5.10: Week 5 Wrap

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From the course by Stanford University

Social and Economic Networks: Models and Analysis

360 ratings

Stanford University

Social and Economic Networks: Models and Analysis

360 ratings

Learn how to model social and economic networks and their impact on human behavior. How do networks form, why do they exhibit certain patterns, and how does their structure impact diffusion, learning, and other behaviors? We will bring together models and techniques from economics, sociology, math, physics, statistics and computer science to answer these questions. The course begins with some empirical background on social and economic networks, and an overview of concepts used to describe and measure networks. Next, we will cover a set of models of how networks form, including random network models as well as strategic formation models, and some hybrids. We will then discuss a series of models of how networks impact behavior, including contagion, diffusion, learning, and peer influences. You can find a more detailed syllabus here: http://web.stanford.edu/~jacksonm/Networks-Online-Syllabus.pdf You can find a short introductory videao here: http://web.stanford.edu/~jacksonm/Intro_Networks.mp4

From the lesson

Diffusion on Networks

Empirical Background, The Bass Model, Random Network Models of Contagion, The SIS model, Fitting a Simulated Model to Data.

5.1: Diffusion12:57

5.2: Bass Model12:21

5.3: Diffusion on Random Networks 9:08

5.4: Giant Component Poisson Case 15:09

5.5: SIS Model17:50

5.6: Solving the SIS Model 9:17

5.7: Solving the SIS Model - Ordering (Optional/Advanced 24:16)24:16

5.8a: Fitting a Diffusion Model to Data (Optional/Advanced 22:47)22:45

5.8b: Application: Financial Contagions (Optional/Advanced 12:47)12:48

5.8c: Application: Financial Contagions - Simulations (Optional/Advanced 13:41)13:42

5.9: Diffusion Summary 3:45

5.10: Week 5 Wrap4:25

Meet the Instructors

Matthew O. Jackson
Professor
Economics

Hi folks. So let's take a look back at what we've

seen in week five, here talking about diffusion.

So diffusion is something that's been studied in a wide variety of different

disciplines so marketing, social psychology, psychology, sociology,

economics. Anthropology.

So diffusion is something which is important in, in many different behaviors

and so there are different stylized facts, and a number of different models

that have been used. Epidemiology.

Medicine. So, so this is something which is very

fundamental to many areas. Basic thing that we've seen in some

empirics is s shaped. Adoption curves.

So things start out slowly, they pick up and then eventually asymptote.

So that kind of nice shape has some intuition to it that we talked about and,

and looked briefly at the Bass model. So the combination of imitation and

complementarities. The fact that the more other people do

seomthing the more likely a given individual is.

If you've got that kind of feature then that can give you the.

initial upswing in acceleration, the eventual saturation is going to tend to

cause the things to, to tail off eventually, so often we're going to see

these kind of curves. The Bass model's been very powerful at,

at capturing these on a macro, big scale level.

We can build tighter models that bring in the network.

And the network then can help us understand when is something going to

spread? When will we get an epidemic?

How many people are going to be reached and so forth?

So initial contagion, when we looked at those kinds of models and, and

understanding say the SIS model. high degree notdes tend to serve as hubs

and enable diffusion. So overall higher density means you're

going to tend to have more connections, more chances of diffusion or contagion.

Higher degree nodes can serve as hubs so higher variance can also increase the

possibility that you see spreading . And we saw differences then between

things like a, a power law network where we've got a scale free degree

distribution can lead to contagion in, in many cases whereas other ones might not

depending on what the degree is. Extent of diffusion.

We also looked at say, the size of the giant component.

And again that got back to our phase transitions and so forth.

And it turns out that there's a fairly rapid shift from no diffusion to a

situation where you've got diffusion starting and then very rapidly you can

hit saturation. And, and in particular between, and when

we're looking at an Erdős–Rényi kind of network, it's between degree one and

degree three, where most of the action happens below, having at least one other

friend you're not going to get diffusion, it's not really going to occur.

Things are going to die off. People tell on average less than one

other individual, you've got a decreasing system.

If they're telling more, then you've got expansion properties, you can begin to

have things spread. And by the time you hit telling three

other individuals, boom. You've got complete saturation.

homophily can begin to affect that. We didn't talk about that so much, but

there are models now that are tending to bring in more structure and breaks in the

network and so forth and that can affect exactly how this spreads.

Okay. Last thing we looked at, diffusion

modeling. Well in, in different situations we can

begin to write down explicit models of what we think is going to be happening.

And by putting those models down they're actually fairly easy to simulate to take

to data, and they can help us understand, for instance, pure effects.

So how much of something is due to information transmission?

As opposed to complementarities in the actions.

we can begin to look at things like financial contagions and understand how

the structure of the network might lead to contagion from one organization to

another. Each different situation is going to have

different kinds of properties in terms of what it takes for one node to end up

affecting another node. And so by, by changing those we can end

up with different models, but those models tend to be fairly tractable in

terms of simulating those processes and getting predictions and then taking those

to data. So, as we go forward, and look now at

learning, and games on network, some of the themes that we've seen here will

carry over there and be embellished in terms of the structures of the

interactions.

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