On the probabilistic transmission of continuous cultural traits

This paper proposes a framework that generalizes the discrete cultural transmission model of Bisin and Verdier (2001) to a continuous trait setting. We find that the resulting cultural evolutionary dynamic can be characterized as a continuous imitative dynamic in a population game. By using the properties of imitative dynamics, we show that as in Bisin and Verdier, cultural substitutability is the key that leads to cultural heterogeneity. Furthermore, we model an agent's cultural intolerance towards another agent as an increasing function of their cultural distance. We find that the curvature of the cultural intolerance function plays an important role in determining the long-run cultural phenomena. In particular, when the cultural intolerance function is convex, only the most extremely polarized state is a stable limit point.