Knowledge sharing, heterophily, and social network dynamics

ABSTRACT

This study formulates a model where (i) players are characterized by a knowledge set that changes endogenously by communication and (ii) some players have homophily preferences, while others have heterophily preferences. The study thus demonstrates that heterophilous players bridge different components and extend networks in an early stage and, subsequently, homophilous players take the role of a network hub that maintains network ties. It also illustrates the long-run knowledge distribution. Further, the model is embedded with new structural components that illustrate the strength of weak ties and the small-world phenomenon.

KEYWORDS:

• Social networks
• knowledge sharing
• heterogeneous preferences
• network formation model

Disclosure statement

Authors declare no conflict of interest.

Notes

¹ As previously mentioned, we assume that players’ original knowledge is heterogeneous per se and is thus defined in the form of an $n$-dimensional vector. In this sense, the summing up of the elements of each vector, as shown above, may not follow the original concept of the model. Moreover, one common way to evaluate the social welfare of the system is to measure the sum of utilities. Nevertheless, we introduced the index $\bar{K}$ for convenience in evaluating the status of the system.

² The dynamic process to generate a network as shown in Figure 5b and its robustness are also confirmed by the dynamics of the standard deviation of the number of each link, which are obtained by $M$ runs of the Monte Carlo simulations. As time goes by (approximately $t>0.1\times {10}^4$), the standard deviation of the number of Hetero–Hetero links decreases gradually to approximately zero, which implies that regardless of runs, a heterophilous player acquires a certain number of links (i.e., no links in this case, as presented in Figure 5b shows those two types of states) with other heterophilous players. On the other hand, the standard deviation of the number of Homo–Homo links increases and stays almost constant (i.e. approximately three), which implies that in some runs, a homophilous player can connect densely with each other, while in other runs, she/he becomes isolated, as Figure 5b shows those two types of states.

³ In fact, with the values of parameters that we set for the simulation, communication costs exceed utility even for isolated players. However, the difference between cost and utility is larger for a member of a component, who therefore has a stronger willingness to reject communication.

⁴ We have found other results: as $\bar{c}$ becomes larger than 0.2, which was the value in the simulation above, the number of links decreases and, in the cases that $\bar{c}$ becomes larger than a specific level, a network is divided into small components and the number of isolated players increases. Such results are in line with those obtained in many other models.

⁵ Works of social capital include the distinction of bonding and bridging social capital (e.g., Granovetter, 1973). Both types of social capital are related with several parts of discussion in this section. For example, the characteristic of rural societies that we discuss in Subsection 5.1 may be interpreted in the context of bonding social capital that is sometimes associated with community closure and exclusiveness as well as strong ties. Moreover, it is often interpreted that the strength of weak ties that we discuss in Subsection 5.4 is attained by bridging social capital. Here we would emphasize again that one of the unique results of this study is that the bridging players are replaced in the process of network development. On the other hand, we should note that some literature highlight that the bonding and bridging are not mutually exclusive, and this distinction could fail to reflect the multidimensional nature of social capital (e.g., Engbers, Thompson, & Slaper, 2017). Careful examination on social capital within this model context is left for a future topic.

⁶ In the formation processes of the basic units, the two-Homo-and-one-Hetero clusters, are completed by homophilous players that form a third link to close a triangle.

Additional information

Funding

This work was partly supported by JSPS (Japan Society for the Promotion of Science) KAKENHI (grant nos. 16K06537 and 18K13845).