Network Beliefs and Behavior with Peer Effects

Individuals often act without knowing the full structure of the social network in which they are or will be embedded. We study how an individual's beliefs about their networks shapes their behavior when actions are peer interactive. Agents use what they know about the network to forecast their peers' actions. Those peers' actions depend on their beliefs, which then generate an iterative expression what we call "Iterative Belief Centrality." Agents' beliefs formed based on what they each see of the network are heterogeneous, depend on their network position, and can be correlated across connected agents. The resulting equilibrium behavior nests both complete-information and degree-based models as special cases, but more generally can differ systematically. If people's beliefs about the network satisfy a natural monotonicity condition in how connected they are, then belief iteration (fully rationally) amplifies behavioral differences across the network, increasing actions of more-connected and decreasing actions of less-connected agents relative to situations with homogeneous beliefs. We also show how positive correlation in people's positions in the network even further amplifies the variance of behavior. The framework provides a unified and tractable theory of network-based behavior with implications for many applications.