Industry clusters consist of firms from the same industry featured with geographical proximity. Industry agglomeration could enhance regional competitiveness through significant exaltation of land leases, employment rates, investment, and taxation. In view of the concernful role of industry clusters to the economy, the dynamic process of how a small number of firms gradually expand into a large-scale cluster network has been a critical issue. Only by fully finding out the expansion mechanism of the industry clusters, could local government manage them more efficiently. In this way, firms could also make better entry decisions based on the expansion mechanism. In the first paper, we partition the knowledge stock of each firm candidate into two components: homogeneous knowledge and heterogeneous knowledge. Based on the knowledge substitution rate, a dynamic allocation algorithm is also constructed to calculate the expected reward and simulate the entry process for each new entrant. In addition, we also study the influence of industry cluster's initial capital volume, local government's preference for knowledge composition, firm candidate's capital volume as well as entry order on the entry decision of new entrants and expansion progress of the industry cluster. Simulation results indicate that no matter how industry cluster's initial capital volume and local government's preference for knowledge composition, when the firm candidate has low capital with low heterogeneous knowledge, the success rate of early entry is higher than late entry; when the firm candidate has low capital with high heterogeneous knowledge, the success rate of late entry is higher than early entry; when the firm candidate has high capital, regardless of the composition of knowledge, the success rate of early entry and late entry are similar. Besides, firms with low heterogeneous knowledge are more likely to enter successfully. However, when an industry cluster's initial capital volume is low, regardless of what the local government's preference for knowledge composition is, entry is no recommended if firm candidate has high capital volume with high heterogeneous knowledge or low capital volume with low heterogeneous knowledge.

In the context of carbon emission reduction, the dynamic game between local governments' supervision of industry clusters and the carbon reduction methods of firms also needs to be studied. In the second paper, we propose the concept of green innovation rate to calculate the proactive carbon abatement cost for each firm. At the same time, we also introduce the local governments' accounting coefficient to calculate the accounting abatement cost. Then, the pure strategy, mixed strategy and dynamic equilibrium solution of the government-enterprise game are calculated. Simulation results indicate that when the carbon quota is greater than the real carbon emission, firms always choose to disclose. Regardless of accounting coefficients, local government choose to supervise if administration expense is no more than the expense of total carbon elimination in the atmosphere plus the penalty. When the carbon quota is less than the real carbon emission, if the accounting coefficient is small enough, the enterprise will not disclose carbon information. And local government choose to supervise if administration expense is no more than the accounting expense of carbon elimination in the atmosphere plus the reward. If the accounting coefficient deems as over emitting, the difference between accounting expense of carbon purchase and the least expense of proactive carbon abatement need to be low enough to keep the firm with the stable state of no carbon disclosure. In the third paper, we divide the topology of industry cluster into polarized and non-polarized mode, and knowledge structure embedded in the cluster network into balanced and unbalanced type. Next, we explore which kind of network structure and knowledge distribution is more conducive to carbon abatement cooperation and carbon disclosure behavior. Simulation results show that carbon abatement cooperation could significantly improve the carbon disclosure level of the cluster compared with non-cooperation. Both non-polarized network with balanced knowledge distribution and polarized network with unbalanced knowledge distribution are not conducive to reducing the cost for carbon abatement cooperation. Policy recommendations for more efficient carbon management of industry cluster by local government are also given in this paper.