Thank you, Anna, and thank you to for inviting me to give this talk.
I hope you can hear me clearly at the end.
Yes. Okay. So it's a pleasure to be here.
This is the first time I'm visiting this building.
And I was recently in Oxford.
So very, very pleased to be in the Mathematical Institute.
A little nervous, especially after a lot of said.
I'm sort of dimly aware that Euler worked on issues of graft a long, long time ago, maybe.
But so today I'll be talking about I'm going to have a lecture, which is going to start with sociology in the forties and fifties of the 20th century,
and it's going to move forward into some online social networks.
And and then I'm going to ask questions about how can we account for phenomena that different social scientists have been talking about?
And I'm going to have a mathematical model to to try and explain the the phenomena
that are off the few this mathematical model will turn on and economic mechanism.
And I'm going to try and convey the sense of this mechanism to you.
And after having done that,
I'm going to then ask whether this mechanism actually works as it's supposed to work by taking this model to a laboratory with human subjects.
And I'm going to show you some experiments that that we've been conducting.
In fact, we are still doing these experiments.
And it's and I'm going to spend a fair bit of time talking about these experiments and what we learn about this,
about the mathematical model from the findings of the experiments.
And there will be things that we will learn which will reassure us about the mathematical model,
but they will also be there will also be patterns in the data which are going to make us question the scope of the model.
And so that's the that's the, you know, the broad outline of of the talk.
And so it's going to combine social sciences, it's going to combine some mathematics, and it's going to combine experimental methods.
And so I hope that you will get a flavour of how economists work with mathematics,
but also how they use experimental methods to enrich their models and advance the,
you know, the, if you like, the nature of the subject, you know, the scope of their understanding of the subject.
Okay. So it's going to be methodological to some extent.
It's going to combine different approaches, but it's also hopefully going to raise some questions in your mind about the methodology of economics,
but also the specific phenomenon that we're going to be talking about.
So what is the law of the few? So so let me start by saying a few words about the origins of this.
So this really goes back to the forties, the 1940s in the United States.
And the background here is that this was a this was a period where mass media was really coming into it all.
Radio, television, newspapers were really coming out in a big way.
And so there was this. And you can see the parallel to what's happening now in a moment.
But what the thought was that with the emergence of mass media.
Social networks of communication would become second order would basically disappear.
And so you will have, on the one hand, these big mass media, they will directly communicate.
They will directly convey information to to ordinary people who will, on the one hand,
be very informed because they will have all those mass media talking to them.
On the other hand, there was this worry that the mass media would be very powerful and it could indeed misinform and mislead ordinary citizens,
ordinary consumers, because it would be so powerful.
So in that context, this these these studies were done by sociologists based in New York, at Columbia University, and in particular,
I would like to draw your attention to always felt who was Viennese born sociologists would move to New York and what they
did in this work in the forties and then subsequently there's been a lot of work in this field is they essentially showed.
A very. So so they found out what they later termed a two way flow of information model of communication.
What do they mean by that? They had this very simple sort of idea that indeed they started with the hypothesis that
social networks and social communication would be becoming less and less important.
But when they went and did this service in different parts of the United States,
they found that there was this two way flow between the mass media and a very small set of people in the cities that surveyed.
And most of the people who were not actually listening to the radio or watching the television or reading the newspapers,
but in fact were mostly talking to a few people in their community to inform themselves about what's happening at the world at large.
And it's a small set of people who are actually having access to the outside world.
Okay. So so this basic observation.
So in their study,
they looked at about 4000 people they surveyed and they found that roughly 20% of these people were actually really exposed to the world out there.
And they were then communicating and summarising this information they have gathered to their fellow citizens in their communities.
So that's sort of the first sort of, you know, the first step in our you know, in our talk today.
So so these are the two books that were published.
People's Choice was about how politics, political decision making,
voting behaviour was shaped not so much by mass media, but for the vast majority of people they surveyed,
it was shaped by their personal preferences, but also by through their communication,
their discussions with these opinion leaders and their local communities.
And subsequently, in a book published in 1955, Personal Influence.
Cats and lizards then expanded the scope of their study beyond politics to address a wide
variety of decisions people make in day to day life and how it's not just in politics,
but also in this many different spheres of life.
Ordinary citizens, ordinary consumers, were not really directly exposed to the mass media,
but indeed they had these intermediaries, a very small set of intermediaries.
So moving forward, if we now move to 2016, 2017,
I want to give you a sense that this idea that a very small fraction of people have access somehow to
lots and lots of information and are indeed being followed and watched by the rest of the population.
To some extent, that sort of pattern is also reflected in this very high level summary of Twitter.
So this is a you know, this is a very, very high level sort of picture.
But you get against the sense that.
You know, for instance, there are over a billion people who have accounts, but almost half of them have never sent a tweet.
So in other words, more than half of them have been quite passive in this community.
The average number of people who follow supposing I have an account,
Aboriginal people who are listening to my tweets is 208, which is quite a large number.
But at the same time, we know that, you know, about one one third,
one fourth of the one third of the accounts, about 400 million accounts have no followers at all.
So no one's actually following them. And on the other hand, there are people we all know who, you know, this is one person, Katy Perry.
But we have you know, we have Donald Trump who is being followed by millions of people.
So this is another instance of a world which has it's very large and a very few.
Account holders. Very few people, in fact, have a lot of connections.
Most people have no connections at all. So that's another instance of this feature of the law of the Few.
So here's another example. This is taken form Nutella, which is an online forum, and it's a typical example of peer to peer networks.
You could you could take you could take your favourite peer to peer network.
You could take forums or blogs. And they have this feature that.
Just to be very brief here you have this feature that.
Very small fraction. In this instance, it's 25% of the people on this on this network provide five and 70%.
You know, almost two thirds of the people provide no files at all.
So this is the world in which most of the activity is being most of the goods, the information,
the files are being provided by a very, very small fraction in roughly 25% of the network.
So this is another instance of what I will refer to as the law of the few.
So here's a very, very sort of informal summary of the law of the few.
And what it says is. You take any large social group and let's think about information as the main
objective of this information sharing as the main objective of this group.
The lofty view says a majority of individuals, it could be, you know,
80 or even more than 80% of them get most of the information from the remaining 20% who are the active acquirers,
applications, purchasers of information.
And what is interesting is when a number of researchers over the last 50 years have looked at the characteristics,
the demographic, the economic characteristics of people who are influencers, who are opinion leaders.
What's interesting is that there are only relatively minor observable differences between the the few and the others, which makes it.
You know, puzzling. Why is it that you see this very sharp differentiation?
Why is it that you see this specialisation in and in these communities?
So that's the background to the mathematical model that I want to now put up.
And this expression, law of the few I borrowed from a very, very nice,
very readable book by Malcolm Gladwell, which many of you probably seen The Tipping Point.
One of the chapters in this book has this title, The Law of the Few.
And that's the that's where we borrowed this sort of title for this talk and also for a paper I wrote some years ago.
So what I'm going to do in the next 15 minutes or so of 15 or 20 minutes is going to walk you through a mathematical model.
The goal of this model would be to develop a very simple.
Sort of develop some ideas, building off a very simple economic intuition.
When I when I need some information to make a decision whether it's to vote for someone or to buy a computer or to buy a pair of shoes,
I can always invest time and I can buy magazines.
I can buy magazines. I can invest time on online. And I can.
And for myself about what the options are, what what the trade offs are.
But I can also connect to others who are informed, who have informed themselves.
And that, of course, would mean I would have to form links with them. I would have to take time to talk to them, which is also costly.
So the key here is that I can inform myself either about directly,
personally buying information or by talking to others who may have bought some information who may be informed.
And so there are two activities here which are both costly.
And I want to kind of decide, make a decision how much should I invest in one versus how much should I invest in the other?
So once I lay out this model, what I'm going to be doing is I'm going to ask it only makes sense for me to link to you if you if you are informed.
In other words, I, my linking behaviour will be very much shaped by how much activity others have around it.
Okay. And also, if it may be that Allan is not himself reading newspapers, even as he's he's he's himself not actually watching television.
But it may be that he's very well connected with others who's who are very active.
So I might connect to Allan, not because he's himself buying information, but because he's very well connected to others who are doing so.
So I need to keep in mind the network structure that's emerging and the activity level of others, and that's going to help,
you know, tell me what I should be doing, how much information should I be buying and how much should I be linking with others?
And then, of course, we are interested in understanding what's going to be the overall architecture of the network that's going to arise.
And finally, of course, we are especially interested in understanding whether people are going to make well-informed decisions.
Are they going to vote for the right person?
Are they going to buy the right product, or are they going to end up being very poorly informed at the end of the day?
So those are the kinds of questions we want to address.
So this is going to be a few slides with some notation and some concepts.
And, you know, this is the first time I'm giving a public lecture in a mathematics institute.
So I'm going to see whether this is going to be the right level of mathematics.
So. So this is a model where there are many people and I think I would like you to imagine hundreds, maybe thousands of people.
What's happening is that each person okay, so each person is making two choices.
Each person is deciding how much information to buy.
And that's captured by this.
This well. Yeah. Okay.
That's captured by this number, IXI. So this is the information that I buy and then that cost me C of sight sees the positive real number
and it says something about how much time I put in or how many magazines I buy and so forth.
Then there is the linking that I do and I create links.
Okay. And so these are links I create with the other members of this community.
And so it's going to be a vector. I'm just I'm being this is a shorthand.
So we put each link I create I'm going to have.
The way the links are created as you can sort of make out from this expression here,
it's saying that as long as one of us, I or one of us creates a link, the link is created.
And so now for person or the number of links he has is, you know, are these links that he has created.
And for each of the links, he pays a price and that's given by key.
So the only item here, the only that I haven't explained is this function F.
So what is f? F is giving me an idea about how valuable the information I have bought Excite
and how valuable is the information that I'm getting from my neighbours,
the people I have links with. So that's exchange for the effort by my you know, that my neighbours are exert.
So what I'm going to assume is that F is the more information I have, the happier I am.
But of course as I get more and more information, the marginal return, the marginal value of additional information is falling.
And so I'm assuming that F is concave.
So it's a sort of I'm going to put up some pictures to to illustrate what f looks like, but that's the essence of the model.
Okay. And people are going to make these choices simultaneously.
And and just recall, I want to understand how much exile should I be choosing and how many links should I be creating?
So the way we solve models like this in economics is we postulate that people are
going to do trial and error and they're going to try and figure out what to do.
Maybe they will link with others and they will find these other people are actually completely passive.
So it's a waste of time to link with them. Maybe they will buy a lot of information and they will then find out.
There are a lot of other people buying information and it would be more economical
cheaper to link with these people rather than buy information oneself.
So. So there would be all these trial and error ads and experimentation going on.
And at the end of this process,
we hope over time people are going to settle into some pattern and we want to understand what the pattern will be, which would be stable.
And that is what is a way to think about Nash equilibrium.
This is named after a famous mathematician, John Nash.
And the idea here is a profile of Xs and GS or network and information acquisition constitute a Nash equilibrium.
If given what others are doing, I'm happy doing what I have chosen to do.
So so that. So in some sense I don't have any reason to want to change my behaviour.
So it's a stable configuration, if you like, in that sense.
So in a paper with Andrea Galeotti, we prove this theorem and I'll go through the intuition, some ideas underlying the theory.
But let me just sort of read out the theorem.
It says something quite, quite sharp and quite, quite, quite precise.
It says that any Nash equilibrium of the game I described will have this law of the few property.
In other words, the network will have a cooperative free structure.
And I'll show you these networks in a moment. The core is the people who are active.
They are buying information. The periphery is constituted of people who buy no information at all, and they simply link with the core.
And finally the core.
Then the people who are buying information, that's going to be a very small set of people and it's going to become negligible as the population grows.
So that's going to be the that's the prediction of this model. So this is what, you know, core periphery network looks like.
So on the left, I have. A network with a three core nodes.
Each of them is buying five units of information. And on the right, I have a core.
There's just one person who's buying information. Okay. And notice that in both cases, the core is buying 15 units of information.
Everybody else is buying zero units of information.
And they are simply linking with the core plans.
So that's these are two simple examples of Oprah Winfrey networks.
It's just to reiterate, it's just the core, which is buying information, and they are specialising in that.
So the vast majority of people in this community are is not buying any information.
Is just linking with the core. So what are the ideas behind the why is it that any stable configuration is going to have a cooperative structure,
is going to have this law of the few property? So I'm just going to walk you through the main steps of the proof.
And before that, let me just pause in this. Take some water.
So the first observation and the proof is to note that we have this number, which I will call my hat,
which is the point at which the marginal return to information given by f prime of
my hat is exactly equal to the cost of buying information which is given by C.
So imagine I'm a by myself in this world then this is exactly the information I would buy.
I would buy y hat and I would be content because if you look on k function to have bought any
more than I had my marginal return would be smaller than the cost of buying information.
If I bought any less then I would be able to do better by buying a little more.
So that's the first observation. This also means that in any equilibrium it must be the case that I must be getting access to at least y hat.
Because if it were the case that I'm getting access to less than y hat, I could always do better by buying some information myself.
So that's the first thing to note.
What's going to be really surprising in this model is going to be the property that not only must everyone access by hand,
but is going to be true that the society put together will by exactly by how to have information independently of the size of the society.
So that's quite dramatic. And we will see later.
That is incredibly inefficient. Okay. So so why is it that put together people will buy ahead?
So that's. So you should bear that in mind and be a going to at the end of the proof, you will see why that has to be the case.
Okay. The other point to note is that it may be that.
I have connection to people who are buying a lot of information and and I don't buy any information.
So it may be that I actually access a lot more than I had.
And I don't mind it because I'm not buying any information myself. So this F primer y doesn't come into play at all.
Okay. But it must be the case that if I'm buying information myself and I'm link to it now,
then it must be the case that I must be accessing exactly what I had.
Why is that? Well, I'm linked to him. He's buying some information.
If I were getting together with him more than I had, I could lower my own purchases of information.
And I would be better off.
Because if I were getting more than what I had, the marginal return would be smaller than C, the cost of buying information.
So it follows that if is acquiring information is linked to B he must access exactly why had.
Now the next point to note is if I were to form a link with Alan, the link cost me key,
so I should only form a link with him if he's buying enough information.
Because if people are buying very little information linking with him would not be economically justified.
It would be better for me to delete the link and buy the information myself.
So it must be the case that if I link with Alan that means the value of the information is providing me is more than the cost of linking key.
But if that's true for me, it must be true for everyone else.
So if I link with him so much, everyone else link with him.
Okay. So that's a key observation driving us towards the corporate free structure.
Finally note that if I buy some information and I buy some information, we are linked.
Anyone else who buys information must also be linked to him because of the earlier argument.
Okay. Because if I find it attractive to link with him, so almost everyone else in particular,
everyone else who buys information, should also want to link to him.
But that implies that everyone who is buying information is linked to Allah and is linked amongst themselves.
But from point the second bullet point, we know if that was the case,
then it implies that all the people who are buying information are linked amongst
themselves and the total information they are accessing is exactly why that.
So that more or less gives us the proof that the total information in society must be.
Why hat and we have not used the number of people here at any point.
Okay. So you can now begin to see that if y how does the total information acquired?
Anyone in the society who has not bought information must be linked with everyone who has bought
information because from the first bullet point everyone must be accessing at least y hat.
So we have completed the argument that we, you know, the statement of the the theorem.
We have a core group. Everyone's linked to the core group.
The core group itself is putting together y hat. And the final point, the fraction of core members is negligible.
This follows from this step. The second the the bullet point, the second from the bottom.
If I'm going to buy information, if I'm going to link with Allah, I pay a K.
He must be buying a certain minimum amount of information, but we know that the total amount of information is by hat.
Since he is buying a certain minimum amount,
I have basically got upper bound on the number of people who are buying information in this society and this upper bound is
independent of the number of people in society and therefore it follows that the core is going to shrink as the population grows.
So that's the basically the proof of this here.
Now moving on to this whole idea, a key idea, for instance, in the current political climate,
a key idea and a notion that you must have heard and read is this whole idea of fake news,
is this idea that somehow people are not informed when they are making important political decisions.
Now, it's hard to know whether that's true or not. But we can ask ourselves in a community where people are buying information, linking with others,
trying to inform themselves to make the right decision whether enough information is going to be acquired.
And so one way of thinking about that is to think about social welfare.
What do I mean by that? I'm thinking about everyone in this community.
Okay. Has this people function. Up here this.
Bye bye i. And. So what I can do.
Very, very sort of simplistic.
What I could do is I could say the society is doing the right thing if it's maximising.
The pay off of all the people put together. Okay.
And so that's the idea that I'm going to. I'm going to just assume that social welfare is given by the sum of the payoffs.
And then I'm just going to ask, what's the outcome that maximises the sum total of payoffs in this community?
Okay. So the so the key observation.
Okay. And before going into the statement of the proof here.
So the key observation is you can begin to see what the issue is by looking at the picture on the right.
So what's happening in this equilibrium is that there is this person in the centre.
He's buying 15 units of information. It is an equilibrium because what happens?
15. Okay. So I buy I'm entirely self interested in this, in this setting.
So I'm equating f prime a y hat to C, which is a marginal cost.
So I'm equating my private gain to my private cost and it's equated at Y equals 15.
Okay. But what's happening of course, in this community is when I'm buying 15 units,
it's not only me who is gaining from this information, who is benefiting, but everyone else who's connecting to me.
But I'm not taking that into account. I'm only looking at F Prime, which is my marginal, private,
marginal benefit from this information, and I'm equating that to the private marginal cost.
What I should be doing is I should be looking at all the people who are connected to me,
which in this case is off the order of RN because there are people in this community.
And so I should be looking at end times f prime, not just f prime.
Okay. And so that's really the key to understanding this proposition.
What we want in the simple setting of hub support network or star network is
that we want the central active player to be equating end of F prime to see.
Okay, now you can see notice that F is a concave function.
So if I now begin to think about what does it mean to have end times have prime rather than f prime?
You can see that.
It would immediately mean that this airframe would have to be a lot smaller in the social benefit case compared to the equilibrium case.
For a frame to be a lot smaller. Means since F is concave, that F tilde is going to be a lot smaller than the equilibrium choice.
Okay. Sorry would be a lot larger. Okay.
That's how I would lower off prime by making f y to do a lot larger.
So that's really the crux of the welfare analysis that's saying that.
The socially optimal outcome is a hub support network with a single hub.
A core is a centre and the hub chooses y Tilda where y Tilda solves this equation.
So you can you can straightaway see that the hub is going to under invest.
And this under's an investment is going to grow with the size of the population.
So we expect the welfare laws to get larger and larger in this information society as the society gets growth.
Okay. So we're going to take these background results and I'm going to make one very quick sort of very quick extension of the model,
just to give you a feel of how the model can be naturally extended.
What I've done here is I've added not just my neighbours, I've added the neighbours of my neighbours.
Okay. So I gain value from ALLAR, but he's connected to that role and I'll get some information from him as well.
That's what for the rest. Everything here is as before and.
What we get here are, in addition to the earlier corporate free equilibrium where the core is active here, you can get a pure connect to outcome.
So this is a central guy who's totally inactive himself but is wonderfully well connected.
So I go and talk to someone who is a hub. He doesn't buy information himself, but everyone talks to him, so he's very well-informed.
Okay, so that's the idea of a pure connect or passive goal.
That's the new phenomenon that you can get in a world with indirect flow of information.
So these are the background to the mathematical results.
And so let me just summarise this before moving to the experiment.
So what we've got here is a very simple and fairly intuitive mechanism and economic mechanism that generates the law of the few.
In addition, it also gives you some sense of the inefficiencies, the the problems with this framework,
you know, the inadequacy of information that would be bought in this in this community.
So what we want to do is we want to ask whether this model captures human behaviour.
And I'm going to now I have about 15 minutes and I'm going to walk you through a set of
experiments we have done to give you a sense of whether people respond to these trade offs,
whether it leads to specialisation. The Law of the few.
And we will also learn a bit about the welfare properties of.
So this is going to be work. Ongoing work.
Joined with Sing You Troy Blues and Soul and Frederick Moss Song was a post-doctoral fellow with me in Cambridge.
So let me just very briefly. Say a few words about the experiment.
And so I imagine many of you are familiar with experimental methods and in the social sciences.
But what I just want to say here very briefly is first of all,
that this is going to be a large scale experiment in network formation because we
have up to 50 subjects and we are now going to do experiments with 100 subjects.
And you will see that scale is going to be an important factor.
I've already said a few words about how scale is going to magnify the inefficiencies of behaviour,
but we will see it's also going to have important implications for behaviour and interesting ways that we will see in a moment.
So what we do in these experiments is that we're going to have people buy information and form links with each other over 6 minutes.
Okay, we will have them. I'll show you, give you a tutorial on how this experiment works.
And. At the start of every round, people would be assigned a random randomly, they would be assigned an identity number.
And so across rounds they will be mixing just to.
So. So we've. Let me give you an example of the function.
So this is the returns function. With this returns function, you can want to look at the cost of buying information, see.
And if I put in substitute C into the this function and I sold for Y had I get nine.
Okay. So that's the equilibrium prediction. And, and remember, this does not depend on the number of subjects.
Okay? So it's always going to be nine. The cost of linking is 95, which is pretty high.
And we will see what it means in particular is that I only want to form at most one link.
Yes, that's for simplicity. So the network will be very sparse.
And finally, the F function. This is the functional form and in particular that we have written it.
It's for simplicity. So as long it's as long as if it is below 14, it's it's a nice concave function.
And above 14, it sort of becomes linear. Okay.
So this is a typical screen shot from the experiment.
What's happening here is you have this player in yellow and he's called me and he's doing 14 units of effort.
There are many people who have linked with with me.
And those arrows in the links indicate the directionality who's forming links with whom.
And there are all these people on the right hand side of the screen who do not have links with.
And in fact, I'm more than three links away. So on the left screen, you see that there is me here.
And I've got a one link, a two second link and a third link.
So I'm looking at my three neighbourhood and on the right are all the people who are outside my three neighbourhood.
So and I'm putting in some effort, which is 14 units.
And so I'm getting you don't have formed. I formed a link, you know.
And so once I work out the net earnings, I get 37 points.
The other feature of this experiment is that the size of the circle,
the size of the node indicates the axis, whereas the darkness indicates the individual effort.
People are putting it. Okay.
So. Let me.
So if he's trying to show you how. Subjects play this game.
So this is a situation where this is a tutorial for the subjects and this is me.
And what I could do is I could increase my effort.
So I click here and I put in seven units of effort and I become bigger because I've got more access to information.
And so my pay off is 77 points.
And now I can click on, let's say, Mr. One.
And link with him. And when I do that, this is the network.
I have noticed that it's the local network which is up to three three neighbourhoods,
the first neighbourhood, second neighbourhood, third neighbourhood. Okay, so that's the way the, you know, the thing this evolves.
Okay. So what's the prediction given these parameters?
The prediction of the theoretical model is the single hub spoke network.
Where the hub does nine. Everybody has a zero and.
And the payoffs, the equilibrium payoffs will be very similar for the hub.
And this book, the roughly 80, 85 for the Spokane, 81 for the hub.
So the hub is earning slightly less. Okay.
So I'm going to now give you a sense of what happens in this experiment before summarising the results.
Okay. Oops. So I'm going to.
Run a small movie where you would begin to see how.
So this would take about a minute. So the dark nodes are the large effort nodes and you can see they are doing 20.
So it's fairly big and it's dark. And as I see all these people, I start linking with them.
And these are the dynamics in real time. And you see this yellow node which is doing 20 units of effort, which is the maximum allowed.
And gradually people are linking with this node. But it's still.
Uh, you know, evolving the network is sort of evolving, and it's quite confused at this point.
And you should keep the yellow node. You keep your eye on the yellow note and he's still but you see, now he's sort of someone else who has become.
More attractive. There's lots of linking and there are these highly active nodes you see at this point.
There are a lot of active nodes because they are dark and they are putting a lot of work.
They are all doing 20. So this is not a world with lot of specialisation.
So what's the difference between two rounds? So this is within one round.
This is each round is roughly 6 minutes. And I'm showing you that we give her rounds.
The market is really fantastic. Yes, it's in semi continuous time.
Yes, I can increase my effort, I can link, I can delete my links.
And so you see that.
What's interesting is that 13 has gone to zero effort,
but all these people have linked with him and then suddenly people realise it's a bad idea to link with
them and you see that they are now abandoning him one by one and they're going off to link with Mr. 14.
And you see all these sort of links pointing to 14, and he started shirking.
He was doing 20, but he's not doing 18. And but, you know, you can see and you can see that the dark nodes, the.
Very many fewer dark note specialisation is emerging as we go along.
And just for people, I think we're really working hard. Everyone else is just linking with these hard working nodes.
14 and now shrunk. Going off and gone off to zero. Okay.
He's completely he's choking fully. Right. And of course, people will now start abandoning him and go to someone else.
So what happened between two different roles? Nothing much happens.
I'm just replaying the round. This is one round. One minute road is over.
So this is actually trying to collect new. This is collecting call it the same people.
So we have six rounds and each of them are 6 minutes.
And so for a group of 50 people, you have you know, you have six rounds.
And this is just a way to give them a we randomly reassign their ID numbers.
Yeah, that's the main change. But you see now there are just two people who are active, maybe three, maybe four, but everyone else is passive.
They're just linking. Okay. You do have a few isolated nodes.
Yes, but you can see it's very few. Most people are connected through.
Of the sites, including the access.
And they are doing nine. Remember, that was the bar they just bought nine.
And they are staying put. For some reason no one has noticed they are dead. Okay, but.
But see, but now you look at this community, there are a few people doing nine or ten, but everyone else is doing zero or one.
Okay. So you're and you can see the emergence of.
A call. You can see the emergence of specialisation and.
You know, and these are the sort of features that we will pick up when we start doing the statistical analysis.
So. Okay.
I think I'm. So now you see this, this person in the centre and he's got most of the links.
There's one of the person below was doing, was doing 11, but 35 is doing I think 16 and he's essentially got everyone linked to him.
Okay. So that's that gives you a flavour of what happens in this experiment.
Kate. So we're going to look at specialisation and you see this very, very clearly here.
Most people are doing no effort at all. This is the average effort, information purchase.
And this is especially true in the NFL 250, where more than 50% of the people are doing.
Basically, they're not buying any information at all. Okay. And so you see this very nice 8020 rule.
Some of you might have read about this and, you know, if you have an economics background, but what you see here is on the x axis,
I'm looking at the cumulative share of people from the lowest to highest output on the Y axis.
I'm looking at cumulative share of efforts.
And what I would like you to focus on is supposing I look at 80% of the lowest effort people you see out here,
they're providing barely 20% of the efforts in the large group.
And if I look at the smallest group and equal to four, you see that in fact, it's a lot more pronounced as I go into larger groups.
Okay. So so that's the first demonstration of the specialisation and effort.
And you see this again with the if I look at this picture here, I see that this is another way of looking at the data.
When you look at this picture, you see that for the and equal to 50 experiment,
more than 50% of the subjects have done essentially are doing zero information purchase.
On the other hand, you have almost 10% of the subjects were doing almost 20 units of purchase.
Get this notice that this is wildly out of the prediction.
The predictions was nine units. Okay, they should never be buying more than nine because privately the marginal return beyond nine falls below C.
So there is no reason to be buying beyond nine units.
And yet you have clearly, you know, a fair number of people, maybe 5 to 10% buying, you know,
close to 20 units of information, which of course, never happens with eight subjects.
So with eight subjects, pretty much no one buys more than ten units.
That's the red line.
The other interesting feature of this experiment, which was also true in the theoretical model, is that access is basically very equal.
Most people are getting access to the same amount of information that's being captured.
If it were perfectly equal, you would get the lines matching the 45 degrees line, but it's pretty close to 45 degrees.
Okay. So so it's it's a very, very egalitarian society in terms of information access.
Now we look at the network and what we see here is even more striking than the information purchase.
If you look at the the blue line, you see that, you know, 80% of the.
Subjects along the X axis, 80% of the subjects are getting barely 10% of the links so badly.
Most of the society, 80% of the society is barely getting 10% of the followers, if you like.
And so this is even more specialised, more unequal than the purchase of information.
And you see this and this. Another way to look at this data is to look at the cumulative distribution.
And you see here that, you know, basically more than 95% of people are hardly getting any links at all.
So so almost all the incoming links in this society are to less than 5% of the society.
So now what I wanted to do was to look at the look a little more closely at the.
The hubs and how much information to buy and how does that vary with the number of subjects?
So a key, key feature of this experiment is this particular picture.
Okay. There are all these people who are buying way, way too much information.
Okay. They shouldn't be buying. No one should be buying more than nine. Here you have a lot of people buying, you know, a lot of information.
So the question is, how does it vary with the group size?
And this picture begins to give you a first impression of this, you know, of this excess of searches of information.
And this one is even better. This is people buying more than 15 units of information.
And what you see here is in the in the smaller group experiments, you know, the red one is, I think, probably the best one to look at.
There's basically almost no one buying more than 15 units, whereas in the large group experiments with 50 subjects,
you have almost 10% of the subjects buying, you know, in excess of 15 units, which is wildly beyond what the theory would predict.
It's wildly beyond what is individually rational. So that's the you know, that's the big question.
Why is it that people are doing this? Okay.
And the consequence of that is this picture here, which tells you that people who are not buying any information,
who are spooks, who are just linking, are the red guides.
And they are earning a lot more than the equilibrium would predict and they are earning a lot more than the hub's.
Remember, the prediction was the hubs should be earning roughly 80 and the spooks should be earning roughly 80 a little more than them.
Okay. What you see in the data here is that the spooks.
Are earning a lot more and they're earning a lot more because the hubs are buying so much information, it's not surprising they're earning more.
What's more puzzling? Why is it the hubs earning so much less?
You know, they're earning almost 30 to 40% less than the prediction.
So so that's sort of the big puzzle.
And you see when you look at the welfare turning, you know, finally to the welfare question,
you get the opposite picture because the hubs are buying so much information.
Everybody is accessing more information than they would have been accessing an equilibrium.
And so you see that the average pay offs are larger. The black line is the theoretical prediction.
And so because people are buying a lot more information and they should be buying everybody else who's benefiting.
You know, very significantly.
And so the pay offs are a lot higher than the equilibrium prediction, and they are a lot lower in the small subject experiments.
So expanding the group size is actually good for welfare.
You know, and this is just aggregating that.
What you see here is that in the small group experiments, pay offs are below the equilibrium prediction.
So already we know the equilibrium is bad, but behaviour is worse than the equilibrium.
Whereas here with the large group behaviour is, you know, because of the excess information purchase relative to equilibrium,
total welfare is a lot higher than, than the equilibrium prediction.
So I think I'm out of time.
So what I've tried to do is to give you a feel of how economists work on problems relating to networks, how they look at social phenomena,
which is, you know, important phenomena like specialisation and effort and network structure that emerges from the specialisation.
Develop mathematical models to understand what the mechanisms are.
An important feature of the work economists do is ask questions about welfare.
And so in the talk today, I've given you a sense of how individual motivations and their behaviour could be out of line with what could be,
what would be collectively desirable.
And then we want to understand whether these models are accurate as a good way of thinking about how people actually behave.
And increasingly, economists conduct experiments both in the laboratory but also in the field.
And indeed, more and more in the field.
And the idea is, we want to ask whether the mechanisms that we have developed, we've explored in our mathematical models,
in fact, work to what extent they work and to what extent they are not quite capturing what drives human beings.
And so what we what we saw in these experiments today was the specialisation that was predicted by the model is very much evident in the experiments.
You have a lot of specialisation in information purchase. You get a lot of specialisation and linking.
But in terms of the exact magnitude of information purchases,
you see that behaviour in these experiments is clearly out of line with, you know, with the models.
People are being driven somehow to become hubs and to become hubs.
They have to they seem to exert far more effort than they really should be doing.
And that leads them to earn a lot less than they should be doing.
But on the other hand, it has this benefit that it makes everyone else better off.
And in the aggregate, it could be a good thing.
So the puzzle for us as as experimenters and as theorists then, is what is it that's driving the hubs to do to make the effort that they do?
And is it that they don't understand what's happening? They don't understand the payoffs?
Or is it that they're driven by an urge to become hubs, you know,
and they have to get pleasure or they get happiness or they feel good about being hubs.
So this is not a world in which hubs are being paid anything by anyone.
So they want to be hubs for reasons which we don't fully understand.
So it's sort of very much ongoing work.
And the next step in our project is going to be to look more closely at the data,
to understand whether the hubs are not understanding their payoffs or they somehow have other motivations,
and if so, develop richer models, mathematical models that can capture these other motivations that hubs might have.
Jen I'm going to stop at this point.