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. Our model also represents an extension of the classical DeGroot model of opinion formation for which we introduce strategic interaction in choice of expressed opinions (in our setup: traits). We show that under strategic interaction convergence is slower and for convergence we need more restrictive necessary and sufficient conditions than in the DeGroot model.