This page shows some pictures from a project with Maggie Penn on the dynamics of informational networks. The model is an extension of our 2014 article, “Sequential Decision-Making & Information Aggregation in Small Networks.” (Political Science Research & Methods, 2(2): 243-271, 2014).
The centerpiece of the theory is that networks depend upon incentive compatibility. We the introduce a random mixing model to “build” networks, where an individual is added to a network if he or she can be truthful with that network and that network is better for him or her than the network that he or she is currently in. Even though we assume that all individuals have an equal chance to be chosen at any time, this process is path-dependent. This is for (at least) three reasons: (1) larger networks are more likely to be chosen, (2) larger networks are more valuable/attractive, per se, than smaller networks, and (3) larger networks tend to be more heterogeneous than smaller networks.
A couple of notes are in order. First, these are undirected networks: communication is bilateral (by construction). Second, the location of a node in the pictures represents its spatial “ideal point”—nodes that are closer together have more similar preferences (and can therefore more easily tell the truth to each other) than those that are far apart. Finally, in the pictures, it’s a little hard to tell who is connected to whom from the links (especially as the network becomes more dense). If you’re interested, each connected component is assigned a unique color. If you watch a node, you can tell it change networks whenever its color changes (with a small probability, a node will retain its color when it switches networks, as the rest of its new network will adopt its color).
A setting with 12 agents.
A setting with 25 agents.
A setting with 50 agents.