Diffusion on Social Networks

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.

[1]  Norman T. J. Bailey,et al.  The Mathematical Theory of Infectious Diseases , 1975 .

[2]  Matthew O. Jackson,et al.  Search in the Formation of Large Networks : How Random are Socially Generated Networks ? , 2005 .

[3]  A. Barabasi,et al.  Halting viruses in scale-free networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Alessandro Vespignani,et al.  Epidemic spreading in scale-free networks. , 2000, Physical review letters.

[5]  Stephanie Forrest,et al.  Email networks and the spread of computer viruses. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  E. Glaeser,et al.  Crime and Social Interactions , 1995 .

[7]  W. Darrow,et al.  Cluster of cases of the acquired immune deficiency syndrome. Patients linked by sexual contact. , 1984, The American journal of medicine.

[8]  Éva Tardos,et al.  Network games , 2004, STOC '04.

[9]  M. Chwe.  Communication and Coordination in Social Networks , 2000 .

[10]  Alessandro Vespignani,et al.  Epidemic dynamics and endemic states in complex networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.