Friendship Networks

This paper develops a model of social networks different from those presented in the recent literature. In contrast to existing models, the level of investment in link formation is a continuous decision variable, and links form stochastically rather than deterministically, with the probability depending on the noncooperative investment choices of both parties. Since the network structure is then stochastic rather than deterministic, the actual pattern of links cannot be specified, as in previous models, with the analysis focusing instead on which links are most likely to form. This alternate approach leads to a much simpler mathematical structure than in previous work. The analysis, which is couched in the context of friendship networks, shows that individual investment in friendship formation is too low. In addition, the analysis shows that, in an asymmetric setting where one individual has personal magnetism or a broad group of acquaintances, friendship links involving this attractive agent are most likely to form.