Identity and Link Reliability in Social Networks

This paper considers a non-cooperative network formation game where identity is introduced as a single dimension to capture the characteristics of a player in the network. Players access to the benefits from the link through direct and indirect connections. We consider cases where cost of link formation paid by the initiator. Each player is allowed to choose their commitment level to their identities. The cost of link formation decreases as the players forming the link share the same identity and higher commitment levels. We then introduce link imperfections to the model. We characterize the Nash networks and we find that the set of Nash networks are either singletons with no links formed or separated blocks or components with mixed blocks or connected.