Joan de Marti and Yves Zenou have written on the formation of social networks in a working paper entitled Social Networks.
We survey the literature on social networks by putting together the economics, sociological and physics/applied mathematics approaches, showing their similarities and differences. We expose, in particular, the two main ways of modeling network formation. While the physics/applied mathematics approach is capable of reproducing most observed networks, it does not explain why they emerge. On the contrary, the economics approach is very precise in explaining why networks emerge but does a poor job in matching real-world networks. We also analyze behaviors on networks, which take networks as given and focus on the impact of their structure on individuals’ outcomes. Using a game-theoretical framework, we then compare the results with those obtained in sociology.
The authors write that sociologists explain most networks via their unintended outcomes—the results of birth, social standing, or choices you make. Economists, on the other hand, explain social networks as the intended outcome of strategic interaction: I get to know somebody because I want to use my expanded network to gain something later. Finally, applied mathematics does not really attempt to explain why social networks form; they emphasize how they form and how they look (3). The authors compare and contrast the three methods of explaining social networks.
One interesting aspect of social networks is that weak ties between individuals foster widespread diffusion of information, whereas strong ties increase the probability that a particular piece of information will spread to members in the network, but can create an echo chamber effect as new information becomes difficult to spread through. In other words, the “quality of information decays with distance” (5). Social networks also tend to be scale-free (7). There are a few individuals around whom most people coalesce, and a large percentage of individuals with relatively few links. In the sociological literature, preferential attachment is the most common explanation (9).
The authors note that, in the economic approach, there are no examples of equilibrium networks that have real-world properties. In economics, we see networks created via mutual consent and as the result of a Nash equilibrium. The end results of these networks, however, does not look much like a real social network (12).
I should note that social utility theory rears its ugly head on page 14. TANSTAASWF, folks (see the continuing series).
If you want to tie this to a real-world case of interest, think about crime. In the standard view of crime, we deter crime by increasing punishment uniformly, which raises the costs of crime for everyone (17). Because there are certain individuals with a comparative advantage in crime, raising these costs will drag some of them out into productive work. We could also increase their benefits in non-criminal activities, which works the same way. But in the network view, we should target/remove criminal hubs and the highly inter-connected nodes. If you isolate these hubs from the rest of the group, entire networks can collapse. This isn’t necessarily the same thing as rolling up criminal networks by taking down the members at the top of the list. Instead, take out the guys with special skills, the guys who keep lists of other guys (in their heads or on paper), and the guys who introduce groups to other groups. In business terms, instead of eliminating the financiers, it may pay to eliminate the sales and marketing folks.
Finally, I have to point out some really poor writing, the kind of writing which can only appear in an academic paper: “for a given farmer, (i) he/she is more likely to change his/her fertilizer use after his/her information neighbors who use similar amounts of fertilizer achieve lower than expected profits; (ii) he/she increases (decreases) his/her use of fertilizer after his/her information neighbors achieve unexpectedly high profits when using more (less) fertilizer than he/she did” (21).
First of all, I hate the whole “increases (decreases) means more (less)” thing that academic writers do. It destroys the flow of the writing and saves you maybe three words. Second of all, do you really need to use “he/she” and “his/her” so much? This is English—“he” is sex-neutral unless used to describe a specific person. It’s writing like this which kicks me out of “this is interesting” mode and into “this is just poor writing” mode. Which is a shame, too, as it’s a rather interesting paper.