“On the evolution of cultural traits in Social Networks”

Abstract

Cultural traits’ evolution is studied in a theoretical setup, where each individual (or minority) is part of a social network. Individuals behave strategically and face a trade-off between acting like their observed peers or keeping faithful to their idiosyncrasy. We characterize the Nash equilibrium of this game using the theory of Finite Markov Processes and find a sufficient statistic that summarizes the effect of the topology of the network in this equilibrium. We extend this to an overlapping generations model, where parents’ actions determine the trait of their offspring. We identify the Nash equilibrium in each period and show that, when the network is strongly connected, all society converges to the same trait. Lastly, we use the results to illustrate, with comparative static, the consequences of the entry of a group of immigrants to a host country and discuss some policy implications of our findings.