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Notes on a Social Transmission Model with a Continuum of Agents

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Document pages: 12 pages

Abstract: This note presents a simple overlapping-generations (OLG) model of thetransmission of a trait, such as a culture. Initially, some fraction of agentscarry the trait. In each time period, young agents are "born " and areinfluenced by some older agents. Agents adopt the trait only if at least acertain number of their influencers have the trait. This influence may occurdue to rational choice (e.g., because the young agents are playing acoordination game with old agents who are already committed to a strategy), orfor some other reason. Our interest is in how the process of social influenceunfolds over time, and whether a trait will persist or die out. We characterizethe dynamics of the fraction of active agents and relate the analysis toclassic results on branching processes and random graphs.

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