Paternalism, Cultural Transmission and Diffusion on Complex Networks

We study cultural diffusion in a complex network where the transition probabilities are determined by a cultural transmission technology with endogenous vertical transmission rates (a la Bisin and Verdier, 2001). We derive a two-way epidemic model in which both the infection and the recovery rates are endogenous and depend on the topology of the network. First, we identify a "social structure bias" in cultural transmission that determines the direction of cultural change relating the economic structure of parental socialization incentives to the social network structure. Second, we characterize two balancing conditions satisfied by the network degree distribution and the vertical transmission rate distribution to ensure the sustainability of long run cultural heterogeneity. Third, we show how paternalistic motivations for endogenous cultural transmission interact with the "social structure bias" channel and maintain steady state cultural diversity for any network structure.