The dynamics of continuous cultural traits in social networks

We consider an OLG model (of a socialization process) where continuous traits are transmitted from an adult generation to the children. A weighted social network describes how children are influenced not only by their parents but also by other role models within the society. Parents can invest into the purposeful socialization of their children by strategically displaying a cultural trait (which need not coincide with their true trait). Based on Nash equilibrium behavior, we study the dynamics of cultural traits throughout generations. We provide conditions on the network structure that are sufficient for long-run convergence to a society with homogeneous subgroups. In the special case of quadratic utility, the condition is that each child is more intensely shaped by its parents than by the social environment. The model is akin to the classical DeGroot model of opinion formation which we generalize by allowing for strategic interaction.