Thread by @KevinZollman

This week in my class, Network Epistemology, we looked at models of strategic network formation from economics. The basic idea is that as people form social networks, they don't just do so at random, but respond to incentives for various types of structures.

The central question: when people respond to incentives what kind of networks do they form? Should we expect them to form the socially-best networks? Or will there be difficulty in building and sustaining social networks that are good for the community?

This week also provided a nice opportunity to venture into a discussion of economic methodology, we looked at papers that used the three major approaches in micro economics: equilibrium-based, evolutionary, and experimental/behavioral.

First we read the now-classic paper by @JacksonmMatt and Wolinsky developing a model of strategic network formation. This paper does a lot of interesting things, but for our purposes we focused on two very interesting results.

sciencedirect.com/science/articl…

First, they show ways that the "star" network can be beneficial. Star networks, intuitively seem quick bad from an epistemic point of view, they have a single bottle neck for information and their is massive inequality in influence.

What Jackson and Wolinsky show is that there is one very important benefit: they maximize how close people are to one another while also minimizing the number of connections. So if it costs something to have a connection, this might be the most efficient way to organize a group.

The second interesting conclusion is that social network formation can have features of a social dilemma, that is the optimal social network might not be compatible with individual incentives to form that network. So, networks may need "active" intervention to keep them working.

Of course, like any model, this requires assumptions. We spent a lot of time discussing conditions under which those assumptions might fail and why one might modify the positive judgment about star-networks or the conflict between individual and social goals.

In addition, the Jackson & Wolinsky paper uses a traditional equilibrium-based game theoretic methodology. It identifies networks that are stable, but not necessarily how we get there. This is important because in a community of size N there are N stars. How do we choose one?

For this question, we turned to this paper by Jackson and Watts. They look at a model of "myopic" learning, where agents experiment with forming or dropping links to friends and keep them if they would improve their situation.

sciencedirect.com/science/articl…

One important conclusion they show is that in some contexts, even when the socially-best network is an equilibrium, you might not always converge to it. That is, it may be impossible to learn. This represents an important problem for the equilibrium-based approach.

This kind of conflict is not unique to the study of networks. Evolutionary game theory has shown how the equilibrium based approach in game theory can be both too narrow and too broad. This particular application is very interesting, but not completely surprising.

Since both the traditional equilibrium based approach and the evolutionary approach are mathematical models, there is an interesting methodological question: when they disagree which one should we believe and why? The class spent a little time discussing this question.

(PS I think this is an interesting dissertation topic about the relationship between evolutionary and traditional game theory broadly, in case anyone is looking for one...)

Finally, we looked at this paper by Goeree, et. al which used laboratory experiments to test a closely related network formation model due to Bala and Goyal. (B&G also predict stars.)

sciencedirect.com/science/articl…

Goeree, et. al shows that in perfectly symmetric situations, stars *do* *not* reliably form despite being the predicted outcome of the equilibrium based approach. This might occur because there are so many potential equilibria and players disagree about which one they should do.

Or it might be because the problem is far too difficult to solve in a short time. They show, however, that when you introduce asymmetries people more reliably form stars. (Although still far from doing so reliably.) This suggests the problem is solvable.

There is an interesting consonance between Goeree's results and the Jackson&Watts paper. Both show that the equilibrium selection problem is difficult. Goeree show a way out, however: people are not all identical.

In class we discussed ways that this heterogeneity might be nefarious, however. Perhaps existing inequalities, like gender or race, might serve to drive us to a particular equilibrium -- which connects with @cailinmeister's book.

In the star-networks, the person at the center is often paying a very high cost to maintain social links that benefit everyone. Several students noted the analogy with how women in male dominated fields are often asked to do the same.

On the methodological front, Goeree represent an interesting third strategy. Implement the highly idealized game in a lab, but have real people make the choices. This has some additional validity, one thinks, because these are real people not idealized agents.

Even though the model is implemented "on meat" instead of "on paper", you still have to wonder if people are deciding in the lab the same way they decide in person. Goeree et. al discuss why more ecologically valid experiments would be very difficult to perform in this domain.

This week's discussion was very interesting because it both allowed us to talk about the central topic of the course, learning in social networks, but also allowed us to peer into the methodology in economics in a little more detail than we've done before.