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Diffusion on Social Networks

Matthew O. Jackson et Leeat Yariv


We analyze a model of diffusion on social networks. Agents are connected according to an undirected graph (the network) and choose one of two actions (e.g., either to adopt a new behavior or technology or  not to adopt it). The return to each of the actions depends on how many neighbors an agent has, which  actions the agent’s neighbors choose, and some agent-specific cost and benefit parameters. At the outset,  a small portion of the population is randomly selected to adopt the behavior. We analyze whether the  behavior spreads to a larger portion of the population. We show that there is a threshold where “tipping”  occurs: if a large enough initial group is selected then the behavior grows and spreads to a significant  portion of the population, while otherwise the behavior collapses so that no one in the population chooses  to adopt the behavior. We characterize the tipping threshold and the eventual portion that adopts if the  threshold is surpassed. We also show how the threshold and adoption rate depend on the network  structure. Applications of the techniques introduced in this paper include marketing, epidemiology,  technological transfers, and information transmission, among others.

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Matthew O. Jackson et Leeat Yariv, « Diffusion on Social Networks »Économie publique/Public economics [En ligne], 16 | 2005/1, mis en ligne le 21 avril 2006, consulté le 23 mai 2024. URL : ; DOI :

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Matthew O. Jackson

Caltech. Division of the Humanities and Social Sciences

Leeat Yariv

Caltech. Division of the Humanities and Social Sciences

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