We generalize the Bisin-Verdier (2000 , 2001a model of intergenerational transmission to permit an arbitrary number of cultural traits. A key observationthat this model is equivalent to an evolutionary game under replicator dynamicsallows us to exploit the extensive literature on replicator systems. For two special cases, obtained by placing substantively meaningful restrictions on the pattern of "cultural distastes" between traits, we demonstrate global stability of the long-run distribution

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... traits using recent results on stable games and potential games. We also provide a full analysis of the general three-trait case, showing that all three traits survive in the long run only if each trait satisfies an "invasion condition" involving the cultural distaste parameters. * Helpful comments were received from seminar audiences at Duke and Wisconsin, and from participants in the conference on Models of Cultural Dynamics and Diversity hosted by the Paris School of Economics. I am especially grateful to Bill Sandholm for providing detailed comments and pointing me toward the mathematical biology literature.