Building Social Networks

We examine the process of building social relationships as a non-cooperative game that requires mutual consent and involves reaching out to others at a cost. Players create their social network from amongst their set of acquaintances. Having acquaintances allows players to form naive beliefs about the feasibility of building direct relationships with their acquaintances. These myopic beliefs describe how the other players are expected to respond to the initiation of a link by a player. We introduce a stability concept called "monadic stability" where agents play a best response to their formed myopic beliefs such that these beliefs are self-confirming. The resulting equilibrium networks form subset of the set of pairwise stable networks.