1 00:00:15,790 --> 00:00:22,990 Thank you, Anna, and thank you to for inviting me to give this talk. 2 00:00:23,320 --> 00:00:26,350 I hope you can hear me clearly at the end. 3 00:00:26,410 --> 00:00:30,400 Yes. Okay. So it's a pleasure to be here. 4 00:00:30,410 --> 00:00:33,610 This is the first time I'm visiting this building. 5 00:00:34,480 --> 00:00:37,600 And I was recently in Oxford. 6 00:00:37,600 --> 00:00:41,530 So very, very pleased to be in the Mathematical Institute. 7 00:00:42,250 --> 00:00:45,910 A little nervous, especially after a lot of said. 8 00:00:47,560 --> 00:00:54,910 I'm sort of dimly aware that Euler worked on issues of graft a long, long time ago, maybe. 9 00:00:55,630 --> 00:01:09,760 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, 10 00:01:10,240 --> 00:01:15,130 and it's going to move forward into some online social networks. 11 00:01:15,790 --> 00:01:25,030 And and then I'm going to ask questions about how can we account for phenomena that different social scientists have been talking about? 12 00:01:25,510 --> 00:01:32,590 And I'm going to have a mathematical model to to try and explain the the phenomena 13 00:01:33,220 --> 00:01:40,750 that are off the few this mathematical model will turn on and economic mechanism. 14 00:01:41,110 --> 00:01:45,460 And I'm going to try and convey the sense of this mechanism to you. 15 00:01:46,870 --> 00:01:48,490 And after having done that, 16 00:01:49,300 --> 00:02:01,150 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. 17 00:02:01,540 --> 00:02:07,179 And I'm going to show you some experiments that that we've been conducting. 18 00:02:07,180 --> 00:02:09,160 In fact, we are still doing these experiments. 19 00:02:09,550 --> 00:02:16,480 And it's and I'm going to spend a fair bit of time talking about these experiments and what we learn about this, 20 00:02:17,200 --> 00:02:22,420 about the mathematical model from the findings of the experiments. 21 00:02:23,350 --> 00:02:30,970 And there will be things that we will learn which will reassure us about the mathematical model, 22 00:02:31,330 --> 00:02:41,080 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. 23 00:02:41,440 --> 00:02:46,360 And so that's the that's the, you know, the broad outline of of the talk. 24 00:02:47,320 --> 00:02:55,240 And so it's going to combine social sciences, it's going to combine some mathematics, and it's going to combine experimental methods. 25 00:02:56,170 --> 00:03:03,879 And so I hope that you will get a flavour of how economists work with mathematics, 26 00:03:03,880 --> 00:03:13,390 but also how they use experimental methods to enrich their models and advance the, 27 00:03:13,750 --> 00:03:20,590 you know, the, if you like, the nature of the subject, you know, the scope of their understanding of the subject. 28 00:03:20,890 --> 00:03:24,100 Okay. So it's going to be methodological to some extent. 29 00:03:24,100 --> 00:03:34,030 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, 30 00:03:34,030 --> 00:03:38,230 but also the specific phenomenon that we're going to be talking about. 31 00:03:38,950 --> 00:03:48,790 So what is the law of the few? So so let me start by saying a few words about the origins of this. 32 00:03:50,260 --> 00:03:55,959 So this really goes back to the forties, the 1940s in the United States. 33 00:03:55,960 --> 00:04:05,980 And the background here is that this was a this was a period where mass media was really coming into it all. 34 00:04:06,340 --> 00:04:11,350 Radio, television, newspapers were really coming out in a big way. 35 00:04:11,590 --> 00:04:18,490 And so there was this. And you can see the parallel to what's happening now in a moment. 36 00:04:18,700 --> 00:04:22,780 But what the thought was that with the emergence of mass media. 37 00:04:24,690 --> 00:04:30,780 Social networks of communication would become second order would basically disappear. 38 00:04:31,200 --> 00:04:38,639 And so you will have, on the one hand, these big mass media, they will directly communicate. 39 00:04:38,640 --> 00:04:43,920 They will directly convey information to to ordinary people who will, on the one hand, 40 00:04:43,920 --> 00:04:47,580 be very informed because they will have all those mass media talking to them. 41 00:04:47,880 --> 00:04:57,570 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, 42 00:04:57,570 --> 00:05:00,270 ordinary consumers, because it would be so powerful. 43 00:05:00,870 --> 00:05:13,290 So in that context, this these these studies were done by sociologists based in New York, at Columbia University, and in particular, 44 00:05:13,290 --> 00:05:23,790 I would like to draw your attention to always felt who was Viennese born sociologists would move to New York and what they 45 00:05:23,790 --> 00:05:31,860 did in this work in the forties and then subsequently there's been a lot of work in this field is they essentially showed. 46 00:05:33,950 --> 00:05:43,760 A very. So so they found out what they later termed a two way flow of information model of communication. 47 00:05:44,000 --> 00:05:51,350 What do they mean by that? They had this very simple sort of idea that indeed they started with the hypothesis that 48 00:05:51,500 --> 00:05:55,310 social networks and social communication would be becoming less and less important. 49 00:05:56,090 --> 00:06:00,470 But when they went and did this service in different parts of the United States, 50 00:06:00,770 --> 00:06:07,790 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. 51 00:06:08,360 --> 00:06:15,230 And most of the people who were not actually listening to the radio or watching the television or reading the newspapers, 52 00:06:15,590 --> 00:06:22,160 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. 53 00:06:22,460 --> 00:06:28,190 And it's a small set of people who are actually having access to the outside world. 54 00:06:28,780 --> 00:06:32,120 Okay. So so this basic observation. 55 00:06:32,120 --> 00:06:33,139 So in their study, 56 00:06:33,140 --> 00:06:44,330 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. 57 00:06:44,600 --> 00:06:54,050 And they were then communicating and summarising this information they have gathered to their fellow citizens in their communities. 58 00:06:54,440 --> 00:07:02,690 So that's sort of the first sort of, you know, the first step in our you know, in our talk today. 59 00:07:02,720 --> 00:07:07,180 So so these are the two books that were published. 60 00:07:07,220 --> 00:07:11,990 People's Choice was about how politics, political decision making, 61 00:07:11,990 --> 00:07:20,450 voting behaviour was shaped not so much by mass media, but for the vast majority of people they surveyed, 62 00:07:20,780 --> 00:07:25,999 it was shaped by their personal preferences, but also by through their communication, 63 00:07:26,000 --> 00:07:30,410 their discussions with these opinion leaders and their local communities. 64 00:07:31,430 --> 00:07:36,260 And subsequently, in a book published in 1955, Personal Influence. 65 00:07:38,450 --> 00:07:46,969 Cats and lizards then expanded the scope of their study beyond politics to address a wide 66 00:07:46,970 --> 00:07:52,370 variety of decisions people make in day to day life and how it's not just in politics, 67 00:07:52,370 --> 00:07:55,940 but also in this many different spheres of life. 68 00:07:57,680 --> 00:08:04,430 Ordinary citizens, ordinary consumers, were not really directly exposed to the mass media, 69 00:08:04,430 --> 00:08:08,840 but indeed they had these intermediaries, a very small set of intermediaries. 70 00:08:10,040 --> 00:08:16,730 So moving forward, if we now move to 2016, 2017, 71 00:08:17,570 --> 00:08:26,209 I want to give you a sense that this idea that a very small fraction of people have access somehow to 72 00:08:26,210 --> 00:08:32,570 lots and lots of information and are indeed being followed and watched by the rest of the population. 73 00:08:33,440 --> 00:08:41,600 To some extent, that sort of pattern is also reflected in this very high level summary of Twitter. 74 00:08:43,340 --> 00:08:48,290 So this is a you know, this is a very, very high level sort of picture. 75 00:08:48,290 --> 00:08:50,720 But you get against the sense that. 76 00:08:52,200 --> 00:08:58,500 You know, for instance, there are over a billion people who have accounts, but almost half of them have never sent a tweet. 77 00:08:58,830 --> 00:09:05,280 So in other words, more than half of them have been quite passive in this community. 78 00:09:06,030 --> 00:09:10,200 The average number of people who follow supposing I have an account, 79 00:09:10,200 --> 00:09:16,740 Aboriginal people who are listening to my tweets is 208, which is quite a large number. 80 00:09:17,430 --> 00:09:23,309 But at the same time, we know that, you know, about one one third, 81 00:09:23,310 --> 00:09:28,530 one fourth of the one third of the accounts, about 400 million accounts have no followers at all. 82 00:09:29,280 --> 00:09:36,780 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. 83 00:09:36,780 --> 00:09:42,330 But we have you know, we have Donald Trump who is being followed by millions of people. 84 00:09:42,870 --> 00:09:50,040 So this is another instance of a world which has it's very large and a very few. 85 00:09:52,550 --> 00:09:56,990 Account holders. Very few people, in fact, have a lot of connections. 86 00:09:57,020 --> 00:10:03,530 Most people have no connections at all. So that's another instance of this feature of the law of the Few. 87 00:10:05,270 --> 00:10:14,660 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. 88 00:10:15,320 --> 00:10:18,559 You could you could take you could take your favourite peer to peer network. 89 00:10:18,560 --> 00:10:23,090 You could take forums or blogs. And they have this feature that. 90 00:10:24,350 --> 00:10:27,350 Just to be very brief here you have this feature that. 91 00:10:28,500 --> 00:10:40,660 Very small fraction. In this instance, it's 25% of the people on this on this network provide five and 70%. 92 00:10:40,670 --> 00:10:44,100 You know, almost two thirds of the people provide no files at all. 93 00:10:44,430 --> 00:10:51,719 So this is the world in which most of the activity is being most of the goods, the information, 94 00:10:51,720 --> 00:10:59,130 the files are being provided by a very, very small fraction in roughly 25% of the network. 95 00:10:59,700 --> 00:11:04,890 So this is another instance of what I will refer to as the law of the few. 96 00:11:06,390 --> 00:11:12,210 So here's a very, very sort of informal summary of the law of the few. 97 00:11:12,570 --> 00:11:21,390 And what it says is. You take any large social group and let's think about information as the main 98 00:11:22,110 --> 00:11:25,950 objective of this information sharing as the main objective of this group. 99 00:11:26,880 --> 00:11:31,640 The lofty view says a majority of individuals, it could be, you know, 100 00:11:32,010 --> 00:11:41,219 80 or even more than 80% of them get most of the information from the remaining 20% who are the active acquirers, 101 00:11:41,220 --> 00:11:43,290 applications, purchasers of information. 102 00:11:44,370 --> 00:11:51,959 And what is interesting is when a number of researchers over the last 50 years have looked at the characteristics, 103 00:11:51,960 --> 00:11:57,120 the demographic, the economic characteristics of people who are influencers, who are opinion leaders. 104 00:11:57,720 --> 00:12:07,650 What's interesting is that there are only relatively minor observable differences between the the few and the others, which makes it. 105 00:12:08,730 --> 00:12:12,830 You know, puzzling. Why is it that you see this very sharp differentiation? 106 00:12:12,840 --> 00:12:18,180 Why is it that you see this specialisation in and in these communities? 107 00:12:18,580 --> 00:12:24,750 So that's the background to the mathematical model that I want to now put up. 108 00:12:24,750 --> 00:12:31,139 And this expression, law of the few I borrowed from a very, very nice, 109 00:12:31,140 --> 00:12:36,810 very readable book by Malcolm Gladwell, which many of you probably seen The Tipping Point. 110 00:12:37,350 --> 00:12:41,100 One of the chapters in this book has this title, The Law of the Few. 111 00:12:41,100 --> 00:12:48,930 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. 112 00:12:50,160 --> 00:12:59,850 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. 113 00:13:01,140 --> 00:13:06,060 The goal of this model would be to develop a very simple. 114 00:13:08,400 --> 00:13:13,500 Sort of develop some ideas, building off a very simple economic intuition. 115 00:13:14,070 --> 00:13:22,590 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, 116 00:13:23,640 --> 00:13:27,719 I can always invest time and I can buy magazines. 117 00:13:27,720 --> 00:13:31,260 I can buy magazines. I can invest time on online. And I can. 118 00:13:32,390 --> 00:13:38,420 And for myself about what the options are, what what the trade offs are. 119 00:13:38,720 --> 00:13:43,220 But I can also connect to others who are informed, who have informed themselves. 120 00:13:43,520 --> 00:13:50,630 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. 121 00:13:51,200 --> 00:13:57,409 So the key here is that I can inform myself either about directly, 122 00:13:57,410 --> 00:14:03,920 personally buying information or by talking to others who may have bought some information who may be informed. 123 00:14:04,520 --> 00:14:07,490 And so there are two activities here which are both costly. 124 00:14:08,510 --> 00:14:14,870 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? 125 00:14:15,980 --> 00:14:29,180 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. 126 00:14:29,390 --> 00:14:37,840 In other words, I, my linking behaviour will be very much shaped by how much activity others have around it. 127 00:14:38,180 --> 00:14:48,560 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. 128 00:14:48,890 --> 00:14:54,350 But it may be that he's very well connected with others who's who are very active. 129 00:14:54,710 --> 00:15:01,430 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. 130 00:15:02,120 --> 00:15:09,320 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, 131 00:15:11,060 --> 00:15:18,410 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? 132 00:15:18,980 --> 00:15:26,390 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. 133 00:15:26,930 --> 00:15:34,070 And finally, of course, we are especially interested in understanding whether people are going to make well-informed decisions. 134 00:15:34,580 --> 00:15:36,500 Are they going to vote for the right person? 135 00:15:36,740 --> 00:15:43,070 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? 136 00:15:44,780 --> 00:15:47,930 So those are the kinds of questions we want to address. 137 00:15:49,130 --> 00:15:55,850 So this is going to be a few slides with some notation and some concepts. 138 00:15:56,720 --> 00:16:02,230 And, you know, this is the first time I'm giving a public lecture in a mathematics institute. 139 00:16:02,240 --> 00:16:06,440 So I'm going to see whether this is going to be the right level of mathematics. 140 00:16:06,450 --> 00:16:15,350 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. 141 00:16:16,840 --> 00:16:23,410 What's happening is that each person okay, so each person is making two choices. 142 00:16:24,490 --> 00:16:28,530 Each person is deciding how much information to buy. 143 00:16:28,960 --> 00:16:32,680 And that's captured by this. 144 00:16:36,510 --> 00:16:39,889 This well. Yeah. Okay. 145 00:16:39,890 --> 00:16:51,770 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 146 00:16:51,770 --> 00:16:57,440 and it says something about how much time I put in or how many magazines I buy and so forth. 147 00:16:58,340 --> 00:17:03,800 Then there is the linking that I do and I create links. 148 00:17:04,150 --> 00:17:09,350 Okay. And so these are links I create with the other members of this community. 149 00:17:09,740 --> 00:17:13,460 And so it's going to be a vector. I'm just I'm being this is a shorthand. 150 00:17:13,700 --> 00:17:18,140 So we put each link I create I'm going to have. 151 00:17:19,420 --> 00:17:25,479 The way the links are created as you can sort of make out from this expression here, 152 00:17:25,480 --> 00:17:31,210 it's saying that as long as one of us, I or one of us creates a link, the link is created. 153 00:17:31,570 --> 00:17:39,160 And so now for person or the number of links he has is, you know, are these links that he has created. 154 00:17:39,520 --> 00:17:43,750 And for each of the links, he pays a price and that's given by key. 155 00:17:44,980 --> 00:17:49,870 So the only item here, the only that I haven't explained is this function F. 156 00:17:50,470 --> 00:17:58,180 So what is f? F is giving me an idea about how valuable the information I have bought Excite 157 00:17:58,510 --> 00:18:02,530 and how valuable is the information that I'm getting from my neighbours, 158 00:18:02,800 --> 00:18:11,710 the people I have links with. So that's exchange for the effort by my you know, that my neighbours are exert. 159 00:18:13,030 --> 00:18:19,150 So what I'm going to assume is that F is the more information I have, the happier I am. 160 00:18:19,900 --> 00:18:26,320 But of course as I get more and more information, the marginal return, the marginal value of additional information is falling. 161 00:18:26,590 --> 00:18:29,260 And so I'm assuming that F is concave. 162 00:18:30,410 --> 00:18:39,610 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. 163 00:18:40,090 --> 00:18:43,360 Okay. And people are going to make these choices simultaneously. 164 00:18:43,960 --> 00:18:52,300 And and just recall, I want to understand how much exile should I be choosing and how many links should I be creating? 165 00:18:57,380 --> 00:19:04,340 So the way we solve models like this in economics is we postulate that people are 166 00:19:04,340 --> 00:19:08,510 going to do trial and error and they're going to try and figure out what to do. 167 00:19:08,840 --> 00:19:13,850 Maybe they will link with others and they will find these other people are actually completely passive. 168 00:19:13,970 --> 00:19:20,150 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. 169 00:19:20,150 --> 00:19:23,540 There are a lot of other people buying information and it would be more economical 170 00:19:23,540 --> 00:19:27,680 cheaper to link with these people rather than buy information oneself. 171 00:19:28,250 --> 00:19:31,940 So. So there would be all these trial and error ads and experimentation going on. 172 00:19:32,330 --> 00:19:33,979 And at the end of this process, 173 00:19:33,980 --> 00:19:42,440 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. 174 00:19:42,860 --> 00:19:48,290 And that is what is a way to think about Nash equilibrium. 175 00:19:48,320 --> 00:19:51,560 This is named after a famous mathematician, John Nash. 176 00:19:52,010 --> 00:20:03,080 And the idea here is a profile of Xs and GS or network and information acquisition constitute a Nash equilibrium. 177 00:20:03,620 --> 00:20:08,630 If given what others are doing, I'm happy doing what I have chosen to do. 178 00:20:09,200 --> 00:20:14,210 So so that. So in some sense I don't have any reason to want to change my behaviour. 179 00:20:14,480 --> 00:20:18,560 So it's a stable configuration, if you like, in that sense. 180 00:20:20,120 --> 00:20:29,920 So in a paper with Andrea Galeotti, we prove this theorem and I'll go through the intuition, some ideas underlying the theory. 181 00:20:29,930 --> 00:20:33,720 But let me just sort of read out the theorem. 182 00:20:33,740 --> 00:20:40,130 It says something quite, quite sharp and quite, quite, quite precise. 183 00:20:40,160 --> 00:20:46,820 It says that any Nash equilibrium of the game I described will have this law of the few property. 184 00:20:47,360 --> 00:20:51,530 In other words, the network will have a cooperative free structure. 185 00:20:52,700 --> 00:20:57,790 And I'll show you these networks in a moment. The core is the people who are active. 186 00:20:57,800 --> 00:21:06,470 They are buying information. The periphery is constituted of people who buy no information at all, and they simply link with the core. 187 00:21:07,160 --> 00:21:08,690 And finally the core. 188 00:21:08,720 --> 00:21:17,120 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. 189 00:21:18,350 --> 00:21:26,360 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. 190 00:21:26,630 --> 00:21:32,540 So on the left, I have. A network with a three core nodes. 191 00:21:32,810 --> 00:21:38,600 Each of them is buying five units of information. And on the right, I have a core. 192 00:21:38,960 --> 00:21:46,670 There's just one person who's buying information. Okay. And notice that in both cases, the core is buying 15 units of information. 193 00:21:47,300 --> 00:21:51,230 Everybody else is buying zero units of information. 194 00:21:51,230 --> 00:21:54,460 And they are simply linking with the core plans. 195 00:21:55,070 --> 00:22:01,280 So that's these are two simple examples of Oprah Winfrey networks. 196 00:22:02,660 --> 00:22:08,270 It's just to reiterate, it's just the core, which is buying information, and they are specialising in that. 197 00:22:08,930 --> 00:22:14,580 So the vast majority of people in this community are is not buying any information. 198 00:22:14,970 --> 00:22:28,650 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, 199 00:22:28,650 --> 00:22:35,970 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. 200 00:22:37,050 --> 00:22:40,590 And before that, let me just pause in this. Take some water. 201 00:22:50,810 --> 00:22:57,590 So the first observation and the proof is to note that we have this number, which I will call my hat, 202 00:22:58,100 --> 00:23:04,790 which is the point at which the marginal return to information given by f prime of 203 00:23:04,790 --> 00:23:09,050 my hat is exactly equal to the cost of buying information which is given by C. 204 00:23:09,920 --> 00:23:15,440 So imagine I'm a by myself in this world then this is exactly the information I would buy. 205 00:23:15,440 --> 00:23:21,019 I would buy y hat and I would be content because if you look on k function to have bought any 206 00:23:21,020 --> 00:23:26,150 more than I had my marginal return would be smaller than the cost of buying information. 207 00:23:26,500 --> 00:23:30,770 If I bought any less then I would be able to do better by buying a little more. 208 00:23:31,340 --> 00:23:42,260 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. 209 00:23:42,560 --> 00:23:49,700 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. 210 00:23:51,100 --> 00:23:53,680 So that's the first thing to note. 211 00:23:54,670 --> 00:24:05,230 What's going to be really surprising in this model is going to be the property that not only must everyone access by hand, 212 00:24:05,800 --> 00:24:15,430 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. 213 00:24:16,840 --> 00:24:20,980 So that's quite dramatic. And we will see later. 214 00:24:21,250 --> 00:24:30,030 That is incredibly inefficient. Okay. So so why is it that put together people will buy ahead? 215 00:24:30,430 --> 00:24:36,580 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. 216 00:24:38,850 --> 00:24:44,040 Okay. The other point to note is that it may be that. 217 00:24:45,270 --> 00:24:53,049 I have connection to people who are buying a lot of information and and I don't buy any information. 218 00:24:53,050 --> 00:24:56,100 So it may be that I actually access a lot more than I had. 219 00:24:56,490 --> 00:25:02,490 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. 220 00:25:02,940 --> 00:25:09,710 Okay. But it must be the case that if I'm buying information myself and I'm link to it now, 221 00:25:10,340 --> 00:25:14,300 then it must be the case that I must be accessing exactly what I had. 222 00:25:14,780 --> 00:25:18,410 Why is that? Well, I'm linked to him. He's buying some information. 223 00:25:18,860 --> 00:25:24,860 If I were getting together with him more than I had, I could lower my own purchases of information. 224 00:25:25,160 --> 00:25:26,209 And I would be better off. 225 00:25:26,210 --> 00:25:32,840 Because if I were getting more than what I had, the marginal return would be smaller than C, the cost of buying information. 226 00:25:33,620 --> 00:25:41,060 So it follows that if is acquiring information is linked to B he must access exactly why had. 227 00:25:44,140 --> 00:25:50,350 Now the next point to note is if I were to form a link with Alan, the link cost me key, 228 00:25:51,520 --> 00:25:55,300 so I should only form a link with him if he's buying enough information. 229 00:25:55,690 --> 00:26:00,969 Because if people are buying very little information linking with him would not be economically justified. 230 00:26:00,970 --> 00:26:04,660 It would be better for me to delete the link and buy the information myself. 231 00:26:05,650 --> 00:26:15,480 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. 232 00:26:15,790 --> 00:26:18,880 But if that's true for me, it must be true for everyone else. 233 00:26:19,450 --> 00:26:22,660 So if I link with him so much, everyone else link with him. 234 00:26:23,560 --> 00:26:28,210 Okay. So that's a key observation driving us towards the corporate free structure. 235 00:26:30,570 --> 00:26:35,880 Finally note that if I buy some information and I buy some information, we are linked. 236 00:26:37,510 --> 00:26:42,880 Anyone else who buys information must also be linked to him because of the earlier argument. 237 00:26:43,280 --> 00:26:48,280 Okay. Because if I find it attractive to link with him, so almost everyone else in particular, 238 00:26:48,280 --> 00:26:51,010 everyone else who buys information, should also want to link to him. 239 00:26:51,940 --> 00:26:57,910 But that implies that everyone who is buying information is linked to Allah and is linked amongst themselves. 240 00:26:58,660 --> 00:27:03,640 But from point the second bullet point, we know if that was the case, 241 00:27:04,390 --> 00:27:08,020 then it implies that all the people who are buying information are linked amongst 242 00:27:08,020 --> 00:27:12,460 themselves and the total information they are accessing is exactly why that. 243 00:27:13,150 --> 00:27:18,219 So that more or less gives us the proof that the total information in society must be. 244 00:27:18,220 --> 00:27:23,260 Why hat and we have not used the number of people here at any point. 245 00:27:24,370 --> 00:27:29,470 Okay. So you can now begin to see that if y how does the total information acquired? 246 00:27:30,160 --> 00:27:35,440 Anyone in the society who has not bought information must be linked with everyone who has bought 247 00:27:35,440 --> 00:27:41,410 information because from the first bullet point everyone must be accessing at least y hat. 248 00:27:42,280 --> 00:27:49,420 So we have completed the argument that we, you know, the statement of the the theorem. 249 00:27:50,380 --> 00:27:55,490 We have a core group. Everyone's linked to the core group. 250 00:27:55,510 --> 00:28:03,400 The core group itself is putting together y hat. And the final point, the fraction of core members is negligible. 251 00:28:03,640 --> 00:28:10,270 This follows from this step. The second the the bullet point, the second from the bottom. 252 00:28:10,960 --> 00:28:16,720 If I'm going to buy information, if I'm going to link with Allah, I pay a K. 253 00:28:16,720 --> 00:28:23,230 He must be buying a certain minimum amount of information, but we know that the total amount of information is by hat. 254 00:28:23,740 --> 00:28:25,870 Since he is buying a certain minimum amount, 255 00:28:26,110 --> 00:28:32,889 I have basically got upper bound on the number of people who are buying information in this society and this upper bound is 256 00:28:32,890 --> 00:28:40,270 independent of the number of people in society and therefore it follows that the core is going to shrink as the population grows. 257 00:28:40,900 --> 00:28:44,830 So that's the basically the proof of this here. 258 00:28:48,980 --> 00:28:56,030 Now moving on to this whole idea, a key idea, for instance, in the current political climate, 259 00:28:56,030 --> 00:29:03,530 a key idea and a notion that you must have heard and read is this whole idea of fake news, 260 00:29:03,950 --> 00:29:10,220 is this idea that somehow people are not informed when they are making important political decisions. 261 00:29:10,910 --> 00:29:19,520 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, 262 00:29:19,520 --> 00:29:24,920 trying to inform themselves to make the right decision whether enough information is going to be acquired. 263 00:29:26,330 --> 00:29:31,490 And so one way of thinking about that is to think about social welfare. 264 00:29:31,940 --> 00:29:36,500 What do I mean by that? I'm thinking about everyone in this community. 265 00:29:36,950 --> 00:29:42,889 Okay. Has this people function. Up here this. 266 00:29:42,890 --> 00:29:47,830 Bye bye i. And. So what I can do. 267 00:29:48,310 --> 00:29:51,430 Very, very sort of simplistic. 268 00:29:51,640 --> 00:29:57,700 What I could do is I could say the society is doing the right thing if it's maximising. 269 00:29:58,720 --> 00:30:02,300 The pay off of all the people put together. Okay. 270 00:30:04,380 --> 00:30:16,140 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. 271 00:30:16,710 --> 00:30:23,400 And then I'm just going to ask, what's the outcome that maximises the sum total of payoffs in this community? 272 00:30:24,090 --> 00:30:29,830 Okay. So the so the key observation. 273 00:30:30,400 --> 00:30:34,150 Okay. And before going into the statement of the proof here. 274 00:30:34,780 --> 00:30:42,370 So the key observation is you can begin to see what the issue is by looking at the picture on the right. 275 00:30:43,030 --> 00:30:48,520 So what's happening in this equilibrium is that there is this person in the centre. 276 00:30:48,850 --> 00:30:54,150 He's buying 15 units of information. It is an equilibrium because what happens? 277 00:30:54,160 --> 00:31:01,610 15. Okay. So I buy I'm entirely self interested in this, in this setting. 278 00:31:02,180 --> 00:31:07,790 So I'm equating f prime a y hat to C, which is a marginal cost. 279 00:31:07,910 --> 00:31:15,110 So I'm equating my private gain to my private cost and it's equated at Y equals 15. 280 00:31:15,470 --> 00:31:21,830 Okay. But what's happening of course, in this community is when I'm buying 15 units, 281 00:31:21,830 --> 00:31:27,650 it's not only me who is gaining from this information, who is benefiting, but everyone else who's connecting to me. 282 00:31:28,430 --> 00:31:33,709 But I'm not taking that into account. I'm only looking at F Prime, which is my marginal, private, 283 00:31:33,710 --> 00:31:39,530 marginal benefit from this information, and I'm equating that to the private marginal cost. 284 00:31:40,370 --> 00:31:44,389 What I should be doing is I should be looking at all the people who are connected to me, 285 00:31:44,390 --> 00:31:48,770 which in this case is off the order of RN because there are people in this community. 286 00:31:49,430 --> 00:31:53,210 And so I should be looking at end times f prime, not just f prime. 287 00:31:53,570 --> 00:31:58,850 Okay. And so that's really the key to understanding this proposition. 288 00:32:00,440 --> 00:32:05,089 What we want in the simple setting of hub support network or star network is 289 00:32:05,090 --> 00:32:15,350 that we want the central active player to be equating end of F prime to see. 290 00:32:15,470 --> 00:32:20,900 Okay, now you can see notice that F is a concave function. 291 00:32:21,900 --> 00:32:28,290 So if I now begin to think about what does it mean to have end times have prime rather than f prime? 292 00:32:28,710 --> 00:32:29,580 You can see that. 293 00:32:30,670 --> 00:32:38,950 It would immediately mean that this airframe would have to be a lot smaller in the social benefit case compared to the equilibrium case. 294 00:32:39,340 --> 00:32:48,030 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. 295 00:32:48,620 --> 00:32:52,079 Okay. Sorry would be a lot larger. Okay. 296 00:32:52,080 --> 00:32:56,370 That's how I would lower off prime by making f y to do a lot larger. 297 00:32:58,040 --> 00:33:03,560 So that's really the crux of the welfare analysis that's saying that. 298 00:33:05,070 --> 00:33:08,700 The socially optimal outcome is a hub support network with a single hub. 299 00:33:08,880 --> 00:33:15,180 A core is a centre and the hub chooses y Tilda where y Tilda solves this equation. 300 00:33:15,720 --> 00:33:20,460 So you can you can straightaway see that the hub is going to under invest. 301 00:33:21,420 --> 00:33:25,860 And this under's an investment is going to grow with the size of the population. 302 00:33:27,420 --> 00:33:39,130 So we expect the welfare laws to get larger and larger in this information society as the society gets growth. 303 00:33:39,400 --> 00:33:54,729 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, 304 00:33:54,730 --> 00:33:58,990 just to give you a feel of how the model can be naturally extended. 305 00:33:59,020 --> 00:34:05,350 What I've done here is I've added not just my neighbours, I've added the neighbours of my neighbours. 306 00:34:05,490 --> 00:34:11,590 Okay. So I gain value from ALLAR, but he's connected to that role and I'll get some information from him as well. 307 00:34:11,890 --> 00:34:16,690 That's what for the rest. Everything here is as before and. 308 00:34:18,270 --> 00:34:27,330 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. 309 00:34:27,780 --> 00:34:35,530 So this is a central guy who's totally inactive himself but is wonderfully well connected. 310 00:34:35,550 --> 00:34:42,690 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. 311 00:34:43,130 --> 00:34:46,530 Okay, so that's the idea of a pure connect or passive goal. 312 00:34:46,800 --> 00:34:52,740 That's the new phenomenon that you can get in a world with indirect flow of information. 313 00:34:55,400 --> 00:34:58,670 So these are the background to the mathematical results. 314 00:34:59,030 --> 00:35:03,080 And so let me just summarise this before moving to the experiment. 315 00:35:03,890 --> 00:35:12,470 So what we've got here is a very simple and fairly intuitive mechanism and economic mechanism that generates the law of the few. 316 00:35:13,490 --> 00:35:21,410 In addition, it also gives you some sense of the inefficiencies, the the problems with this framework, 317 00:35:21,410 --> 00:35:25,550 you know, the inadequacy of information that would be bought in this in this community. 318 00:35:26,150 --> 00:35:30,710 So what we want to do is we want to ask whether this model captures human behaviour. 319 00:35:31,610 --> 00:35:38,389 And I'm going to now I have about 15 minutes and I'm going to walk you through a set of 320 00:35:38,390 --> 00:35:44,150 experiments we have done to give you a sense of whether people respond to these trade offs, 321 00:35:44,480 --> 00:35:48,320 whether it leads to specialisation. The Law of the few. 322 00:35:48,860 --> 00:35:52,550 And we will also learn a bit about the welfare properties of. 323 00:35:54,400 --> 00:35:57,220 So this is going to be work. Ongoing work. 324 00:35:57,760 --> 00:36:05,170 Joined with Sing You Troy Blues and Soul and Frederick Moss Song was a post-doctoral fellow with me in Cambridge. 325 00:36:09,650 --> 00:36:19,010 So let me just very briefly. Say a few words about the experiment. 326 00:36:21,620 --> 00:36:27,949 And so I imagine many of you are familiar with experimental methods and in the social sciences. 327 00:36:27,950 --> 00:36:31,790 But what I just want to say here very briefly is first of all, 328 00:36:32,240 --> 00:36:38,299 that this is going to be a large scale experiment in network formation because we 329 00:36:38,300 --> 00:36:43,430 have up to 50 subjects and we are now going to do experiments with 100 subjects. 330 00:36:43,430 --> 00:36:46,220 And you will see that scale is going to be an important factor. 331 00:36:46,640 --> 00:36:53,450 I've already said a few words about how scale is going to magnify the inefficiencies of behaviour, 332 00:36:53,780 --> 00:37:01,430 but we will see it's also going to have important implications for behaviour and interesting ways that we will see in a moment. 333 00:37:02,420 --> 00:37:11,600 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. 334 00:37:11,870 --> 00:37:16,700 Okay, we will have them. I'll show you, give you a tutorial on how this experiment works. 335 00:37:19,190 --> 00:37:27,130 And. At the start of every round, people would be assigned a random randomly, they would be assigned an identity number. 336 00:37:27,520 --> 00:37:30,820 And so across rounds they will be mixing just to. 337 00:37:33,350 --> 00:37:38,540 So. So we've. Let me give you an example of the function. 338 00:37:38,540 --> 00:37:47,180 So this is the returns function. With this returns function, you can want to look at the cost of buying information, see. 339 00:37:47,690 --> 00:37:54,080 And if I put in substitute C into the this function and I sold for Y had I get nine. 340 00:37:54,390 --> 00:38:00,980 Okay. So that's the equilibrium prediction. And, and remember, this does not depend on the number of subjects. 341 00:38:01,370 --> 00:38:07,760 Okay? So it's always going to be nine. The cost of linking is 95, which is pretty high. 342 00:38:08,690 --> 00:38:14,120 And we will see what it means in particular is that I only want to form at most one link. 343 00:38:14,660 --> 00:38:18,050 Yes, that's for simplicity. So the network will be very sparse. 344 00:38:19,400 --> 00:38:26,110 And finally, the F function. This is the functional form and in particular that we have written it. 345 00:38:26,780 --> 00:38:33,979 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. 346 00:38:33,980 --> 00:38:40,270 And above 14, it sort of becomes linear. Okay. 347 00:38:40,270 --> 00:38:45,190 So this is a typical screen shot from the experiment. 348 00:38:46,090 --> 00:38:55,300 What's happening here is you have this player in yellow and he's called me and he's doing 14 units of effort. 349 00:38:55,960 --> 00:38:58,960 There are many people who have linked with with me. 350 00:38:59,170 --> 00:39:04,810 And those arrows in the links indicate the directionality who's forming links with whom. 351 00:39:05,350 --> 00:39:10,320 And there are all these people on the right hand side of the screen who do not have links with. 352 00:39:10,330 --> 00:39:17,320 And in fact, I'm more than three links away. So on the left screen, you see that there is me here. 353 00:39:17,770 --> 00:39:21,940 And I've got a one link, a two second link and a third link. 354 00:39:21,940 --> 00:39:28,390 So I'm looking at my three neighbourhood and on the right are all the people who are outside my three neighbourhood. 355 00:39:29,040 --> 00:39:34,930 So and I'm putting in some effort, which is 14 units. 356 00:39:35,140 --> 00:39:41,780 And so I'm getting you don't have formed. I formed a link, you know. 357 00:39:42,230 --> 00:39:46,970 And so once I work out the net earnings, I get 37 points. 358 00:39:48,830 --> 00:39:52,550 The other feature of this experiment is that the size of the circle, 359 00:39:53,090 --> 00:39:59,600 the size of the node indicates the axis, whereas the darkness indicates the individual effort. 360 00:39:59,600 --> 00:40:02,660 People are putting it. Okay. 361 00:40:03,960 --> 00:40:07,380 So. Let me. 362 00:40:16,450 --> 00:40:21,980 So if he's trying to show you how. Subjects play this game. 363 00:40:22,520 --> 00:40:29,179 So this is a situation where this is a tutorial for the subjects and this is me. 364 00:40:29,180 --> 00:40:31,490 And what I could do is I could increase my effort. 365 00:40:32,000 --> 00:40:38,960 So I click here and I put in seven units of effort and I become bigger because I've got more access to information. 366 00:40:40,160 --> 00:40:43,190 And so my pay off is 77 points. 367 00:40:45,110 --> 00:40:48,230 And now I can click on, let's say, Mr. One. 368 00:40:49,280 --> 00:40:53,090 And link with him. And when I do that, this is the network. 369 00:40:53,210 --> 00:40:59,660 I have noticed that it's the local network which is up to three three neighbourhoods, 370 00:40:59,660 --> 00:41:07,400 the first neighbourhood, second neighbourhood, third neighbourhood. Okay, so that's the way the, you know, the thing this evolves. 371 00:41:18,890 --> 00:41:23,459 Okay. So what's the prediction given these parameters? 372 00:41:23,460 --> 00:41:29,550 The prediction of the theoretical model is the single hub spoke network. 373 00:41:29,550 --> 00:41:33,540 Where the hub does nine. Everybody has a zero and. 374 00:41:35,930 --> 00:41:41,870 And the payoffs, the equilibrium payoffs will be very similar for the hub. 375 00:41:41,870 --> 00:41:47,990 And this book, the roughly 80, 85 for the Spokane, 81 for the hub. 376 00:41:48,080 --> 00:41:54,090 So the hub is earning slightly less. Okay. 377 00:41:54,090 --> 00:41:59,730 So I'm going to now give you a sense of what happens in this experiment before summarising the results. 378 00:42:00,180 --> 00:42:13,410 Okay. Oops. So I'm going to. 379 00:42:15,290 --> 00:42:19,490 Run a small movie where you would begin to see how. 380 00:42:27,580 --> 00:42:40,979 So this would take about a minute. So the dark nodes are the large effort nodes and you can see they are doing 20. 381 00:42:40,980 --> 00:42:48,780 So it's fairly big and it's dark. And as I see all these people, I start linking with them. 382 00:42:50,990 --> 00:43:08,110 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. 383 00:43:09,540 --> 00:43:13,620 And gradually people are linking with this node. But it's still. 384 00:43:17,940 --> 00:43:23,160 Uh, you know, evolving the network is sort of evolving, and it's quite confused at this point. 385 00:43:25,160 --> 00:43:37,760 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. 386 00:43:41,370 --> 00:43:47,340 More attractive. There's lots of linking and there are these highly active nodes you see at this point. 387 00:43:47,730 --> 00:43:51,360 There are a lot of active nodes because they are dark and they are putting a lot of work. 388 00:43:52,110 --> 00:43:56,070 They are all doing 20. So this is not a world with lot of specialisation. 389 00:44:00,480 --> 00:44:06,750 So what's the difference between two rounds? So this is within one round. 390 00:44:08,010 --> 00:44:15,450 This is each round is roughly 6 minutes. And I'm showing you that we give her rounds. 391 00:44:18,000 --> 00:44:21,930 The market is really fantastic. Yes, it's in semi continuous time. 392 00:44:22,410 --> 00:44:26,370 Yes, I can increase my effort, I can link, I can delete my links. 393 00:44:26,370 --> 00:44:29,490 And so you see that. 394 00:44:29,790 --> 00:44:32,819 What's interesting is that 13 has gone to zero effort, 395 00:44:32,820 --> 00:44:38,129 but all these people have linked with him and then suddenly people realise it's a bad idea to link with 396 00:44:38,130 --> 00:44:45,060 them and you see that they are now abandoning him one by one and they're going off to link with Mr. 14. 397 00:44:47,520 --> 00:44:53,630 And you see all these sort of links pointing to 14, and he started shirking. 398 00:44:53,640 --> 00:45:03,500 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. 399 00:45:04,520 --> 00:45:08,960 Very many fewer dark note specialisation is emerging as we go along. 400 00:45:09,350 --> 00:45:14,030 And just for people, I think we're really working hard. Everyone else is just linking with these hard working nodes. 401 00:45:14,540 --> 00:45:17,930 14 and now shrunk. Going off and gone off to zero. Okay. 402 00:45:18,620 --> 00:45:26,690 He's completely he's choking fully. Right. And of course, people will now start abandoning him and go to someone else. 403 00:45:32,170 --> 00:45:36,700 So what happened between two different roles? Nothing much happens. 404 00:45:36,720 --> 00:45:41,360 I'm just replaying the round. This is one round. One minute road is over. 405 00:45:41,570 --> 00:45:47,059 So this is actually trying to collect new. This is collecting call it the same people. 406 00:45:47,060 --> 00:45:51,260 So we have six rounds and each of them are 6 minutes. 407 00:45:51,800 --> 00:45:57,560 And so for a group of 50 people, you have you know, you have six rounds. 408 00:45:57,740 --> 00:46:02,060 And this is just a way to give them a we randomly reassign their ID numbers. 409 00:46:02,450 --> 00:46:11,030 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. 410 00:46:11,060 --> 00:46:19,480 They're just linking. Okay. You do have a few isolated nodes. 411 00:46:19,480 --> 00:46:23,820 Yes, but you can see it's very few. Most people are connected through. 412 00:46:24,890 --> 00:46:29,240 Of the sites, including the access. 413 00:46:31,300 --> 00:46:35,920 And they are doing nine. Remember, that was the bar they just bought nine. 414 00:46:35,920 --> 00:46:40,090 And they are staying put. For some reason no one has noticed they are dead. Okay, but. 415 00:46:41,080 --> 00:46:47,410 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. 416 00:46:47,650 --> 00:46:52,570 Okay. So you're and you can see the emergence of. 417 00:46:54,080 --> 00:46:57,890 A call. You can see the emergence of specialisation and. 418 00:46:59,860 --> 00:47:07,480 You know, and these are the sort of features that we will pick up when we start doing the statistical analysis. 419 00:47:08,800 --> 00:47:13,900 So. Okay. 420 00:47:13,990 --> 00:47:22,700 I think I'm. So now you see this, this person in the centre and he's got most of the links. 421 00:47:23,690 --> 00:47:35,150 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. 422 00:47:37,150 --> 00:47:40,820 Okay. So that's that gives you a flavour of what happens in this experiment. 423 00:47:44,850 --> 00:47:52,270 Kate. So we're going to look at specialisation and you see this very, very clearly here. 424 00:47:52,630 --> 00:47:57,490 Most people are doing no effort at all. This is the average effort, information purchase. 425 00:47:58,450 --> 00:48:04,300 And this is especially true in the NFL 250, where more than 50% of the people are doing. 426 00:48:04,630 --> 00:48:12,140 Basically, they're not buying any information at all. Okay. And so you see this very nice 8020 rule. 427 00:48:12,160 --> 00:48:21,370 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, 428 00:48:22,180 --> 00:48:27,129 I'm looking at the cumulative share of people from the lowest to highest output on the Y axis. 429 00:48:27,130 --> 00:48:29,020 I'm looking at cumulative share of efforts. 430 00:48:29,470 --> 00:48:37,410 And what I would like you to focus on is supposing I look at 80% of the lowest effort people you see out here, 431 00:48:37,420 --> 00:48:42,580 they're providing barely 20% of the efforts in the large group. 432 00:48:43,330 --> 00:48:55,570 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. 433 00:48:55,900 --> 00:49:01,120 Okay. So so that's the first demonstration of the specialisation and effort. 434 00:49:03,020 --> 00:49:10,580 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. 435 00:49:11,420 --> 00:49:16,940 When you look at this picture, you see that for the and equal to 50 experiment, 436 00:49:17,780 --> 00:49:23,390 more than 50% of the subjects have done essentially are doing zero information purchase. 437 00:49:23,690 --> 00:49:29,630 On the other hand, you have almost 10% of the subjects were doing almost 20 units of purchase. 438 00:49:30,140 --> 00:49:34,040 Get this notice that this is wildly out of the prediction. 439 00:49:34,040 --> 00:49:44,690 The predictions was nine units. Okay, they should never be buying more than nine because privately the marginal return beyond nine falls below C. 440 00:49:44,840 --> 00:49:47,900 So there is no reason to be buying beyond nine units. 441 00:49:48,290 --> 00:49:55,990 And yet you have clearly, you know, a fair number of people, maybe 5 to 10% buying, you know, 442 00:49:56,330 --> 00:50:03,110 close to 20 units of information, which of course, never happens with eight subjects. 443 00:50:03,710 --> 00:50:07,160 So with eight subjects, pretty much no one buys more than ten units. 444 00:50:07,400 --> 00:50:08,240 That's the red line. 445 00:50:11,170 --> 00:50:19,390 The other interesting feature of this experiment, which was also true in the theoretical model, is that access is basically very equal. 446 00:50:19,720 --> 00:50:24,280 Most people are getting access to the same amount of information that's being captured. 447 00:50:24,520 --> 00:50:31,240 If it were perfectly equal, you would get the lines matching the 45 degrees line, but it's pretty close to 45 degrees. 448 00:50:31,650 --> 00:50:36,520 Okay. So so it's it's a very, very egalitarian society in terms of information access. 449 00:50:38,970 --> 00:50:46,380 Now we look at the network and what we see here is even more striking than the information purchase. 450 00:50:47,130 --> 00:50:55,050 If you look at the the blue line, you see that, you know, 80% of the. 451 00:50:57,260 --> 00:51:05,800 Subjects along the X axis, 80% of the subjects are getting barely 10% of the links so badly. 452 00:51:06,560 --> 00:51:11,450 Most of the society, 80% of the society is barely getting 10% of the followers, if you like. 453 00:51:13,430 --> 00:51:18,770 And so this is even more specialised, more unequal than the purchase of information. 454 00:51:21,730 --> 00:51:27,070 And you see this and this. Another way to look at this data is to look at the cumulative distribution. 455 00:51:27,070 --> 00:51:38,500 And you see here that, you know, basically more than 95% of people are hardly getting any links at all. 456 00:51:39,450 --> 00:51:46,270 So so almost all the incoming links in this society are to less than 5% of the society. 457 00:51:49,370 --> 00:51:56,390 So now what I wanted to do was to look at the look a little more closely at the. 458 00:51:58,870 --> 00:52:06,040 The hubs and how much information to buy and how does that vary with the number of subjects? 459 00:52:06,250 --> 00:52:14,950 So a key, key feature of this experiment is this particular picture. 460 00:52:15,180 --> 00:52:19,540 Okay. There are all these people who are buying way, way too much information. 461 00:52:19,990 --> 00:52:26,710 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. 462 00:52:27,580 --> 00:52:30,460 So the question is, how does it vary with the group size? 463 00:52:30,790 --> 00:52:39,489 And this picture begins to give you a first impression of this, you know, of this excess of searches of information. 464 00:52:39,490 --> 00:52:44,340 And this one is even better. This is people buying more than 15 units of information. 465 00:52:44,350 --> 00:52:54,880 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. 466 00:52:55,060 --> 00:53:02,020 There's basically almost no one buying more than 15 units, whereas in the large group experiments with 50 subjects, 467 00:53:02,410 --> 00:53:11,680 you have almost 10% of the subjects buying, you know, in excess of 15 units, which is wildly beyond what the theory would predict. 468 00:53:11,680 --> 00:53:19,059 It's wildly beyond what is individually rational. So that's the you know, that's the big question. 469 00:53:19,060 --> 00:53:21,290 Why is it that people are doing this? Okay. 470 00:53:22,060 --> 00:53:29,740 And the consequence of that is this picture here, which tells you that people who are not buying any information, 471 00:53:29,740 --> 00:53:33,910 who are spooks, who are just linking, are the red guides. 472 00:53:33,910 --> 00:53:40,690 And they are earning a lot more than the equilibrium would predict and they are earning a lot more than the hub's. 473 00:53:41,650 --> 00:53:48,100 Remember, the prediction was the hubs should be earning roughly 80 and the spooks should be earning roughly 80 a little more than them. 474 00:53:48,340 --> 00:53:52,450 Okay. What you see in the data here is that the spooks. 475 00:53:54,260 --> 00:54:00,620 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. 476 00:54:01,430 --> 00:54:05,390 What's more puzzling? Why is it the hubs earning so much less? 477 00:54:05,430 --> 00:54:09,430 You know, they're earning almost 30 to 40% less than the prediction. 478 00:54:10,230 --> 00:54:13,360 So so that's sort of the big puzzle. 479 00:54:13,370 --> 00:54:18,319 And you see when you look at the welfare turning, you know, finally to the welfare question, 480 00:54:18,320 --> 00:54:24,860 you get the opposite picture because the hubs are buying so much information. 481 00:54:25,220 --> 00:54:30,080 Everybody is accessing more information than they would have been accessing an equilibrium. 482 00:54:30,350 --> 00:54:36,650 And so you see that the average pay offs are larger. The black line is the theoretical prediction. 483 00:54:37,430 --> 00:54:43,340 And so because people are buying a lot more information and they should be buying everybody else who's benefiting. 484 00:54:44,260 --> 00:54:45,940 You know, very significantly. 485 00:54:46,150 --> 00:54:54,250 And so the pay offs are a lot higher than the equilibrium prediction, and they are a lot lower in the small subject experiments. 486 00:54:54,760 --> 00:54:58,390 So expanding the group size is actually good for welfare. 487 00:54:59,320 --> 00:55:02,710 You know, and this is just aggregating that. 488 00:55:03,250 --> 00:55:08,970 What you see here is that in the small group experiments, pay offs are below the equilibrium prediction. 489 00:55:09,000 --> 00:55:14,440 So already we know the equilibrium is bad, but behaviour is worse than the equilibrium. 490 00:55:14,830 --> 00:55:25,870 Whereas here with the large group behaviour is, you know, because of the excess information purchase relative to equilibrium, 491 00:55:26,170 --> 00:55:31,240 total welfare is a lot higher than, than the equilibrium prediction. 492 00:55:33,180 --> 00:55:35,670 So I think I'm out of time. 493 00:55:37,140 --> 00:55:49,530 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, 494 00:55:49,530 --> 00:55:59,340 which is, you know, important phenomena like specialisation and effort and network structure that emerges from the specialisation. 495 00:56:00,120 --> 00:56:04,230 Develop mathematical models to understand what the mechanisms are. 496 00:56:05,850 --> 00:56:11,910 An important feature of the work economists do is ask questions about welfare. 497 00:56:12,480 --> 00:56:22,770 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, 498 00:56:22,770 --> 00:56:25,080 what would be collectively desirable. 499 00:56:25,740 --> 00:56:35,940 And then we want to understand whether these models are accurate as a good way of thinking about how people actually behave. 500 00:56:38,600 --> 00:56:44,540 And increasingly, economists conduct experiments both in the laboratory but also in the field. 501 00:56:44,840 --> 00:56:48,260 And indeed, more and more in the field. 502 00:56:49,040 --> 00:56:56,600 And the idea is, we want to ask whether the mechanisms that we have developed, we've explored in our mathematical models, 503 00:56:56,840 --> 00:57:04,760 in fact, work to what extent they work and to what extent they are not quite capturing what drives human beings. 504 00:57:05,180 --> 00:57:15,730 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. 505 00:57:15,740 --> 00:57:21,680 You have a lot of specialisation in information purchase. You get a lot of specialisation and linking. 506 00:57:23,180 --> 00:57:26,900 But in terms of the exact magnitude of information purchases, 507 00:57:27,740 --> 00:57:35,230 you see that behaviour in these experiments is clearly out of line with, you know, with the models. 508 00:57:35,780 --> 00:57:39,520 People are being driven somehow to become hubs and to become hubs. 509 00:57:39,530 --> 00:57:43,610 They have to they seem to exert far more effort than they really should be doing. 510 00:57:44,870 --> 00:57:48,410 And that leads them to earn a lot less than they should be doing. 511 00:57:48,930 --> 00:57:54,410 But on the other hand, it has this benefit that it makes everyone else better off. 512 00:57:54,740 --> 00:57:57,650 And in the aggregate, it could be a good thing. 513 00:57:58,130 --> 00:58:09,350 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? 514 00:58:09,620 --> 00:58:14,180 And is it that they don't understand what's happening? They don't understand the payoffs? 515 00:58:14,540 --> 00:58:18,400 Or is it that they're driven by an urge to become hubs, you know, 516 00:58:18,770 --> 00:58:23,900 and they have to get pleasure or they get happiness or they feel good about being hubs. 517 00:58:24,680 --> 00:58:28,100 So this is not a world in which hubs are being paid anything by anyone. 518 00:58:28,400 --> 00:58:32,300 So they want to be hubs for reasons which we don't fully understand. 519 00:58:32,750 --> 00:58:36,829 So it's sort of very much ongoing work. 520 00:58:36,830 --> 00:58:43,069 And the next step in our project is going to be to look more closely at the data, 521 00:58:43,070 --> 00:58:49,940 to understand whether the hubs are not understanding their payoffs or they somehow have other motivations, 522 00:58:49,940 --> 00:58:57,650 and if so, develop richer models, mathematical models that can capture these other motivations that hubs might have. 523 00:58:58,300 --> 00:58:59,600 Jen I'm going to stop at this point.