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.