Siegel, 2009, Social Networks and Collective Action

Ref: Sigel, D. A. (2009). Social networks and collective action. American Journal of Political Science, 53, 122-138. 

A really nice overview of social network structure with a simple model of participation. Agents have intrinsic motivations, and increase their extrinsic motivation based on the fraction of neighbors who are currently participating. He analyzes this model using a number of network structures.


The Model: 
Individual's have a total motivation M = b + c, where b is the intrinsic, agent-specific motivation, and c is the extrinsic motivation that depends on one's neighbors. An individual either "participates" or not. All individuals start out not participating. They are randomly assigned intrinsic motivations from a normal distribution.
For the extrinsic motivation, c = -(1 - p), where p is the fraction of neighbors who are participating. Thus, c varies between -1 and 0. An agent participates if b + c > 0.
A "rabble rouser" is an individual for whom b ≥ 1, and so begins participating right away.
A "wet blanket is an individual for whom b < 0, and so will never participate.
Updating is simultaneous, which doesn't matter, since there is no negative feedback.

For these simulations, N = 1,000, the mean b is 0.6, and the standard deviation of b can vary for different classes of runs: 0.23 (weak motivation), 0.25 (intermediate motivation), and 0.3 (strong motivation).  

Simple Networks:
- Fully connected
- Random
- Ring

Empirically interesting networks: 
- Small world
- Village (or Clique)
- Opinion Leader
- Hierarchical
(for these last two, the distributions of motivation levels can be correlated with the position in the network)

Some conclusions:
[I'll come back to this.] The graphs in the paper are very informative.