A signalling explanation for preferential attachment in the evolution of social networks

Abstract

The network theory developed by physicists has several critical drawbacks in characterizing the structure of social networks. First, they largely neglect considering the link cost and the link benefit that agents usually take into account in forming their links. Second, they view a social network as a consequence of unilateral decisions of agents, not of bilateral decisions of linking parties, although a link of an agent can be formed only after he obtains the consent of the other side. Third, there is no logical justification for the assumption of preferential attachment upon which their analysis heavily relies. In this paper, we provide several models that overcome the three drawbacks. By analyzing the models, we can explain preferential attachment as rational equilibrium behavior. The main idea is that people are not certain of the value that they can obtain from forming a link with someone. Based on this assumption, we will argue that a person has an incentive to form a link with another who has many links because the number of his links can convey some information about his value.