Identity and Fragmentation in Networks∗

This paper looks at the role of identity in the fragmentation of networks. Identity here is defined as the set of all exogenously given characteristics of an individual. I model how identity causes fragmentation by incorporating identity into a noncooperative network formation game. Players are allowed to choose how much weight/commitment they attach to different aspects of their identity as well as with whom to form links. The more similar in identity two players are, the lower are the costs of a link between them. The Nash network will not only divide society into groups based on identity, it will have layers of such divisions. Using the refinement of strictness, I get structures where highly committed players form center-sponsored stars and these stars are linked together by less committed players. Next, using insight gained from the theoretical analysis, I estimate which dimensions of identity are actually important in fragmentation given data on links, identities and commitment levels. For this, I construct an empirical strategy to see the impact of identity dimensions in sorting people into groups. The strategy involves a maximum likelihood approach to deduce which dimensions of identity lead to the formation of groups as well as which groups are actually formed. I propose a practical algorithm for the estimation and apply this to data on link formations and on identity characteristics collected from four villages in Eastern Region of Ghana