Friendship Networks

This paper develops a model of social networks di®erent from those presented in the recent literature. In contrast to existing models, the level of investment in link formation is a decision variable rather than being exogenous, and links form stochastically rather than deterministi-cally, with the probability depending on the noncooperative investment choices of both parties. Since network structure is then stochastic rather than deterministic, the actual pattern of links cannot be speci¯ed, 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, in an asym-metric setting where one individual has personal magnetism or a broad group of acquaintances, the analysis shows that friendship links involving this attractive agent are most likely to form