Friendship Networks

Abstract

Building upon a long tradition in sociology, economists have recently turned their attention to the analysis of social networks. The present paper adds to this emerging literature by proposing a different approach to social-network formation. As in the model of Jackson and Wolinsky (1996), formation of a link between two individuals requires two-sided investments in the present framework. But in contrast to their approach, where the required investments are exogenously specified and link formation is deterministic, the level of individual investment is a decision variable in the present model and link formation is stochastic. Thus, the probability that a link is formed between two individuals depends on the ``effort" both agents devote to creating the link. These effort levels are chosen noncooperatively via Nash behavior. As in the Jackson-Wolinsky model, indirect links are worth less than direct linkages to other individuals. But, in contrast to their assumption of a smooth benefit decay as link distance increases, the present framework assumes that benefits are zero when more than two links are involved. The model can be viewed as a portrayal of friendship networks. For two individuals to form a friendship, each must exert effort, which could involve inviting the other person to dinner at his house, arranging other types of social outings, or buying gifts on special occasions. Effort creates ``direct" friendships, and the combination of such links leads to ``indirect" friendships. Concretely, a particular individual may invite all of his direct friends to a dinner party at his house, and through socializing with one another, these people enjoy indirect friendships. The paper analyzes the effort externalities that are present in the model, showing the effort levels are universally too low. In addition, the analysis explores the effect of several types of asymmetries on the network structure, as reflected in effort levels and the probability of link formation.social networks