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diffusion[1]

by Gabriel Rossman (Submitted: 08/24/2010)

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VERSION

This is version 1.1 (8/19/2010) of this program. It is written in NetLogo 4.1.

DIFFUSION SIMULATION

This program first creates a social network and then simulates the diffusion of an innovation through the network following a combination of the Bass model and a network contagion model. Agents turn red as they adopt the innovation. New adopters are shown as hollow red circles and incumbent adopters as solid red circles. In a Bass model (unlike an S-I-R model) adoption is permanent. Small green numbers show the number of neighbors having adopted.

HOW TO USE IT

Press "setup-preferential-attachment" to create the social network following Barabasi's preferential attachment model. Alternately, press "setup-giant-component" to create following the algorithm given in "Giant Component." Note that the preferential attachment will have stronger "hubs," which is important to some theories of diffusion. Also note that "Giant Component" may have some isolates, which is also consequential for some models, but not others.

"Wipe" will reset the diffusion process but keep the social network. "Go" and "go-once" simulate the diffusion process.

Adjust the sliders to see how the diffusion reacts to different assumptions. The default settings approximate the description of how consumer appliances spread amongst US households after WWII (Bass 1969).

The "constant effect" is an effect that applies to all agents and has the same effect at all time periods. Substantively it can be taken to reflect things like advertising or government mandates. It is sometimes referred to as a "mass media effect," "a," or "p."

The "endogenous effect" is a non-spatial cumulative advantage effect that applies to all agents but is a function of popularity (including among "strangers"). Substantively it can be taken to reflect things like bestseller lists or search algorithms like PageRank. It is sometimes referred to as an "information cascade," "network externalities," "b," or "q."

The "cohesion effect" is how sensitive an agent is to neighbors. (This is similar to the "endogenous" effect but applies only to neighbors rather than the whole population). It substantively reflects "word of mouth." This effect is sometimes referred to as "network diffusion," "contagion," or "local network externalities."

Note that under some circumstances the "endogenous" and "cohesion" effects behave similarly and both usually produce an "s-curve." In many works (e.g., Bass 1969, Rogers 2003) a model specification that lacks network structure (and thus is similar to the "endogenous effect") is given a substantive interpretation of a "cohesion effect."

THINGS TO NOTICE

Study the shape of the "Totals" plot. Look both at how steep the plot is and whether the shape is convex or s-shaped. Notice which parameters are associated with which shapes and at when the parameters are specified in combination, when you tend to get a blend and when you tend to get one dominating the other.

Notice that the "patient zero" appears randomly whenever you hit "wipe." Does it matter where? Does it matter more for which diffusion parameter settings and which kind of network?

EXTENDING THE MODEL

Possible changes include
-Allow even more network structures, several of which are found in the model library.
-Model the awareness/adoption distinction. Usually in awareness/adoption models, awareness readily spreads by the "constant effect" but adoption only spreads by the "endogenous" and "cohesion" effects (Ryan and Gross 1943).
-Model a stable component to each agent's threshold.

CREDITS AND REFERENCES

This model was written by Gabriel Rossman of the UCLA Depatment of Sociology. Substantial parts of the code are borrowed from Wilensky's "Preferential Attachment" and "Giant Component" models.

For additional information:

Abrahamson, Eric and Lori Rosenkopf. 1997. “Social Network Effects on the Extent of Innovation Diffusion: A Computer Simulation.” Organization Science 8:289–309.

Bass, Frank M. 1969. “A New Product Growth for Model Consumer Durables.” Management Science 50:1825–1832.

DiMaggio, Paul J. and Filiz Garip. 2010. “Intergroup Inequality as a Product of Diffusion of Practices with Network Externalities under Conditions of Homophily: Applications to the Digital Divide in the U.S. and Rural/Urban Migration in Thailand.” Princeton University Center for the Study of Social Organization Working Paper #2.

Rogers, Everett M. 2003. Diffusion of Innovations. New York: Free Press, 5th edition.

Ryan, Bryce and Neal C. Gross. 1943. “The Diffusion of Hybrid Seed Corn in Two Iowa Communities.” Rural Sociology 8:15–24.

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