Wow, so that's been quite a trip we've taken through the analysis and modeling of social networks. Social and economic networks, so this is just going to be a wrap up of the course. And so, let me say a few things in terms of, before we get to the overall course, just on games and networks, sort of our last topic. what have we learned? Well, we've learned that one useful distinction is going to be in terms of what kinds of pure effects are there in terms of behaviors. What, really what kind of influence does one individual have on another? And strategic complements and strategic substitutes are going to have different properties. Understanding that is going to be important in understanding what the implications of network structure are for behavior. position matters, so people that are more connected are going to take, you know, higher actions and, and complements and earlier they're going to, lower actions in substitutes. You can say certain kinds of things in certain settings about how position matters in a network. structure's going to matter, so some networks are going to lead to more diffusion of behavior, or wider-spread behavior than others. Homophily and cohesion are going to be critical determinants of whether you can sustain diversity of actions, what kinds of actions might be going on in different parts of the network. So, there is a, a literature that's sort of growing on this top-, topic at present. There's a lot more to be done in terms of understanding how network structure, and behavior co-evolved, how they are related to each other, and how that depends on the type of interactions that are present. What more can we say systematically about this? So it's a very interesting area and it has, obviously many applications and ultimately is one of the most important questions we can ask here because it's why the real consequences of networks are in terms of the behavior of the individuals and the resulting welfare that comes out on the network. Okay, to do list you know, studying homophily, clustering, and other kinds of network characteristics. How does that impact network behavior? More integration of behavior with network formations. So we, we saw one glimpse of that in terms of this favor exchange. But there's a lot of other settings where we can begin to do that. It's been looked at, to some extent, in trading networks. there are other settings where there are co-determination kinds of analyses that have been done. But that's going to be important in really understanding why networks look the way they do. and ultimately, that's going to involve taking models of games on networks to data, to really understand whether we see the kinds of structures that we predict, whether we see the behaviors we predict, what's the implications of the network structure for behavior, a whole series of issues. And I think one, one thing to sort of add here is that often we think of, of networks one dimension at a time. And in fact, there's a lot that goes on in networks, and so understanding there's interrelationships between different kinds of things could be important. So, somebody might be a colleague, a coauthor, but they, we might also exchange information or do favors for each other at a different times. There's a whole series of different relationships, risk sharing, information sharing, that goes on on the same set of relationships. And so understanding how all of those different things play into each other and how they depend on network structure and how they determine network structure is still a wide open field. So, in terms of the overall course, I think, you know, what, what was the intention here? The intention was to expose you to a whole series of different ways of thinking about networks and, and different empirical facts and different and types of analyses, different types of models. So we've pulled things from random graph theory, from sociology from economics. we've looked at statistical models. We've looked at some of the models coming out of the statistical physics. So we've looked a whole series of different types of models. And the idea was not to make you experts on any particular model, but to give you a general feeling for the lay of the land, the types of models that are being used. We've looked at some in more depth than others, and the idea here is just to give you a toolkit so that you have a feeling for what's out there, what the questions are, how these different tools can be used to answer questions. And so in terms of, you know, I think whither now, and again whither is where, not withering. so the idea here is, is, you know, what do we do next? what, I think part of the reason that, that network analysis is so exciting these days has to do with the set of open questions there are. So, it's a pretty wide open landscape. There's a lot that's still to be learned both in terms of the structure of networks and the impacts that's had for societies. And, it's also a very interesting area because of its interdisciplinary nature. So, it's not just it, it having activity and questions popping up in one area, but it's, it's popping up all over because these things are such an important part of our life. And so we're seeing a lot of different literatures coming to bare on one thing and, and it's an interesting area in terms of the interaction between these. Now, in terms of what to be done. You know, bridging these, these random and, and more strategic models is important because the strategic models have welfare implications, behavioral implications. The random models allow you to fit to data. So we need these kinds of things. And associated with that is sort of enriching the stable of models that we have where we can do really careful statistical analysis and we can answer questions of you know did this happen random? Or do we have some belief that this is a significant aber-, a significant finding in some particular setting. relating networks to outcomes, I think there's a lot more to be done here. So there's a lot of case studies over the years that have been done. But case studies tend to fall into a couple of different categories. Often they are looking at network structure itself, or they're looking at situations where you know you, you're studying some peer effect. And it's only recently that we've seen a lot of analyses where we've got a combination of the networks and some of the behaviors diffusing over those. The, the diffusion literature had some of that early on, but the, the availability of data has exploded in the last decade especially with internet kinds of data sets and other things. So that the amount of data that's there to be analyzed is much larger. And the applications here are very wide and very important. So things like you know, labor networks, who you find jobs from, basic communication and knowledge, social mobility, voting, who you trade with, collaboration networks, crime networks how the worldwide web's evolving, risk sharing you know, understanding markets, international trade growth in developing countries. all of these things involve relating networks to outcomes, and so there's a huge set of important areas for study. again, in terms of understanding these formation things co, co-evolving behavior and, and networks is, is going to be critical. And, in terms of empirical and experimental, you know, when we're working with models, that gives us more of a feeling for what should be going on in different empirical applications, so having structural models that we can take to data is important. And so building these, these sets of models is important. There's also important areas, both in terms of laboratory experiments, which have been growing over time, and field experiments, which are also starting to grow more over time. Where one can actually control carefully what what's happening on the network, and then see, what are the implications in terms of various behaviors? So this is another area which I think will, will be expanding over time. And one thing to sort of, you know, say in closing, in terms of the course. as we develop a richer and richer set of tools, different models and so forth a lot of these things are, are developed for particular applications or with particular questions in mind. And there's very little that's been done systematically to say okay, look we've got now ten to 20 different centrality measures. which ones would I use in which context? Which ones are the right ones? So, I can apply them all and see which ones work best. But is there something systematically systematic that we can say about which ones should be applied in which situation. So, understanding, you know, how this, how things work. There's an area that we didn't talk about which is fairly rich, in terms of detecting community structures. So you're given a network, and you're trying to uncover who are the individuals that sit in communities that are more likely to be interacting with each other than others. So can we identify communities? There's many different algorithms for doing that. Which are the right algorithms? What, what's the right techniques for doing that? how is, is value allocated over a network? There's a whole series of, of questions that can be addressed technically using modeling, but we would want to understand which approaches should we use in which situations. And so there needs to be more foundational work done, just in understanding what are the properties of different, say, centrality measures. which ones, you know, what, which ones react in which ways to different network changes? What are they measuring? What, what are we getting out of this? So there's a very rich set of research topics in, in social and economic network analysis. the idea here has been to give you an introduction, an overview of some of the things and introduce you to some modeling and, and techniques that you're aware of, of the way that this literature works and some of the main questions that have been answered. it's a great area for research. it's been fun talking with you and and hope you enjoy the, have enjoyed the course, and best wishes for your future analysis of social and economic networks.
