Industrial cluster theory has important guiding significance for regional industrial development and industrial agglomeration advantages. Cooperation among enterprises is the corner stone of industrial clusters. The purpose of the paper is to explore the effects of cluster informal contracts on cluster enterprises and the behavior of external partners. Based on the dynamic evolutionary game theory, this paper constructs a model, which incorporates several main factors influencing the innovative cooperation among local and external cluster enterprises. By calculating the replicator dynamics equations and analyzing the evolutionary stable strategies, this paper discusses the evolution process of cooperation strategies of enterprises in different situation. Furthermore, by using MATLAB software to simulate the model, this paper verifies the accuracy and reliability of the game model. Results show that, in addition to the formal market contract, effective implementations of cluster informal contracts can reduce opportunistic behavior in innovative cooperation among internal and external enterprises. Meanwhile, we should pay attention to strengthen the external innovative cooperation, increase severity of penalties, enhance the credit network externality, and avoid the relevant risks. The paper enriches our understanding about how informal contracts can help promote and cultivate good cooperative order in innovative cooperation of clusters.
Nowadays, the development issues about industrial cluster is becoming increasingly compelling, as cluster development is still one of the most effective ways to increase competitiveness [
Industrial clusters are a practical example of a synthesis of organization and complexity. One striking feature of industrial clusters is their ability to enable efficient production organization with high levels of space diversity, time variability, and uncertainty in the field of possibilities [
The main point of the interactive cooperation is to obtain higher profits, enhance the competitive advantage, and ultimately ensure long-term survival and development. Innovation is an effective way for enterprises to increase profits. Cooperative innovation model has become increasingly prevalent, and it is a suitable model for further innovation. SMEs are in great need for innovative cooperation as they have limited resources to increase productivity and fuel creativity. However, as mentioned above, the cluster itself has a very important feature with complex adaptive characteristics [
Cooperation can reduce transaction costs and share knowledge, but it also involves risks related to opportunistic behavior and lack of trust [
Industrial clusters are widely recognized as an important way of promoting regional innovation, entrepreneurship, and high-tech industries [
In recent years, there has been an improvement in the understanding of industrial clusters [
The paper is organized as follows. In Section
The model variables were proposed based on the above description about characteristics of cluster informal contracts and innovative cooperation behavior in industrial cluster. In addition, it also puts forward the hypothesis for the evolutionary game of innovative cooperation in industrial cluster.
When the informal contracts in the industrial cluster are valid, the overall benefit of an industrial cluster is
Payoff matrix of two game sides.
Industrial Cluster | |||
---|---|---|---|
Valid Informal Contracts | Invalid Informal Contracts | ||
External | Honest Behavior | | |
Enterprises | Opportunistic | | |
Supposing that the probability when the cluster chooses strategy “valid informal contracts” is x, the probability to choose strategy “invalid informal contracts” is 1 –x; supposing that the probability when external enterprises choose strategy “honest behavior” is y, the probability to choose strategy “opportunistic behavior” is 1 – y, of which 0<x<1 and 0<y<1. The value of x and y changes in constant imitating and learning process of external enterprise and industrial cluster, but the initial value is established.
Expected benefit of industrial cluster when it chooses strategy “valid informal contracts”:
The replicator dynamic evolutionary game model describes the progressive process of the transformation of both sides’ favorable strategy. Both sides are not adjusting their strategies at the same time. One side needs to decide its strategy by considering the other side’s strategy and the payoff the strategy brings. Hence, it is a learning process. The specific calculation process is as follows [
Replicator dynamic equation of industrial cluster and external enterprise is, respectively,
In order to obtain the ESS of this evolutionary game, get a stable point of the replication dynamics equation, the premise, and stable points x
The stability of the evolution system can be studied by using the local stability of the Jacobian matrix by the proposed method of Friedman and Fung [
Local stability analysis of the evolution system.
Stable Points | | | Local Stability |
---|---|---|---|
| + | - | ESS |
| - | Uncertainty | Saddle point |
| + | + | Unstable |
| - | Uncertainty | Saddle point |
In this case, when the benefit the informal contracts bring to the industrial cluster is less than the difference between the maintenance cost of informal contracts and the loss of invalidity, and the expected punishment for the opportunistic behavior is less than the opportunistic benefits, the informal contracts will be completely invalid, and the external enterprise and cluster enterprise will also exhibit opportunistic behavior; this will be the serious impediment to the development of industrial clusters.
Local stability analysis of the evolution system.
Stable Points | | | Local Stability |
---|---|---|---|
| - | Uncertainty | Saddle point |
| - | Uncertainty | Saddle point |
| - | Uncertainty | Saddle point |
| - | Uncertainty | Saddle point |
The Table
Local stability analysis of the evolution system.
Stable Points | | | Local Stability |
---|---|---|---|
| - | Uncertainty | Saddle point |
| + | + | Unstable |
| - | Uncertainty | Saddle point |
| + | - | |
Case 3 shows that when the informal contracts bring more benefit to the industrial cluster than its maintenance cost, and the expected punishment of the opportunistic behavior of external cluster is less than the opportunistic benefits, the development of the industrial cluster presents a virtuous cycle: on one hand, industrial clusters informal contracts can be well maintained and implemented; on the other hand, the external enterprises and cluster enterprises can have an honest cooperative relationship.
Local stability analysis of the evolution system.
Stable Points | | | Local Stability |
---|---|---|---|
| - | Uncertainty | Saddle point |
| + | - | ESS |
| + | + | Unstable |
| - | Uncertainty | Saddle point |
Local stability analysis of the evolution system.
Stable Points | | | Local Stability |
---|---|---|---|
| + | + | Unstable |
| + | - | ESS |
| - | Uncertainty | Saddle point |
| - | Uncertainty | Saddle point |
In cases 4 and 5, it can be found that when the benefits of informal contracts are less than their maintenance cost, and the expected punishment of the opportunistic behavior is greater than the opportunistic benefits, even if the informal contracts are invalid, the external enterprises will be genuine in innovative cooperation and not be deceitful.
Local stability analysis of the evolution system.
Stable Points | | | Local Stability |
---|---|---|---|
| + | + | Unstable |
| - | Uncertainty | Saddle point |
| - | Uncertainty | Saddle point |
| + | - | ESS |
When the benefits that informal contracts can bring to the industrial cluster are more than the maintenance cost, and expected punishment of the opportunistic behavior is greater than the opportunistic benefits, the informal contracts can be sustainably developed in the industry cluster, and honest behavior in the innovative cooperation can be also increased. Similar to situation 3, at this time, the industrial cluster will also show a good momentum of development; the innovative cooperation can be operated under the order of informal contracts.
Based on the evolutionary game in Section
The following can be seen from the simulated analysis results:
Innovative cooperation evolutionary game results of case 1 (
Stochastic game result of cluster enterprises
Stochastic game result of external enterprises
Innovative cooperation evolutionary game results of case 2 (
Stochastic game result of cluster enterprises
Stochastic game result of external enterprises
Innovative cooperation evolutionary game results of case 3 (
Stochastic game result of cluster enterprises
Stochastic game result of external enterprises
Innovative cooperation evolutionary game results of cases 4 and 5 (
Stochastic game result of cluster enterprises
Stochastic game result of external enterprises
Innovative cooperation evolutionary game results of case 6 (
Stochastic game result of cluster enterprises
Stochastic game result of external enterprises
The empirical evidence from clusters in Jinjiang City can also demonstrate the impact of informal contracts. We use Jinjiang industrial cluster as a typical case because it is famous for its listed companies, which has the highest number of all the counties in China, and represents an upgrading process from made to innovation. Although Jinjiang maintains a high economic growth rate, Jinjiang’s manufacturing clusters have traditionally been mainly labor-intensive, and these industries have been facing fierce competition from domestic and overseas markets. However, local industrial clusters, especially the footwear and apparel industries, have achieved significant industrial upgrades in global competition [
In Jinjiang cluster, there exist many kinds of informal organization, like Jinjiang textile association, Jinjiang equipment manufacturing industry association, Jinjiang footwear industry association, and so on; the mission of these informal organization is to gather resources, build platform for resource sharing, complementary advantages, as well as exchange, cooperation, and development and thus formed the informal contract. Jinjiang’s informal contracts restrict cluster enterprises’ behavior mainly through the way of collective sanction. Informal organizations usually formulate relevant industry norms to punish and exclude behaviors that violate the overall interests such as cluster norms and values, including gossip, rumors, and ostracism. [
Industrial clusters have generated conducive scenarios to coopetition to compete at the global level [
First, innovative cooperation is a way of strategizing for enterprises to maintain market share. It means establishing long-term relations of innovation between economically and legally independent firms [
Second, the informal contracts of industrial cluster can positively restrain the opportunistic cooperative behavior of cluster enterprises. We can observe the underlying factors relevant to the causal logic and dynamic interaction between cluster informal contracts and enterprises innovative cooperation behavior. From the game results, it can be seen that there are few opportunistic behaviors between the cluster enterprises and external enterprises in valid cluster informal contracts. The current research has not paid enough attention to the informal governance management, such as tradition and local culture, including the reputation and trust of informal institutions. However, in reality, we can see that large amount of enterprises opportunistic behavior will cause great losses to their partners; thus, the cooperation without governance is not reliable. In the practice of cluster enterprises’ cooperation, valid informal arrangements to regulate the cooperative behaviors of enterprises are of vital importance. Therefore, with the evolution of these clusters, the participation of cluster informal contracts will restrict the generation of opportunistic behavior of enterprises.
Third, when industrial clusters expand their scope of cooperation, the industrial enterprises should also pay attention to avoid the relevant risks. The combination of external and internal sources of knowledge can enhance the success of innovation [
The data used to support the findings of this study are included within the article.
The authors declare that they have no conflicts of interest.
This work was financially supported by the Chinese National Natural Science Foundation of China (71403052 and 71403055) and the Chinese National Social Science Foundation of China (15FGL005).