On The Transmission of Continuous Cultural Traits

This paper generalizes the discrete cultural transmission model proposed by Bisin and Verdier (2001) to continuous trait space. The resulting cultural evolutionary dynamic can be characterized by a continuous imitative dynamic in a population game in which a player's payoff is equal to the aggregate cultural intolerance he has towards other agents. We show that cultural heterogeneity is always preserved. In addition, we model each agent's cultural intolerance towards another agent as an increasing function of cultural distance --- the distance between that other agent's trait and his own trait in the trait space. This captures people's general tendencies of evaluating culturally more distant people with stronger biases, and it is most easily modeled on a continuous trait space. We find that the curvature of the cultural intolerance function plays an important role in determining the long-run cultural phenomena. In particular, when cultural intolerance is a convex function of cultural distance, only the most extremely polarized state is a stable limit point.