Intergenerational Cultural Transmission as an Evolutionary Game

We generalize the Bisin and Verdier (2000, 2001) model of intergenerational transmission to permit an arbitrary number of cultural traits. A key observation – that this model is equivalent to an evolutionary game under replicator dynamics – allows us to exploit the extensive literature on replicator systems. For some substantively interesting special cases, we demonstrate global stability of equilibrium outcomes using recent results on stable games and potential games. Drawing on mathematical biology, we also apply results on the long-term survival (permanence) of traits, and highlight the analogy between catalytic networks and systems of cultural traits. ∗I am grateful to Bill Sandholm for helpful comments and suggestions, and especially for pointing me toward the mathematical biology literature on permanence.