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Notes on a Social Transmission Model with a Continuum of Agents

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  • Benjamin Golub

Abstract

This note presents a simple overlapping-generations (OLG) model of the transmission of a trait, such as a culture. Initially, some fraction of agents carry the trait. In each time period, young agents are "born" and are influenced by some older agents. Agents adopt the trait only if at least a certain number of their influencers have the trait. This influence may occur due to rational choice (e.g., because the young agents are playing a coordination game with old agents who are already committed to a strategy), or for some other reason. Our interest is in how the process of social influence unfolds over time, and whether a trait will persist or die out. We characterize the dynamics of the fraction of active agents and relate the analysis to classic results on branching processes and random graphs.

Suggested Citation

  • Benjamin Golub, 2020. "Notes on a Social Transmission Model with a Continuum of Agents," Papers 2002.03569, arXiv.org, revised Apr 2020.
    • Handle: RePEc:arx:papers:2002.03569
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