The dynamics of continuous cultural traits in social networks

Abstract

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.

Opinion Dynamics and Wisdom Under Conformity

“…The recent model by Foerster et al (2013) studies agents who increase the learning weights others have for them. In a context of cultural transmission of traits, Buechel et al (2011) introduce strategic interaction for the DeGroot model in an OLG framework.…”

Convergence of Cultural Traits with Time-Varying Self-Confidence in the Panebianco (2014) Model--A Corrigendum

“…By contrast, Büchel, Hellmann, and Pichler (2014) pursue a different approach to ensure con-vergence for the general case with time-varying transition matrices they study in Appendix C.…”

“…This type of model is also used in naive learning and opinion formation literature, including for example, Cavalli-Sforza and Feldman (1973), DeGroot (1974) and, more recently, DeMarzo, Vayanos, and Zwiebel (2003), Golub and Matthew O. Jackson (2010) and Büchel, Hellmann, and Pichler (2014). Here the transition matrix X t acts as an influence matrix that describes how next period attitudes are derived as the weighted average of current-period attitudes with element x ij (t) giving the weight that individual i assigns to the trait of individual j.…”

Polarization and Segregation through Conformity Pressure and Voluntary Migration: Simulation Analysis of Co-Evolutionary Dynamics

“…9 Each individual person interacts only with a more or less restricted part of society. Conformity pressure works among people who meet and communicate casually and regularly, but not significantly with 6 Buechel et al [18] and Cheung and Wu [19] extend the BV model to continuous cultural traits. 7 Precisely, this is a reduced form of the KS model.…”