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Wow, so that's been quite a trip we've taken through the analysis and modeling

Â of social networks. Social and economic networks, so this is

Â just going to be a wrap up of the course. And so, let me say a few things in terms

Â of, before we get to the overall course, just on games and networks, sort of our

Â last topic. what have we learned?

Â Well, we've learned that one useful distinction is going to be in terms of

Â what kinds of pure effects are there in terms of behaviors.

Â What, really what kind of influence does one individual have on another?

Â And strategic complements and strategic substitutes are going to have different

Â properties. Understanding that is going to be

Â important in understanding what the implications of network structure are for

Â behavior. position matters, so people that are more

Â connected are going to take, you know, higher actions and, and complements and

Â earlier they're going to, lower actions in substitutes.

Â You can say certain kinds of things in certain settings about how position

Â matters in a network. structure's going to matter, so some

Â networks are going to lead to more diffusion of behavior, or wider-spread

Â behavior than others. Homophily and cohesion are going to be

Â critical determinants of whether you can sustain diversity of actions, what kinds

Â of actions might be going on in different parts of the network.

Â So, there is a, a literature that's sort of growing on this top-, topic at

Â present. There's a lot more to be done in terms of

Â understanding how network structure, and behavior co-evolved, how they are related

Â to each other, and how that depends on the type of interactions that are

Â present. What more can we say systematically about

Â this? So it's a very interesting area and it

Â has, obviously many applications and ultimately is one of the most important

Â questions we can ask here because it's why the real consequences of networks are

Â in terms of the behavior of the individuals and the resulting welfare

Â that comes out on the network. Okay, to do list you know, studying

Â homophily, clustering, and other kinds of network characteristics.

Â How does that impact network behavior? More integration of behavior with network

Â formations. So we, we saw one glimpse of that in

Â terms of this favor exchange. But there's a lot of other settings where

Â we can begin to do that. It's been looked at, to some extent, in

Â trading networks. there are other settings where there are

Â co-determination kinds of analyses that have been done.

Â But that's going to be important in really understanding why networks look

Â the way they do. and ultimately, that's going to involve

Â taking models of games on networks to data, to really understand whether we see

Â the kinds of structures that we predict, whether we see the behaviors we predict,

Â what's the implications of the network structure for behavior, a whole series of

Â issues. And I think one, one thing to sort of add

Â here is that often we think of, of networks one dimension at a time.

Â And in fact, there's a lot that goes on in networks, and so understanding there's

Â interrelationships between different kinds of things could be important.

Â So, somebody might be a colleague, a coauthor, but they, we might also

Â exchange information or do favors for each other at a different times.

Â 3:11

There's a whole series of different relationships, risk sharing, information

Â sharing, that goes on on the same set of relationships.

Â And so understanding how all of those different things play into each other and

Â how they depend on network structure and how they determine network structure is

Â still a wide open field. So, in terms of the overall course, I

Â think, you know, what, what was the intention here?

Â The intention was to expose you to a whole series of different ways of

Â thinking about networks and, and different empirical facts and different

Â and types of analyses, different types of models.

Â So we've pulled things from random graph theory, from sociology from economics.

Â we've looked at statistical models. We've looked at some of the models coming

Â out of the statistical physics. So we've looked a whole series of

Â different types of models. And the idea was not to make you experts

Â on any particular model, but to give you a general feeling for the lay of the

Â land, the types of models that are being used.

Â We've looked at some in more depth than others, and the idea here is just to give

Â you a toolkit so that you have a feeling for what's out there, what the questions

Â are, how these different tools can be used to answer questions.

Â And so in terms of, you know, I think whither now, and again whither is where,

Â not withering. so the idea here is, is, you know, what

Â do we do next? what, I think part of the reason that,

Â that network analysis is so exciting these days has to do with the set of open

Â questions there are. So, it's a pretty wide open landscape.

Â There's a lot that's still to be learned both in terms of the structure of

Â networks and the impacts that's had for societies.

Â And, it's also a very interesting area because of its interdisciplinary nature.

Â So, it's not just it, it having activity and questions popping up in one area, but

Â it's, it's popping up all over because these things are such an important part

Â of our life. And so we're seeing a lot of different

Â literatures coming to bare on one thing and, and it's an interesting area in

Â terms of the interaction between these. Now, in terms of what to be done.

Â You know, bridging these, these random and, and more strategic models is

Â important because the strategic models have welfare implications, behavioral

Â implications. The random models allow you to fit to

Â data. So we need these kinds of things.

Â And associated with that is sort of enriching the stable of models that we

Â have where we can do really careful statistical analysis and we can answer

Â questions of you know did this happen random?

Â Or do we have some belief that this is a significant aber-, a significant finding

Â in some particular setting. relating networks to outcomes, I think

Â there's a lot more to be done here. So there's a lot of case studies over the

Â years that have been done. But case studies tend to fall into a

Â couple of different categories. Often they are looking at network

Â structure itself, or they're looking at situations where you know you, you're

Â studying some peer effect. And it's only recently that we've seen a

Â lot of analyses where we've got a combination of the networks and some of

Â the behaviors diffusing over those. The, the diffusion literature had some of

Â that early on, but the, the availability of data has exploded in the last decade

Â especially with internet kinds of data sets and other things.

Â So that the amount of data that's there to be analyzed is much larger.

Â And the applications here are very wide and very important.

Â So things like you know, labor networks, who you find jobs from, basic

Â communication and knowledge, social mobility, voting, who you trade with,

Â collaboration networks, crime networks how the worldwide web's evolving, risk

Â sharing you know, understanding markets, international trade growth in developing

Â countries. all of these things involve relating

Â networks to outcomes, and so there's a huge set of important areas for study.

Â 7:11

again, in terms of understanding these formation things co, co-evolving behavior

Â and, and networks is, is going to be critical.

Â And, in terms of empirical and experimental, you know, when we're

Â working with models, that gives us more of a feeling for what should be going on

Â in different empirical applications, so having structural models that we can take

Â to data is important. And so building these, these sets of

Â models is important. There's also important areas, both in

Â terms of laboratory experiments, which have been growing over time, and field

Â experiments, which are also starting to grow more over time.

Â Where one can actually control carefully what what's happening on the network, and

Â then see, what are the implications in terms of various behaviors?

Â So this is another area which I think will, will be expanding over time.

Â And one thing to sort of, you know, say in closing, in terms of the course.

Â as we develop a richer and richer set of tools, different models and so forth a

Â lot of these things are, are developed for particular applications or with

Â particular questions in mind. And there's very little that's been done

Â systematically to say okay, look we've got now ten to 20 different centrality

Â measures. which ones would I use in which context?

Â Which ones are the right ones? So, I can apply them all and see which

Â ones work best. But is there something systematically

Â systematic that we can say about which ones should be applied in which

Â situation. So, understanding, you know, how this,

Â how things work. There's an area that we didn't talk about

Â which is fairly rich, in terms of detecting community structures.

Â So you're given a network, and you're trying to uncover who are the individuals

Â that sit in communities that are more likely to be interacting with each other

Â than others. So can we identify communities?

Â There's many different algorithms for doing that.

Â Which are the right algorithms? What, what's the right techniques for

Â doing that? how is, is value allocated over a

Â network? There's a whole series of, of questions

Â that can be addressed technically using modeling, but we would want to understand

Â which approaches should we use in which situations.

Â And so there needs to be more foundational work done, just in

Â understanding what are the properties of different, say, centrality measures.

Â which ones, you know, what, which ones react in which ways to different network

Â changes? What are they measuring?

Â What, what are we getting out of this? So there's a very rich set of research

Â topics in, in social and economic network analysis.

Â the idea here has been to give you an introduction, an overview of some of the

Â things and introduce you to some modeling and, and techniques that you're aware of,

Â of the way that this literature works and some of the main questions that have been

Â answered. it's a great area for research.

Â it's been fun talking with you and and hope you enjoy the, have enjoyed the

Â course, and best wishes for your future analysis of social and economic networks.

Â