies. Quantitatively, the carbon tax rate exhibits a threshold effect; enterprises shift to positive energy sharing when the tax rate exceeds 0.8, while a subsidy rate above 0.4 leads the government to withdraw from regulation. This indicates that a reasonable design of carbon regulations can help achieve coordinated energy emission reduction between the government and enterprises. The findings provide theoretical support for optimizing carbon regulations and designing cooperation strategies.

In order to study how the production network, energy network and carbon trading network interact with each other in the process of distributed energy sharing in industrial parks under the carbon emissions trading mechanism, this paper constructs a supernetwork model of distributed energy sharing in industrial parks by using variational inequality, analyzes the behavioral patterns of each participant in the pursuit of their own interests and their impact on the equilibrium state of the network, and obtains the conditions for the network to reach an equilibrium state. Then, the projection correction algorithm is applied to solve the model in equilibrium, and the optimal decisions of product trading volume, distributed energy low carbon level and carbon trading are obtained. Finally, through numerical examples, the influence of carbon cap and carbon trading price on the network equilibrium decision is analyzed. The results show that the government's elevation of carbon emission cap for enterprises will reduce the enthusiasm for distributed energy sharing in industrial parks and expand the polarization of enterprise profits. Higher carbon trading price will increase the carbon trading cost of enterprises, which has a negative impact on distributed energy sharing in industrial parks.