The hallmarks of cultural behavior include consistency within and across individuals, variance between populations, behavioral stickiness, and possibly suboptimal performance. In this article, we build a formal framework within which these behavioral attributes emerge from the interactions of purposive agents. We then derive mathematical results showing these behaviors are optimal given our assumptions. Our framework rests on two primary assumptions: (1) agents play ensembles of games, not just single games as is traditionally the case in evolutionary game theory models; and (2) agents have finite cognitive capacity. Our analysis combines agent-based techniques and mathematics, enabling us to explore dynamics and to prove when the behaviors produced by the agents are equilibria. Our results provide game theoretic foundations for cultural diversity and agent-based support for how cultural behavior might emerge.
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