Latest / ContraMinds Podcast - Unlocking Personal Growth and Professional Excellence / Prof. Y. Narahari on Seeking Wisdom in the Theory of Games (#026)
Transcript
- 0:00SPEAKER_03: This is my my view of life needs to be very positive about everything.
- 0:12SPEAKER_03: And anybody and everybody you know makes mistakes, right?
- 0:20SPEAKER_03: Just ignore the mistakes and then move on.
- 0:24SPEAKER_03: This is something that I firmly believe in.
- 0:28SPEAKER_03: I don't think anybody in this world agrees with me on this.
- 0:32SPEAKER_02: Nobody agrees with me on this.
- 0:35SPEAKER_03: Because they don't want to they don't want to not punish.
- 0:38SPEAKER_03: They don't want to not punish people who have done big mistakes.
- 0:42SPEAKER_03: And they think that is my greatest weakness.
- 0:56SPEAKER_01: Hey everyone, welcome to a brand new episode of ContraMinds.
- 1:01SPEAKER_01: In today's episode, we are in conversation with Professor Yadati Narahari of the Indian Institute of Science, Bangalore.
- 1:08SPEAKER_01: Professor Narahari's research work focuses on game theory, mechanism design, and artificial intelligence techniques to research problems at the intersection of computer science and economics.
- 1:20SPEAKER_01: He has a long history with the IISE where he has earned his bachelor's, master's and doctoral degrees.
- 1:27SPEAKER_01: Since 1988, he has been on the faculty of the IIC and has held numerous leadership positions within the university, most notably serving as a dean in the Division of Electrical, Electronics and Computer Sciences from 2014 to 2021.
- 1:42SPEAKER_01: We had a wide-ranging discussion with Professor Marahit.
- 1:45SPEAKER_01: He spoke about the work and influence of John von Neumann, the convergence of AI, economics, and game theory, and the principles that form the foundation of a current science.
- 1:56SPEAKER_01: If you enjoy the work you do at ContraMind, keep us a ring on Spotify and Apple Podcasts.
- 2:01SPEAKER_01: You can also send us what you think via Twitter.
- 2:04SPEAKER_01: Our Twitter handlers at ContraMise.
- 2:06SPEAKER_01: So without further ado, here is our conversation with Professor Yadati Marah.
- 2:26SPEAKER_01: So hello everyone.
- 2:28SPEAKER_01: Greetings of today wherever you are.
- 2:31SPEAKER_01: In today's episode, we have with us Professor Narahari from the Indian Institute of Science.
- 2:37SPEAKER_01: His research is focused on a very interesting intersection of AI, game theory, and mechanism design.
- 2:43SPEAKER_01: And uh thank you so much, Professor, for taking the time and being with us uh today on ContraMinds.
- 2:49SPEAKER_03: Thank you very much.
- 2:50SPEAKER_03: Thank you very much.
- 2:51SPEAKER_03: I think it's uh it's an excellent opportunity for me to reach out.
- 2:56SPEAKER_03: The pleasure is entirely ours, Professor.
- 2:58SPEAKER_01: Professor, let's uh kick things off.
- 2:59SPEAKER_01: And I want to start off with a question that I really want to know what your thoughts are, which is uh when preparing for this interview, we heard you speak about this particular person, and we want to we want our listeners to share in uh in the excitement and the legacy that this person has left behind.
- 3:15SPEAKER_01: So, my question to you is who is John von Neumann and uh why do we owe him a great deal of debt as a modern society?
- 3:23SPEAKER_03: Okay, I think this is a great question to start with.
- 3:26SPEAKER_03: So, I mean uh John von Neumann is easily my biggest hero.
- 3:33SPEAKER_03: Um, he has done several wonderful things.
- 3:39SPEAKER_03: Um, and uh you know uh a number of visionary things he has done right from the 1920s.
- 3:48SPEAKER_03: Uh the most prominent that I would like to mention is that uh from 1928 to 1944, uh there was this beautiful partnership between uh a computer scientist, uh, of course, he was also a mathematician and physician uh for Naiman, and also a celebrated economist of those times, uh Oscar Morgenston.
- 4:13SPEAKER_03: So this was uh a fantastic collaboration for 16 years at the Center for Advanced Study at Princeton, and during this time I think they came up with a huge big tome called the theory of games and economic behavior.
- 4:32SPEAKER_03: It's a it's almost like a thousand-page book which lays all the foundations of uh game theory.
- 4:40SPEAKER_03: Even to this day, if you want to recapture all the important significant results of those times, this is the source which contains the most authentic version of all those results.
- 4:54SPEAKER_03: And during this time, uh you know they also completely settled the issue of existence of equilibria or the so-called saddle points for two-player zero sum games, uh, the so-called matrix games.
- 5:11SPEAKER_03: Uh, these are games where there are two players, call them one and two, and whenever for every strategy profile, whenever player one gets uh let's say a real number X as the utility, the player two will get minus X.
- 5:26SPEAKER_03: So it's a it's called a strictly competitive game game or a two-player zero sum games.
- 5:33SPEAKER_03: Uh it was not known whether such games will have uh an equilibrium because there are many of those games where if you are playing a pure strategy, then you can actually show that equilibria don't exist.
- 5:48SPEAKER_03: But uh what Forneiman and Morganston were able to show, and that was a big step forward for game theory that uh you know every two-player zero-sum game will have what is called as a randomized saddle point, it will have an equilibrium in what are called mixed strategies, which are like probabilistic strategies.
- 6:11SPEAKER_03: Uh, of course, this result was taken to the next level by you know uh John Nash in 1950 when he showed that you know every finite strategic form game will have an equilibrium.
- 6:29SPEAKER_03: In fact, uh the equilibrium there is so-called mixed strategy Nash equilibrium.
- 6:34SPEAKER_03: So that is settled by John Nash for multiplayer games, but it was settled for two-player zero-sum games by von Neumann and Morganston.
- 6:43SPEAKER_03: This is only one of the many results that uh they developed.
- 6:47SPEAKER_03: So there is a string of uh you know very significant results that uh you know they have captured in their book.
- 6:56SPEAKER_03: And um astonishingly, I think in the 1930s, von Neumann also was working on uh you know his model of computing.
- 7:08SPEAKER_03: So there is a von Neumann model of computing uh which we study in every textbook on computer science, and uh von Neumann is the inventor of that, and uh he he is also credited with uh you know um talking about the notion of an algorithm and the complexity of an algorithm.
- 7:31SPEAKER_03: So, in other words, in the 1930s, uh here is a visionary who was laying the foundations of computer science, and at the same time, he was also laying the foundations of game theory, and so there were two intellectual currents that this person had initiated during the 20s and 30s, and uh you know something like 60 years later, there was a complete convergence of these two intellectual disciplines into what is now called as algorithmic game theory.
- 8:04SPEAKER_03: It's a beautiful interface area between computer science and microeconomics.
- 8:10SPEAKER_03: Uh so now you can imagine uh how visionary for Neumann should have been in order to think about uh two disciplines which actually converged uh together after 60 years.
- 8:25SPEAKER_03: And ever since the late 1990s, when this happened, I think every leading computer science department in the world now has a group working on algorithmic aspects of game theory, and game theory itself has come to play a very important role in many high impact applications.
- 8:49SPEAKER_03: Um another thing that I would uh like to mention here is that game theory now can be considered as an essential tool in the modern toolkit that people talk about.
- 9:05SPEAKER_03: Now, everybody talks about machine learning, deep learning, and the toolkit that is required for us to do things, right?
- 9:13SPEAKER_03: And game theory is also a part of that toolkit.
- 9:16SPEAKER_03: So just as you know, we have linear programming as a toolkit, game theory is also like uh a part of a toolkit.
- 9:24SPEAKER_03: So I think all the wonderful contributions made by people starting with Fawn Eman have ensured that game theory is now an integral part of the mathematical toolkit that everybody should be equipped with.
- 9:36SPEAKER_01: Can you can you talk to us a little bit more about this convergence of AI and uh of computer science and game theory?
- 9:44SPEAKER_01: Because uh on the onset, uh like you said, that uh yes, there was an intuitive connection between those two.
- 9:50SPEAKER_01: But can you talk a little bit about how that connection has been broadened and deepened and expanded in today's world where data has become very cheap and developing algorithms has gone through has grown by leaps and bounds.
- 10:04SPEAKER_01: So can you talk a little bit about that convergence as well?
- 10:06SPEAKER_03: Yes, absolutely.
- 10:08SPEAKER_03: I think um you know um economists always were concerned with the existence of uh certain desirable states for any system, any economic system.
- 10:23SPEAKER_03: Um, you know, uh games uh are an excellent model for modeling the dynamics of all economic systems, and the desirable points of these economic systems are called as equilibria.
- 10:39SPEAKER_03: And uh economics has always been concerned with uh you know whether these equilibria exist.
- 10:47SPEAKER_03: And they were not really concerned about uh how to compute those equilibria.
- 10:53SPEAKER_03: Uh so I think uh computer scientists uh you know um and then the algorithms and complexity community, they're always worried about can we design an algorithm for a given problem, right?
- 11:07SPEAKER_03: And then if we are able to design an algorithm, then what is the computational complexity of that algorithm?
- 11:13SPEAKER_03: So this this is the you know the this is these are the fundamental questions that computer science, theoretical computer scientists always ask from the late 1960s.
- 11:24SPEAKER_03: So naturally, uh I think one uh question that was asked is well, uh you know, Nash equilibrium is such an important concept.
- 11:33SPEAKER_03: And uh, as you know, Professor John Nash uh got the Nobel Prize in 1994, and suddenly I think the notion of uh Nash equilibrium caught the attention of uh many people, including theoretical computer scientists.
- 11:46SPEAKER_03: So now they knew that the existence of Nash Equilibria has been uh settled, so they wanted to look at uh how easy it is to compute Nash equilibria, and uh to their delight, they found that this is a very difficult problem.
- 12:04SPEAKER_03: And uh so computer scientists, theoretical computer scientists, especially the algorithms and complexity theory people, they love to work with the difficult problems, right?
- 12:14SPEAKER_03: Because they want to show that a problem is NP hard, right, or NP complete, right?
- 12:18SPEAKER_03: So there's a whole lot of uh complexity theory uh you know um you know framework uh around uh very difficult problems.
- 12:29SPEAKER_03: So then um so they started looking at what is the complexity of computing an ash equilibrium, and uh so they came up with new complexity classes.
- 12:39SPEAKER_03: There is a complexity class called PPAD complete.
- 12:43SPEAKER_03: Uh so they actually showed that the problem of computing the mixed strategy Nash equilibrium of a strategic form game belongs to this uh class of uh highly complex problems.
- 12:56SPEAKER_03: So this is how the you know appetite of computer scientists and algorithm designers uh was wetted by the notion of the Nash equilibrium.
- 13:08SPEAKER_03: And and then um what happens is that uh you know um when data now becomes available, and that is the trend these days, uh now people are um you know trying to design applications and systems which will use this data in order to you know uh in order to increase your revenues uh in your business.
- 13:35SPEAKER_03: Uh so what I'm referring to here are all the e-commerce and the e-business uh uh kind of uh you know companies who came up in the late 90s and early 2000s and so on.
- 13:49SPEAKER_03: So all of these companies uh you know started uh building uh you know recommendation systems from the data, and you know, disciplines like data mining became extremely popular.
- 14:04SPEAKER_03: Uh so then um when all of these applications were getting developed and then machine learning also started becoming uh popular and so on, the question arose uh, what will happen to all of these applications?
- 14:20SPEAKER_03: What uh what will happen to all these recommendations when the information that is required for all these recommendations is held by strategic agents who may not be willing to give you the truthful information, right?
- 14:37SPEAKER_03: Uh so to give you uh an example, take the case of internet advertising.
- 14:43SPEAKER_03: Right.
- 14:44SPEAKER_03: So, in the case of internet advertising, um, if you consider a very simple example where you have a keyword search, so if you go to any portal or any search engine and then you do a keyword search, uh then what would happen is that um you know you will get uh a number of organic results on the left side of the page that could run into lakhs and millions, and on the right side you have these sponsored slots where companies which have got anything to do with this keyword, for example, if the keyword is camera, right?
- 15:21SPEAKER_03: Companies which wants to sell cameras, if the if the keyword is Christmas, the companies which would like to sell Christmas uh gifts and so on, all of them their advertisements can be found on the right side.
- 15:34SPEAKER_03: And then what would happen is that if somebody clicks uh on any one of those slots, any one of those links, then the company uh corresponding to which uh that click has been uh made will end up paying a certain amount of money to the search engine, and this is how you know search engine companies make a huge amount of their revenue.
- 15:56SPEAKER_03: In fact, a major fraction of the revenue comes from all these uh internet advertising, which happens because of auctions and so on.
- 16:07SPEAKER_03: Now the question comes how do we design uh auctions so that you can maximize the revenue of the search engine?
- 16:15SPEAKER_03: So, this is a problem which involves uh data science, machine learning, and also game theory.
- 16:24SPEAKER_03: Now, how is data science involved here?
- 16:27SPEAKER_03: Because you would like to you you would like to you know look at that uh data about various uh you know advertisers in order to in order to slot them in those positions that you have here.
- 16:41SPEAKER_03: Because naturally a person would like to do a click on the very first advertisement rather than the tenth advertisement or so.
- 16:49SPEAKER_03: So the relative positions that you are going to give to the advertisers will pretty much depend on the historical uh information about how popular those companies are and so on.
- 17:01SPEAKER_03: So there is data science involved there.
- 17:04SPEAKER_03: Secondly, there is machine learning involved there because what you want to do is you want to learn the click probabilities.
- 17:13SPEAKER_03: Now, what are click probabilities?
- 17:15SPEAKER_03: So, click probability is the probability with which a typical user will click the advertisement belonging to a certain company.
- 17:24SPEAKER_03: So this is called a click probability.
- 17:26SPEAKER_03: So, using the enormous amount of data that you have collected uh over a long period of time, you would like to learn the click probability.
- 17:35SPEAKER_03: So there is a machine learning problem there.
- 17:37SPEAKER_03: Now, all the advertisers are rational and intelligent uh people.
- 17:43SPEAKER_03: Now they are supposed to do a bid in order to participate in the auction.
- 17:48SPEAKER_03: What is this auction?
- 17:49SPEAKER_03: So, what uh the search engine will do is uh for getting a slot on the right side, so they have each company will have to bid a certain amount of money, right?
- 18:03SPEAKER_03: How much of money uh does a does a company want to bid?
- 18:08SPEAKER_03: Well pretty much depend on you know so many factors belonging to the company, which is up which are which are all private information of the company.
- 18:16SPEAKER_03: Now, what uh the search engine would like to do is to get as high a bid as possible, whereas the advertisers would like to bid as low as possible.
- 18:27SPEAKER_03: So now game theory comes into picture directly here.
- 18:31SPEAKER_03: How do you how do you induce a game among the advertisers so that they bid as high as possible so that the revenue of the search engine uh will be maximized?
- 18:44SPEAKER_03: So there is a game theory problem there.
- 18:46SPEAKER_03: The design of the auction that determines what slots the different advertisers will get and how much of payment will be done by the advertisers when a user clicks on those links is uh done using pure game theory.
- 19:02SPEAKER_03: In fact, it's called mechanism design.
- 19:05SPEAKER_03: So, using mechanism design, they came up with what is called the generalized uh second price auction and uh there is the Vikree auction, there is a wide variety of auction mechanisms.
- 19:17SPEAKER_03: So you can see that there is data science, there is machine learning, there is game theory, all of them are involved in this internet advertising problem here.
- 19:26SPEAKER_03: So you can see that if you now want to get an extremely rigorous solution to some of the problems in modern applications like internet advertising, you see that uh you have to have machine learning and also game theory uh capabilities, right?
- 19:46SPEAKER_03: So you can see that this convergence uh of uh game theory and computer science has also led to how game theory and machine learning can be combined in order to design uh the best possible algorithms in the presence of rational and intelligent and strategic agents.
- 20:07SPEAKER_03: I hope that answers your question.
- 20:09SPEAKER_03: It was a very long answer to a very relevant question.
- 20:14SPEAKER_03: Yeah.
- 20:15SPEAKER_00: So uh one of the questions uh that I had was uh at one end you have a search engine which is actually using game theory uh to maximize the revenue of uh the advertiser, right?
- 20:30SPEAKER_03: Imagine I am an advertiser and no search engine is trying to maximize its own revenue.
- 20:36SPEAKER_00: I'm just saying it's the ma uh maximize its own revenue, sorry.
- 20:40SPEAKER_00: Maximize its own revenue.
- 20:41SPEAKER_00: I get it.
- 20:42SPEAKER_00: So imagine if I were an advertiser and I'm putting billions of dollars into advertising, right?
- 20:49SPEAKER_00: And today uh you know digital marketing itself globally has become probably 50% of spends of most companies, and I am a company uh spending a couple of millions or billions of dollars on uh you know advertising.
- 21:05SPEAKER_00: Uh how do I really reverse engineer game theory for my decision making, right?
- 21:11SPEAKER_00: So because I want to bid the lowest, right?
- 21:13SPEAKER_00: So which means that I need to have all the data, right?
- 21:17SPEAKER_00: And I need to uh you know apply the game theory from my point of view, which is the advertiser's point of view, to say I have spent and bid so much of uh you know on so much of words, these are the results that I getting, that I'm getting.
- 21:31SPEAKER_00: And would there be a model for advertisers to apply game theory to their bits to optimize their budgets?
- 21:39SPEAKER_03: Absolutely.
- 21:39SPEAKER_03: So this is the this is called the bid optimization problem.
- 21:43SPEAKER_03: So, which is a problem which has been studied.
- 21:46SPEAKER_03: Uh, you know, there are hundreds of papers written on this bid optimization problem.
- 21:52SPEAKER_03: But one way in which uh game can sometimes simplify the decision making for everybody is through water.
- 22:00SPEAKER_03: Called as incentive compatible auctions.
- 22:03SPEAKER_03: To give you an example, I will this will require about two to three minutes to spend on this.
- 22:12SPEAKER_03: The so-called Vickery auction.
- 22:14SPEAKER_03: So William Vickery got the Nobel Prize in 1996 for a beautiful twist he gave to auction mechanisms.
- 22:22SPEAKER_03: His auction mechanism is called the second prize auction.
- 22:25SPEAKER_03: Now it goes like this.
- 22:28SPEAKER_03: Suppose there is a single indivisible item, suppose there is a bicycle for which there are three bidders.
- 22:41SPEAKER_03: Now these three players will place the bids, and then whoever bids the highest is usually selected as the winner.
- 22:52SPEAKER_03: So suppose A has bid uh let's say 1000 rupees, B has bid 800 rupees, and C has bid 600 rupees.
- 23:03SPEAKER_03: Fine.
- 23:03SPEAKER_03: So naturally, A will win the auction and will pay 1000 rupees.
- 23:08SPEAKER_03: This is called the first price auction.
- 23:11SPEAKER_03: Now it turns out that first price auction doesn't have this property called incentive compatibility.
- 23:18SPEAKER_03: That is, the the bidders will not bid their true valuations.
- 23:24SPEAKER_03: What they will do is they will bid something lower than their true valuations because they they want to get some utility out of it, right?
- 23:33SPEAKER_03: So, for example, uh the bidder A, the true valuation for the bidder A may be 1500 rupees.
- 23:42SPEAKER_03: He is willing to pay up to 1500 rupees, but he will not bid 1500, he will bid 1000 rupees.
- 23:49SPEAKER_03: Fine.
- 23:50SPEAKER_03: So similarly, similar is the case with B and C.
- 23:54SPEAKER_03: Now let us say the valuation of A is 1000, the valuation of B is 800, and the valuation of C is 600.
- 24:05SPEAKER_03: That is, this is in some sense their willingness to buy.
- 24:12SPEAKER_03: Now the question is can you extract this willingness to buy information from these bidders in a truthful way?
- 24:20SPEAKER_03: Fine.
- 24:21SPEAKER_03: So Vikri said that it is possible.
- 24:25SPEAKER_03: What he did, what he did was to simply twist the first price auction by saying, whoever bids the highest will be the winner.
- 24:34SPEAKER_03: However, the winner will not pay whatever he has, he or she has bid, will pay the second highest bid.
- 24:43SPEAKER_03: So now everybody knows that they have to bid high enough so that they will win.
- 24:49SPEAKER_03: Because if you want to win, you have to bid very high.
- 24:52SPEAKER_03: However, right, you know, you know that when you win, you are not paying whatever you have bid, you are paying something less than what you have bid.
- 25:01SPEAKER_03: So your bid will be very aggressive.
- 25:03SPEAKER_03: Fine.
- 25:04SPEAKER_03: How much aggressive will it be?
- 25:06SPEAKER_03: So basically, he said the aggression will be the highest bid minus the second highest bid.
- 25:14SPEAKER_03: Fine, you would be willing to pay an amount, an additional amount of the difference between the highest bid and the second highest bid.
- 25:23SPEAKER_03: Fine.
- 25:24SPEAKER_03: And using pure game theory, uh, William Vickri was able to show that this particular auction satisfies a property called incentive compatibility.
- 25:34SPEAKER_03: In fact, it satisfies a very strong property called dominant strategy incentive compatibility.
- 25:39SPEAKER_03: What it means is that your best response bid in the second price auction will be to bid your true valuation, right, regardless, regardless of what the other players are going to bid.
- 25:55SPEAKER_03: You don't have to worry about the bids of the other people.
- 25:58SPEAKER_03: All that you have to do is to bid your own true valuation.
- 26:02SPEAKER_03: This is the this is the principle of Satya Meva Jayate, right?
- 26:06SPEAKER_03: And William Vickri basically showed that this property is satisfied by the second price auction.
- 26:12SPEAKER_03: If you are so that is the ultimate in game theory, if you are able to design such auctions, then neither the search engine nor the advertisers have to worry about anything.
- 26:24SPEAKER_03: Advertisers have to just bid whatever their true valuation is, right?
- 26:29SPEAKER_03: And if the search engine has to bid in some other context, the search engine has to bid whatever its true valuation is, right?
- 26:36SPEAKER_03: Okay, but uh real world is very different, so people are not incentive compatible, but game theory gives you all the building blocks which are necessary to design auctions which will have some very desirable properties, right?
- 26:53SPEAKER_03: So coming back to your question, right?
- 26:56SPEAKER_03: Um in a game where the search engine is a player and the advertisers are also uh players, then the advertisers uh you know knowing the mechanism, they should know.
- 27:10SPEAKER_03: They should know what mechanism is being adopted by the search engine.
- 27:13SPEAKER_03: Is it first price auction or is it second price auction or whatever?
- 27:18SPEAKER_03: So knowing the mechanism that the search engine is going to employ, they can formulate and solve a bid optimization problem, which will actually give the optimal bits that they should be placing in any given uh you know auction.
- 27:32SPEAKER_00: That's a brilliant, brilliant uh uh answer, uh Professor.
- 27:36SPEAKER_00: I think uh the fact that uh you're pretty much reversing the uh you know uh the approach, I think was uh brilliant.
- 27:45SPEAKER_00: And uh I think the other thing that uh that I that I saw really was somebody like Google uh you know really hired uh economist as a part of their uh you know uh uh the first uh you know the first uh employee or the early employees I would call.
- 28:04SPEAKER_00: And uh I think uh that's something that was very interesting because they really believed in the game theory and the auction model, right?
- 28:12SPEAKER_00: Uh Vignesh, you had a few things to say about that.
- 28:15SPEAKER_01: Yeah, so since you were talking about algorithmic game theory and the availability of information to basically support the advertising model on which a lot of Google's revenue is built today.
- 28:26SPEAKER_01: We were discussing this some time back, and I we had a short uh you know sidebar where we were talking about how Google's a large swath of Google's revenue and success today can be pinned down directly to one man and his name is Hal Varyan.
- 28:42SPEAKER_01: And uh, you know, I uh so I just want to know what is the impact that uh if you look at, I mean, if if if I had to phrase it differently, a lot of great technology companies look for great founding engineers, right?
- 28:55SPEAKER_01: So, what are the qualities of a great founding economist, if you might even have one in a company or in a startup?
- 29:01SPEAKER_01: Because I think that's the role that Halvarian played for Google.
- 29:03SPEAKER_03: Yes, so um talking about Halvarian, uh I'm like to say that uh, you know, uh again, he's one of my heroes, and for the wonderful book that he has written on intermediate microeconomics, uh, I must tell you that there are uh four or five books which have inspired me in game theory.
- 29:26SPEAKER_03: I personally learned game theory through a book written by Maskulel, Winston, and Green.
- 29:32SPEAKER_03: It is called uh you know Microeconomic Theory.
- 29:36SPEAKER_03: It's a thousand-page book, uh, excellent uh book, and I learned my game theory and mechanism design through that book.
- 29:44SPEAKER_03: And around the same time, um, you know, reading Maskolel's book, you know, it needs a lot of math, and it's actually you have to really you know concentrate uh to understand what's going on there.
- 29:57SPEAKER_03: So I wanted to get uh a I wanted to get conceptual clarity about uh microeconomics concepts.
- 30:09SPEAKER_03: So that is when I was recommended uh this book, uh Intermediate Microeconomics by Hall Varion.
- 30:16SPEAKER_03: And the beautiful way in which he has structured the book uh in fact inspired me later on to structure my book also in a somewhat similar form.
- 30:26SPEAKER_03: Uh he has got these little chapters, and every chapter has a fantastic takeaway, and he has very illustrative examples, doesn't get into too much of math and so on.
- 30:39SPEAKER_03: I think what is great about Hallvarian is the conceptual clarity.
- 30:44SPEAKER_03: Uh I think it was a master stroke to get Hallvarian into their ranks, and he made all the important first moves in designing the internet advertising strategy for Google in those days.
- 31:02SPEAKER_03: Um it is very important uh that companies uh you know get the help of very rigorous computer scientists or mathematicians and so on.
- 31:18SPEAKER_03: And all the leading companies have been doing that, whether it is uh Google or Microsoft Research or Facebook or Amazon and so on, um they have actually hired many Turing awardiners, leading economists, and people with stellar research records.
- 31:39SPEAKER_03: Because you know, behind behind any algorithm that works very well, so there is there is also uh pure theory that is associated, which should ensure that the algorithm itself will work under all conditions.
- 31:58SPEAKER_03: So there is mathematical rigor required if you want to design robust algorithms.
- 32:04SPEAKER_03: And I think uh this is something which has driven all the leading companies uh to take the help of uh whether leading economists or leading computer scientists into their ranks, and some of these companies have the best talents, and you you you know that the people who won the deep learning Turing prize, right, you can see the kind of jobs they are holding in all the leading companies, right?
- 32:29SPEAKER_03: So I think uh I would say that Google made uh the best move possible in getting people like Halvarian.
- 32:38SPEAKER_03: Halvarian is only one example, but there are so many other people who also got hired by all the leading companies during those times.
- 32:45SPEAKER_03: I think uh early 2000s was a golden age for that.
- 32:49SPEAKER_03: So 2000 to 2006 or so was the golden age for that.
- 32:54SPEAKER_03: And uh it was it was a it was purely accidental that I was also uh working in that area during those times, right?
- 33:03SPEAKER_03: And uh thanks to my excellent uh you know PhD students.
- 33:08SPEAKER_01: So, Professor, one of when you were researching for this episode, we were listening to a talk that you had given about game theory and mechanism design and computer science.
- 33:17SPEAKER_01: And one statement that you said really stood out to me that when I was listening to that episode uh when I was listening to that conversation, uh to that lecture, and it was that uh it's the following incentives are everything.
- 33:28SPEAKER_01: So you said that if you want to achieve anything, you got to have relevant incentives that are mapped against it for people to go ahead and do what you want them to do.
- 33:37SPEAKER_01: So, a question that I have is what are some of the principles that lie at the foundation of a good incentive?
- 33:44SPEAKER_03: Okay, um, I just gave you the example of Vickri auction.
- 33:50SPEAKER_03: Right?
- 33:50SPEAKER_03: So in Vickri auction, the incentive that is being given to the winning player is that the winning player has to pay not 1000 rupees but 800 rupees.
- 34:01SPEAKER_03: So there is an incentive of 200 rupees that is given.
- 34:04SPEAKER_03: Now you consider the reverse auction, the procurement auction.
- 34:08SPEAKER_03: Now, in the procurement auction, there is a buyer and there are suppliers or sellers, and now there is a certain item that you are trying to buy.
- 34:19SPEAKER_03: So let us say that you know there are three possible suppliers.
- 34:24SPEAKER_03: First supplier says, I will give it to you at 1000 rupees.
- 34:28SPEAKER_03: The second one will say I will give it to you at 800 rupees, and the third one will say I will give it to you at 600 rupees.
- 34:34SPEAKER_03: I'm just reversing the problem here, and now your winner will be the supplier who has quoted uh 600 rupees because now you're buying, you're trying to minimize your cost.
- 34:45SPEAKER_03: Now, here your aim is to sort of uh induce honest behavior from the suppliers by making the suppliers bid their true costs, right?
- 34:59SPEAKER_03: So now uh the the player C who has bid 600 right has bid very low because he knows that 600 is his cost, and then if he bids very low, he the probability of his winning is very high, and when he wins, right, he's not getting just 600 rupees, but he's getting 800 rupees.
- 35:25SPEAKER_03: He's going he's going to get that second lowest bit.
- 35:28SPEAKER_03: So you're giving an incentive of 200 rupees to the player, right?
- 35:34SPEAKER_03: So that way you can see that uh auctions or in general, you know, when you do mechanism design, it is all about incentives, it is all about incentives, and you know, the most important property for an auction, as I told you, is incentive compatibility.
- 35:52SPEAKER_03: Fine.
- 35:52SPEAKER_03: That is what are the incentives that you should be giving to the various players in the game so that you are able to induce honest behavior from all the players.
- 36:04SPEAKER_03: That is that is the real meaning of incentive compatibility, and now you can take any problem.
- 36:12SPEAKER_03: For example, let us say uh you know you have uh you are a product company, and uh then there is a sales force and there is a sales manager, uh, so you have the sales executives, sales managers, and then the actual sales uh you know professionals.
- 36:36SPEAKER_03: There is a an entire there is an entire sales network for you.
- 36:40SPEAKER_03: Now the question is uh you know what kind of incentives should you be giving to all your sales uh force, all your sales personnel, so that uh you know your product uh sales are maximized, right?
- 36:57SPEAKER_03: It's actually a game theory problem.
- 37:00SPEAKER_03: It's actually a game theory problem.
- 37:02SPEAKER_03: So, there what you have to do is you have to look at uh what kind of incentives you should be giving to the sales executives, to the sales personal at the lower levels, and so on, so that your sales are getting maximized.
- 37:14SPEAKER_03: You can actually now capture this or model this as a game where all of these are players, and now if you are able to if you are able to uh induce all of them to reveal to you their true efforts, then in recognition of these true efforts, you will be able to pay them the kind of amounts that uh they would deserve.
- 37:43SPEAKER_03: This is basically you are designing the incentives which are proportional to the efforts that are put in by the players and also the impact that it is making on the overall uh you know sales uh of the product and so on.
- 37:57SPEAKER_03: So you can see that uh incentive design itself can be formulated in any given problem by coming up with an appropriate game model and uh then looking at how a mechanism can be designed so that these incentives uh are obtained as a byproduct of that mechanism.
- 38:19SPEAKER_01: I would just also sort of add that you know, since we've brought the words out game theory and mechanism design, it'll be a little more helpful if you could just give a formal definition for our listeners as well as to what is game theory and what is mechanism design and what is the relationship between the two.
- 38:35SPEAKER_01: Two.
- 38:36SPEAKER_01: Okay.
- 38:36SPEAKER_03: Um so game theory and mechanism design are uh two phrases that you will use to describe analysis and design.
- 38:47SPEAKER_03: Game theory is analysis of games, mechanism design is design of games.
- 38:54SPEAKER_03: One is analysis, another is design.
- 38:56SPEAKER_03: Mechanism design also can be called as reverse engineering of games, and the best example with which uh you know I can illustrate uh both game theory and mechanism design is through the cake cutting example.
- 39:12SPEAKER_03: All of you know about the cake cutting example.
- 39:15SPEAKER_03: So there is a cake, uh there is a mother, she has two kids, one is a boy, another is a girl, and both are fighting over the cake.
- 39:26SPEAKER_03: Now the mother has to distribute the cake equally between the two players, right?
- 39:32SPEAKER_03: So, what does the mother do?
- 39:34SPEAKER_03: Mother may take the best knife in the world and then slice the cake uh into exactly two equal portions, right?
- 39:44SPEAKER_03: And then place these equal portions in front of uh the two kids, or give one of one to uh one each to the kid, then each kid will go away with the feeling that what he or she got is the smaller of the two slices.
- 40:02SPEAKER_03: Howsoever equal those two slices may look like.
- 40:07SPEAKER_03: Fine now, how do you solve this problem?
- 40:11SPEAKER_03: This problem is uh may look very innocuous, but when you look at uh how Karnataka and Tamil Nadu are fighting over the Kauri waters, so the Kauvery waters is the cake, and uh SR Bomai is the is one of the kids, and Stalin is the other kid, and Narendra Modi is the mother.
- 40:36SPEAKER_03: So you can map this problem uh to this problem right away, right?
- 40:41SPEAKER_03: It's actually a very difficult problem to solve.
- 40:45SPEAKER_03: Now, how does mechanism design and game theory solve this problem?
- 40:50SPEAKER_03: The mother induces a game, the mother induces a game on the two kids, and then in an equilibrium of that game, what gets implemented is uh a desirable solution for the game.
- 41:08SPEAKER_03: Okay, what is the what is the game that is induced here?
- 41:12SPEAKER_03: The mother says, uh, you know, I have the knife with me, I will give it to kid A.
- 41:20SPEAKER_03: Now, kid A will have to slice it into two portions, and then kid B will get the chance to pick up one of those two slices, right?
- 41:33SPEAKER_03: So now here is a situation where you have two rational and intelligent players, the two kids.
- 41:40SPEAKER_03: Each one wants to get the lion's share of the cake.
- 41:44SPEAKER_03: Now the first kid who gets the knife knows that the second kid is going to pick up the larger of the two slices.
- 41:53SPEAKER_03: So we'll cut the cake with so much precision that there will be two equal portions only, right?
- 42:02SPEAKER_03: And then now there are two slices there.
- 42:05SPEAKER_03: Now what does the second kid do?
- 42:07SPEAKER_03: The second kid will look at both these slices and will pick up what she thinks is the larger of the two slices.
- 42:14SPEAKER_03: Fine.
- 42:15SPEAKER_03: So the first kid is very happy, the second kid is very happy, the mother is happy, Stalin is happy, Bombay is happy, and Naredramodi is also happy, right?
- 42:30SPEAKER_03: So now there is both game and mechanism design here.
- 42:34SPEAKER_03: What is the mechanism design?
- 42:36SPEAKER_03: The protocol of cutting the cake and so on is the mechanism.
- 42:43SPEAKER_03: When a mechanism is implemented, it induces a game among the players.
- 42:48SPEAKER_03: So, what is a game that is induced?
- 42:50SPEAKER_03: Because uh now Kid 1 has a strategy space.
- 42:56SPEAKER_03: What is the strategy space?
- 42:57SPEAKER_03: There is a cake that has to be cut into two portions, right?
- 43:01SPEAKER_03: So can I cut it as one third, two-thirds, or one fourth, three-fourths, or half and half?
- 43:07SPEAKER_03: This is the strategy space, right?
- 43:10SPEAKER_03: And chooses the strategy half half.
- 43:13SPEAKER_03: Fine, and then the other kit also has a strategy space.
- 43:18SPEAKER_03: There are two slices, has to pick up one of these two slices, right?
- 43:23SPEAKER_03: So you can see that there is a game that is being played out, and that has been induced by a protocol, and that protocol is mechanism.
- 43:32SPEAKER_03: So now you see that you know there is an equilibrium for this game, and what is the equilibrium?
- 43:38SPEAKER_03: In the equilibrium of the game, the first kid you know, sort of cuts the cake into exactly two equal slices in the equilibrium, and then the second kid will pick up what he or she thinks is the larger of the two slices.
- 43:57SPEAKER_03: So that is the equilibrium of this game, fine.
- 44:00SPEAKER_03: But in the equilibrium of the game, you have actually implemented what is called as a social choice function.
- 44:06SPEAKER_03: What is good for the society.
- 44:08SPEAKER_03: You have implemented a function which is good for the society and which is good for all the players in this particular case.
- 44:14SPEAKER_03: So that is the difference between game theory and mechanism design.
- 44:19SPEAKER_03: Both of them go well with each other, right?
- 44:23SPEAKER_03: And one is completely concerned with equilibrium analysis, and the other is concerned with how you can induce a game in which in the equilibrium of the game something very desirable will happen.
- 44:42SPEAKER_03: Now equilibrium has many, many notions, right?
- 44:46SPEAKER_03: So the most famous notion, as all of us know, is Nash equilibrium, but there are other notions called dominant strategy equilibria.
- 44:55SPEAKER_03: There you have strong, weak, very weak dominant strategy equilibria.
- 45:01SPEAKER_03: You also have what are called mixed strategy Nash equilibria.
- 45:05SPEAKER_03: You have got what are called correlated equilibria, and you also have what are called as max min values and min max values.
- 45:14SPEAKER_03: So these are all different solution concepts in the analysis of games.
- 45:19SPEAKER_03: So given a game, game theory will tell you how to look for all the solution concepts.
- 45:26SPEAKER_03: And we'll look at the um we'll look at the existence of these equilibria, we'll also look at the computation of these equilibria and so on.
- 45:35SPEAKER_00: That's a brilliant uh you know explanation of uh game theory and uh you know mechanism design.
- 45:42SPEAKER_00: It can't be more simple than what you explained so beautifully, Professor.
- 45:47SPEAKER_03: Uh actually, I you know, in order to explain how uh you know a game can be defined, I use a very simple example.
- 45:56SPEAKER_03: This is the first example that I you usually use in my class.
- 46:01SPEAKER_03: So this is uh the example of uh IISC versus MG road example.
- 46:08SPEAKER_03: So there are two students, call them as A and B.
- 46:12SPEAKER_03: They're very good friends, and if they are together, then there is some utility that they get out of their uh you know being together.
- 46:21SPEAKER_03: And uh they have two um, you know, they they have two um strategies in front of them.
- 46:28SPEAKER_03: One is uh I they choose either IISC or they choose MG Road.
- 46:36SPEAKER_03: IISC means they will go to the library and like very sincere students, they will be studying in the library and so on.
- 46:42SPEAKER_03: In MG Road, people you know what people do, right?
- 46:46SPEAKER_03: MG Road is Mahatma Gandhi Road, uh, and everything that happens on uh MG Road is anti-Mahatmaganthi, as you know.
- 46:54SPEAKER_03: So they have only two strategies to play with.
- 46:59SPEAKER_03: Now the question is that if both of them are in IISC, they get a utility of uh 10, 10.
- 47:08SPEAKER_03: 10 units, 10 units of utility player A gets, student B also gets.
- 47:14SPEAKER_03: Whereas if one of them is in IISC and the other is in MG road, they will get 0,000 because they are not together.
- 47:22SPEAKER_03: If both of them are in MG road, if both of them are in MG road, then they will get 1 comma 1, right?
- 47:31SPEAKER_03: Which is much less than 10, 10.
- 47:34SPEAKER_03: Fine.
- 47:35SPEAKER_03: So now what are the rules of the game?
- 47:37SPEAKER_03: So in game theory, this so this matrix is there, right?
- 47:41SPEAKER_03: This matrix which will tell you the numbers of the utilities that you will get in different strategy profiles, right?
- 47:48SPEAKER_03: This matrix is known to both the players.
- 47:52SPEAKER_03: Not only that, both the players know that both the players know the matrix.
- 47:58SPEAKER_03: Not only that, both the players know that both the players know that both the players know the matrix.
- 48:05SPEAKER_03: So it is common knowledge.
- 48:07SPEAKER_03: The matrix is common knowledge, but they are supposed to make simultaneous moves.
- 48:13SPEAKER_03: They are supposed to decide whether they want to be in uh whether each one wants to be in IISC or MG road simultaneously.
- 48:20SPEAKER_03: Student A does not know what student B has decided, student B does not know what student A has decided.
- 48:29SPEAKER_03: This is called a simultaneous move strategic form game.
- 48:33SPEAKER_03: Now the question is what is an equilibrium in this game?
- 48:37SPEAKER_03: Right?
- 48:39SPEAKER_03: Now the intuitive part here is that game theory rightly predicts that IISC, IISC is an equilibrium.
- 48:49SPEAKER_03: Right?
- 48:50SPEAKER_03: Because you know both of them will get 10, 10.
- 48:53SPEAKER_03: It also says that IISC, M0D is not an equilibrium.
- 48:59SPEAKER_03: It also tells you that M0, M0D is also an equilibrium.
- 49:04SPEAKER_03: Right?
- 49:04SPEAKER_03: They are getting a utility, but you know, it is less than the utility that they are going to get.
- 49:09SPEAKER_03: So you can see in different equilibria they can get different utilities.
- 49:14SPEAKER_03: But what is uh counterintuitive and what game theory brilliantly reveals is that there is another equilibrium here, that is a mixed strategy Nash equilibrium, and the mixed strategy nash equilibrium here is the following with probability 10 by 11, you are in MG road, and with probability 1 by 11, you are in IISC.
- 49:42SPEAKER_03: So if both the players follow this strategy profile, player A is in IASC with probability 1 by 11 with MG road with probability 10 by 11.
- 49:56SPEAKER_03: Player B also is in IASC with probability 1 by 11 and in MG road with probability 10 by 11.
- 50:04SPEAKER_03: Then also you can show that there is an equilibrium.
- 50:10SPEAKER_03: And I tell the students this is the reason why the students are mostly in MG road and not in IASC.
- 50:18SPEAKER_03: This is predicted beautifully by game theory using the notion of a mixed allergy Nash equilibrium.
- 50:24SPEAKER_03: So, in order to understand this, I will have to get into some math, which I don't want to now, right?
- 50:31SPEAKER_03: But you can see how you know what happens as the outcome of the interesting dynamics among rational and intelligent agents is beautifully explained by game theory.
- 50:45SPEAKER_03: I have used these two words rational and intelligent too many times.
- 50:49SPEAKER_03: I must tell you what these two uh actually mean.
- 50:54SPEAKER_03: Rationality means that every player has a certain utility function.
- 51:02SPEAKER_03: There is a certain utility that you derive by playing a certain strategy.
- 51:07SPEAKER_03: Fine?
- 51:08SPEAKER_03: So rationality means that each player will choose a strategy such that it will maximize the utility function.
- 51:18SPEAKER_03: More generally, it should maximize an expected value of that utility function in a probabilistic sense.
- 51:25SPEAKER_03: This is called rationality.
- 51:27SPEAKER_03: Whereas intelligence, intelligence basically means that every player, every player knows how to compute the best response, and a player's best response is a strategy which will maximize his or her utility when the other players are playing their best response strategies, and the best response strategies of the other players are best responses against the best responses of the players.
- 52:03SPEAKER_03: You can see there's a beautiful recursion there, and game theory basically you know helps you to break this recursion with the notion of an equilibrium.
- 52:15SPEAKER_03: So you define this equilibrium right by making just the assumption of rationality and intelligence.
- 52:23SPEAKER_03: Now, rationality does not mean that you are always selfish, rationality only means that you are maximizing your utility function.
- 52:31SPEAKER_03: This utility function, right, if it is in your self-interest, then rationality means selfishness.
- 52:39SPEAKER_03: Whereas if the utility function captures the fact that you want every player to be happy in the game, then you can see that such a game represents altruistic behavior.
- 52:54SPEAKER_03: You can actually represent altruism also using game theory.
- 52:58SPEAKER_03: So rationality and intelligence have to be viewed in that very general light, which will enable you to model all kinds of uh human behaviors and uh dynamics among uh you know human beings, right, as a mathematical abstraction.
- 53:16SPEAKER_00: Um Professor, I have uh uh one question around uh this big thing that's happening around us, which is social media, right?
- 53:27SPEAKER_00: And there is a lot of uh you know information diffusion and online discussion forums where a lot of uh you know uh opinions and you know data is available.
- 53:41SPEAKER_00: And uh and information diffusion is one great example of virality that uh you know that can hit uh you know the uh overall uh social media as a network.
- 53:55SPEAKER_00: Uh how do you really uh you know how can game theory be used to ensure that uh you know it can be uh optimized for common good and for probably uh what you call as uh reducing fake news and ability to therefore build value for the user?
- 54:18SPEAKER_03: Yes, um, I think this is this is one problem on which uh we did uh some work.
- 54:25SPEAKER_03: Um this is the information diffusion problem.
- 54:29SPEAKER_03: So suppose you have a social network with uh a very large number of nodes, millions of nodes, and now information diffusion happens.
- 54:39SPEAKER_03: Uh for example, rumors can spread very fast, and as you said, viral uh you know, viral behavior can be exhibited by the social network and so on.
- 54:52SPEAKER_03: So now the there is a problem called as the influence maximization problem.
- 54:58SPEAKER_03: That is, if there is a positive news and you want to spread it uh you know very fast in the network, right?
- 55:07SPEAKER_03: Then how how do you how do you design your information diffusion process is a is a very important question.
- 55:16SPEAKER_03: So there is what is called as the influential nodes problem.
- 55:21SPEAKER_03: So if you're given a social network with millions of nodes, it turns out that uh there are a small number of nodes, uh the so-called influential nodes, which are actually playing a very important role in the information diffusion.
- 55:42SPEAKER_03: These are the well-connected nodes.
- 55:44SPEAKER_03: These are the well-connected nodes.
- 55:47SPEAKER_03: Game theory can be used to discover the most influential nodes in a social network.
- 55:56SPEAKER_03: Now, uh suppose you want to find who are the mo who are the hundred most influential nodes.
- 56:05SPEAKER_03: So what happens is uh you know you can actually use some plain graph theory.
- 56:09SPEAKER_03: You can use some graph theory, construct a graph of the social network, and then you can connect find out uh which are the most connected nodes and declare the most connected nodes as the most influential nodes.
- 56:23SPEAKER_03: But that is not the end of the story.
- 56:27SPEAKER_03: Because what happened, what happens is the most connected node may be in a very small cluster.
- 56:35SPEAKER_03: Fine.
- 56:36SPEAKER_03: If so, if it's in a very small cluster but very well connected, the news will spread only to that cluster.
- 56:43SPEAKER_03: So you have to look at inter-cluster connections also.
- 56:48SPEAKER_03: So we actually hit upon this idea that uh the influence of a node in a social network in terms of information diffusion can be determined using uh a cooperative game theory concept called the Shapley value.
- 57:07SPEAKER_03: So Lloyd Shapley, very celebrated game theorist.
- 57:12SPEAKER_03: Shapley and John Nash were PhD students with the same advisor, Professor Alan Tucker, uh, you know, in the Princeton University, and both were doing PhD at the same time.
- 57:28SPEAKER_03: So Nash was working on non-cooperative game theory, and Shapley was working on cooperative game theory.
- 57:35SPEAKER_03: And um, you would have known the famous Gail Shapley algorithm, which is a matchmaking algorithm.
- 57:43SPEAKER_03: So this the so-called stable marriage problem, matchmaking, you know, matching students to colleges, matching doctors to hospitals, matching kidney donors to kidney recipients.
- 57:56SPEAKER_03: So these this famous matching problem.
- 57:58SPEAKER_03: So, Gail Shapley algorithm is a very famous algorithm, which uh which is supposed to be the most fundamental contribution there.
- 58:08SPEAKER_03: Shapley has done wonderful things, he has contributed to non-cooperative game theory also, and he was the originator of what are called stochastic games, potential games, and so on.
- 58:19SPEAKER_03: So, there is what is called Shapley value.
- 58:22SPEAKER_03: What the Shapley value says is that if you have a cooperative game where the people are trying to cooperate with each other and they are also trying to bargain among themselves, and they engage themselves in what are called effective negotiations, then if there is a certain amount of surplus right that has to be shared among the players, what is the best way in which that can be shared among the players?
- 58:50SPEAKER_03: Is a is a central issue in cooperative game theory.
- 58:54SPEAKER_03: So, for example, if if there is a if uh there is 1000 rupees available and there are five players who are vying for that, right?
- 59:05SPEAKER_03: And how much should each player get based on the contributions that they have made?
- 59:10SPEAKER_03: So Shapley came up with a solution concept based on some axioms, very simple axioms.
- 59:18SPEAKER_03: He looked at what are all the desirable properties that should be satisfied by you know any such surplus sharing arrangements.
- 59:28SPEAKER_03: John Nash solved this problem completely for the two-player game.
- 59:31SPEAKER_03: It's called the Nash bargaining solution.
- 59:34SPEAKER_03: So if there are two players who are trying to share a certain uh surplus, then what is the best way in which they can share the surplus so that both of them are happy?
- 59:49SPEAKER_03: That problem was solved completely by John Nash.
- 59:52SPEAKER_03: So Shapley was looking at the problem in the context of multiplayer games.
- 59:56SPEAKER_03: So, in the context of cooperative games, it defined the Shapley value as a unique solution concept, which will tell you what fraction of the surplus should go to each player based on the contribution that each player is making to the overall game.
- 1:00:15SPEAKER_03: So we uh hit upon this idea that the information diffusion that happens in a social network can be actually modeled as a cooperative game because the information diffusion has to happen, two nodes have to come together, or multiple nodes will have to be involved when the information diffuses.
- 1:00:34SPEAKER_03: So, by defining the cooperative game appropriately, then we we computed the Shapley value, and the Shapley value basically gives the marginal contribution.
- 1:00:45SPEAKER_03: The intuitive meaning of Shapley value is if there are three players, right, then A, B, and C, what is the marginal contribution that A is making to B and C right in any coalition?
- 1:01:01SPEAKER_03: What's the marginal contribution that B is making to the game?
- 1:01:04SPEAKER_03: What is the marginal contribution that C is making the game?
- 1:01:07SPEAKER_03: So you can compute the marginal contributions of each one of these nodes to information diffusion game, and all that you have to do is to pick up if you're interested in the hundred most influential nodes, you have to pick up the hundred nodes having the highest shapely values and then do a little more work and you you have solved the problem.
- 1:01:28SPEAKER_03: Once you are able to get the most influential nodes, right, the rest of it can be managed.
- 1:01:34SPEAKER_03: Fine.
- 1:01:35SPEAKER_03: It can be either influence maximization.
- 1:01:38SPEAKER_03: So influence maximization means you give a t-shirt to each one of these hundred players free of cost and tell them why don't you advertise about my t-shirt?
- 1:01:48SPEAKER_03: T-shirt brand.
- 1:01:49SPEAKER_03: That is the influence maximization problem.
- 1:01:52SPEAKER_03: The influence there is also an influence limitation problem.
- 1:01:55SPEAKER_03: That is, if a rumor is spreading very fast, right?
- 1:01:58SPEAKER_03: And you want to contain the rumor, fine, then also you catch hold of these influential people.
- 1:02:05SPEAKER_03: And uh so what they do is there is a negative campaign which is uh getting diffused in the network.
- 1:02:12SPEAKER_03: Now these people start a positive campaign, right?
- 1:02:15SPEAKER_03: So these positive campaigns can be you know sort of triggered at the influential nodes.
- 1:02:21SPEAKER_03: Whether you want to trigger it in one phase or two phase or three phases and so on is another research question on which also we worked.
- 1:02:28SPEAKER_03: So whether it is information diffusion or influence maximization or influence limitation, right?
- 1:02:34SPEAKER_03: Uh game theory has certain toolkits, solution concepts which can be leveraged to solve this problem.
- 1:02:42SPEAKER_01: So, so Professor, I think one thing that I'm actually seeing is that if you take a very you if you take a particular stylo of knowledge and you add game theory into it, you get a cornucopy of excitement that actually comes out of it.
- 1:02:57SPEAKER_01: You take computer science plus game theory, you get algorithmic game theory, right?
- 1:03:02SPEAKER_01: You take uh evolutionary biology plus game theory, you get the cooperative Robert Axelrod sort of evolution of cooperation uh sort of a situation.
- 1:03:12SPEAKER_01: So I I want to know what happens when you take something like uh the human mind.
- 1:03:18SPEAKER_01: So, for example, if you 2002 the Nobel Prize was won by Carneman and uh Towerski, who were not really economists, they were actually cognitive scientists, right?
- 1:03:28SPEAKER_01: And what happens when you take those behavioral economics, you take a behavioral economist uh a behavioral economics sort of a stream and you add game theory into that, what does it really tell about how humans think and how humans behave and how humans make choices?
- 1:03:45SPEAKER_03: Yes, so um you can see that behavioral economics uh has um you know very close connections to game theory.
- 1:03:55SPEAKER_03: So, because game theory is all about how the human dynamics uh play out, and um the hardest problem in game theory is to define the game itself.
- 1:04:08SPEAKER_03: When you have to define the game, uh you have to first of all understand who are the players of this game.
- 1:04:15SPEAKER_03: For example, when we talked about uh the procurement auction, uh, there is a buyer and there are suppliers.
- 1:04:24SPEAKER_03: We have to decide whether buyer is also a part of the game or buyer is outside the game and only suppliers are participating in the game.
- 1:04:32SPEAKER_03: In the cake cutting example, we have to decide whether the mother is also a game player or only the two kids are playing the game.
- 1:04:40SPEAKER_03: So the first thing is to identify who are playing the game.
- 1:04:44SPEAKER_03: Second important task is you know what are the strategies available to each one of the players?
- 1:04:52SPEAKER_03: Right, is the strategy space same or different?
- 1:04:56SPEAKER_03: Third one is uh utility functions.
- 1:05:01SPEAKER_03: How do you define the utility of a player?
- 1:05:05SPEAKER_03: Utility of a player is basically if player one is playing strategy one, player two is playing strategy two, player n is playing strategy n, so that vector of strategies being played by the n players is called a strategy profile.
- 1:05:25SPEAKER_03: So in each and every strategy profile, right, you have to identify what is the utility that if player one plays strategy one, player n plays strategy, and what is the utility that is going to accrue to each of the players is what you are supposed to decide with the utility functions.
- 1:05:47SPEAKER_03: Now, in behavioral economics, you're basically looking at how one uh person will respond to you know.
- 1:06:00SPEAKER_03: The moves made by the other person or the group behavior of a coalition of players and so on.
- 1:06:07SPEAKER_03: So you have to find a way of codifying that behavior in the form of utility functions, having defined a strategy space.
- 1:06:18SPEAKER_03: If you are able to do that, there is a close connection established between behavioral economics and game theory.
- 1:06:27SPEAKER_03: I would go to the extent of saying that game theory gives you a mathematical abstraction to get an initial analysis of behavioral economics.
- 1:06:43SPEAKER_03: But game theory may not help you to capture each and every aspect of behavioral economics, and that is when you have to get into you know field experiments, you have to get into you know agent-based simulations in order to you know make more sense out of the behavioral dynamics that happens among the players.
- 1:07:10SPEAKER_01: Sorry, Professor, sorry for the interruption.
- 1:07:11SPEAKER_01: But is that is that uh is that is that juncture because game theory is based on the premise that the people playing in the game are intelligent and rational, as you say, whereas the opposing belief is what drives behavioral economics that people are irrational and people are not as intelligent as they seem and they are bound to make mistakes.
- 1:07:32SPEAKER_03: Absolutely.
- 1:07:33SPEAKER_03: So um it is not it is not true that uh game theory does not model situations where people are irrational.
- 1:07:41SPEAKER_03: Um well, rationality and intelligence are two fundamental assumptions which are made in game theory, however, when you define the solution concepts in game theory, so there are worst-case solution concepts.
- 1:07:56SPEAKER_03: What are these worst-case solution concepts?
- 1:07:59SPEAKER_03: An example is what is called maxim value.
- 1:08:02SPEAKER_03: Maximan value of a player is in some sense the minimum utility that is guaranteed to the player when all the other players gang up against him and play the worst possible strategy profile against this player.
- 1:08:22SPEAKER_03: That's called the maximum value.
- 1:08:25SPEAKER_03: Minimum guaranteed payoff that you can get under the very worst case.
- 1:08:30SPEAKER_03: Now you can see you are now assuming that the other players may not be rational, they can be they can do anything, whatever the other players do, whatever the other players do, what is the minimum guaranteed payoff that you can get is the maximum value.
- 1:08:46SPEAKER_03: Similarly, there is also what is called a min-max value which proceeds on the same lines by assuming worst case behavior from the rest of the players.
- 1:08:53SPEAKER_03: Fine.
- 1:08:54SPEAKER_03: So you can see that game theory is founded on principles of rationality and intelligence in order to develop all the central notions of game theory.
- 1:09:04SPEAKER_03: However, you also have solution concepts which take into account irrational behavior of the rest of the players.
- 1:09:13SPEAKER_03: That is point number one.
- 1:09:15SPEAKER_03: Point number two is behavioral economists essentially fundamentally question the assumptions of rationality and intelligence.
- 1:09:25SPEAKER_03: Right?
- 1:09:26SPEAKER_03: But behavioral economists also require a certain baseline model to get a grounding of the problem first.
- 1:09:34SPEAKER_03: Having got the grounding of the problem, then they can actually relax assumptions of rationality and intelligence and then derive all the other interesting behavior that can be exhibited.
- 1:09:50SPEAKER_03: So, in either case, uh game theory happens to be a very valuable tool that can be used by behavioral economists also.
- 1:09:58SPEAKER_00: So, Professor, uh I have this uh interesting uh you know question that I've been asking myself.
- 1:10:06SPEAKER_00: Uh there are businesses which have a lot of data and they are able to apply you know various game theory models to optimize and to maximize their revenue, right?
- 1:10:20SPEAKER_00: So that's the typical model that every business has got, whether it's on the procurement side, whether it's on the revenue maximizer maximization side.
- 1:10:30SPEAKER_00: But imagine the most exploited is this individual human being, right?
- 1:10:37SPEAKER_00: If I'm a you know player and I want to maximize my uh you know utility function, right?
- 1:10:47SPEAKER_00: And I want to beat the business in their games, okay.
- 1:10:52SPEAKER_00: Uh, how do I do it given the fact that I don't capture data, I don't do machine learning.
- 1:10:58SPEAKER_00: Uh, you know, therefore, this conflict between intuition and optimization, okay, is something that uh you know I've been thinking about.
- 1:11:07SPEAKER_00: And uh, how do we how do you see that happening in the future?
- 1:11:10SPEAKER_03: So I think this is where um you know policy making comes into picture.
- 1:11:16SPEAKER_03: Policies are very important.
- 1:11:19SPEAKER_03: Um, whoever is responsible for making these policies uh has to apply their mind and put in place policies by which uh everybody in the system is able to maximize their utilities.
- 1:11:38SPEAKER_03: Now there are two uh philosophies.
- 1:11:44SPEAKER_03: One is the egalitarian philosophy, another is a utilitarian philosophy.
- 1:11:50SPEAKER_03: Egalitarian philosophy is the philosophy of uh you know, in some sense, um equal share for everybody, some sense, fairness, whereas utilitarian principle says that you maximize the sum of the utilities of all the players who are involved, and there is usually a conflict between these two.
- 1:12:16SPEAKER_03: There is usually a conflict between these two.
- 1:12:19SPEAKER_03: Egalitarian solutions are not necessarily utilitarian, and utilitarian solutions are not necessarily egalitarian.
- 1:12:27SPEAKER_03: Now, policymakers, for example, you are you were talking about businesses trying to maximize their revenue, and uh individuals are helpless against these strategies and so on, but there is also an agency called the Central Design Authority or the government, which is supposed to put in place certain policies so that uh this can be completely you know prevented.
- 1:12:58SPEAKER_03: Fine.
- 1:12:59SPEAKER_03: So that is where I think what they will have to do is to look at how one can achieve a very nice trade-off between egalitarianism and utility utilitarianism.
- 1:13:16SPEAKER_03: Such solutions are possible, and game theory gives lots of pointers to such solutions.
- 1:13:22SPEAKER_03: To give you a very simple example, I was talking about the Nash bargaining solution.
- 1:13:29SPEAKER_03: Now, if there is a surplus that has to be shared by two players, right now one approach is egalitarianism, egalitarian, another is utilitarian, right?
- 1:13:44SPEAKER_03: But then what is good for the players, right, may not be egalitarian, may not be pure egalitarianism, may not be pure utilitarianism.
- 1:13:55SPEAKER_03: So what you do is that you define a solution which is in some sense what is called lambda egalitarian and lambda utilitarian.
- 1:14:08SPEAKER_03: That is these are approximately egalitarian, approximately utilitarian because you are trying to achieve a trade-off, and this approximateness you are capturing using a factor called lambda.
- 1:14:25SPEAKER_03: John Nash brilliantly showed that there is one meeting point for lambda egalitarian and lambda utilitarian solutions.
- 1:14:35SPEAKER_03: Showed that there exists a lambda such that lambda egalitarian solution is the same as the lambda utilitarian solution, and that precisely happens to be the Nash Burgering solution.
- 1:14:51SPEAKER_03: So I think uh I'm I'm giving a very devious answer to your question.
- 1:14:56SPEAKER_03: I'm only saying that this kind of uh you know situations can be somewhat taken care of by designing very sound policies, and these policies should be based on you know principles like you know egalitarianism, utilitarianism, and so on.
- 1:15:15SPEAKER_03: And the policy makers should apply their mind in order to put in place uh certain protocols by which you know this kind of uh situations can be avoided.
- 1:15:28SPEAKER_03: I know that I'm not answering your question completely, I'm only saying that game theory gives you certain tools with which you can approach the problem.
- 1:15:38SPEAKER_01: Okay, uh we now head into a rapid fire sort of a situation that we have prepared for you, Professor.
- 1:15:44SPEAKER_01: So we'll ask you a question, you can give an answer as short or as long as you like, uh, based on how you feel about the question.
- 1:15:52SPEAKER_01: So, my first question to you is Professor, what are some of the books that have influenced you the most over the course of your life and career?
- 1:15:59SPEAKER_03: Okay, so uh the four or five books which have influenced me the most, I will tell you Maskalel, Winston and Green, Microeconomic Theory, Hallvarian, Intermediate Microeconomics, Roger Meyerson, uh, who wrote this book on game theory, and uh finally the book on auctions by Vijay Krishna.
- 1:16:21SPEAKER_03: So these are the four books which have influenced me the most uh in the recent times, I would say in the last 20 years.
- 1:16:29SPEAKER_00: Professor, my question uh to you is uh if you were to advise an 18-year-old in college on how he should look at his future skills and what should he be building for the future, what are the three or four top things that uh the 18-year-old should focus and uh build uh their skills on?
- 1:16:54SPEAKER_03: I think the first one I would suggest is uh mathematical rigor and no compromise on you know the mathematical content in whatever they are studying.
- 1:17:09SPEAKER_03: That's uh number one because mathematics is behind almost everything these days, and sound mathematics will give you sound solutions.
- 1:17:18SPEAKER_03: That is number one.
- 1:17:20SPEAKER_03: Number two, problem solving.
- 1:17:23SPEAKER_03: Don't focus on you know all the textbook type of things, uh, don't read just the theory part and not solve the problems, solve the problems, try to solve the problems first and then study the theory, right?
- 1:17:38SPEAKER_03: So, problem solving is very important.
- 1:17:41SPEAKER_03: Uh, the third thing that I would uh say is that instead of uh watching the TV and looking at the mobile phone, read a non-technical book, read some nice novels, and uh for example, read Wodehouse that will go a long way in elevating the quality of your life.
- 1:18:09SPEAKER_03: That's the third thing I would uh like to advise them.
- 1:18:14SPEAKER_03: And uh the fourth thing that I would uh like to tell them is that you know there is a place for non-technical things in life, and uh they should also try to do many non-technical things and try to implement things rather than imagining you know how to do things.
- 1:18:38SPEAKER_03: They should actually try to implement things even if it is very, very small things, and uh the best way to do that in the house itself, you can start that in the home itself.
- 1:18:49SPEAKER_03: So I have personally found that I get a lot of uh delight, a lot of satisfaction by cooking in the house, which I may not do every day, but I think this is a beautiful diversion that uh one can have.
- 1:19:05SPEAKER_03: And uh well, I think uh you wanted only three or four things.
- 1:19:12SPEAKER_01: So, Professor, my next question is uh if you could invite four guests for a dream dinner, who would they be and why it's a very it's a very difficult question.
- 1:19:28SPEAKER_03: So dream dinner, certainly my father, my mother.
- 1:19:37SPEAKER_03: Um okay, my professor, and uh of course my wife.
- 1:19:46SPEAKER_03: So these are the four people that I love most.
- 1:19:53SPEAKER_03: This is not a very fair question.
- 1:19:58SPEAKER_00: Uh Professor, uh, my next question to you is what does the word uh successful mean to you?
- 1:20:06SPEAKER_03: The word successful, you know, sort of um means uh that you should be able to make a difference somewhere.
- 1:20:16SPEAKER_03: Um I think uh you know last uh one and a half to two years, there is something that uh I'm trying to do, right?
- 1:20:27SPEAKER_03: And uh in the next three years, what I do there will either become a blockbuster hit or it will be a miserable failure.
- 1:20:37SPEAKER_03: But I'll be happy either way.
- 1:20:40SPEAKER_03: I'll be happy either way.
- 1:20:41SPEAKER_03: I'm telling you what I'm doing.
- 1:20:44SPEAKER_03: I'm just trying to look at uh Indian agriculture and uh I'm trying to see whether something can be done there, right?
- 1:20:53SPEAKER_03: Obviously, you know, game theory is a tool that I'm familiar with.
- 1:20:57SPEAKER_03: So, game theory is like a hammer for me.
- 1:21:00SPEAKER_03: I'm looking for nails, right?
- 1:21:04SPEAKER_03: And I I'm also reasonably familiar with uh AI ML techniques.
- 1:21:09SPEAKER_03: In fact, last semester I offered a course on AI for social good.
- 1:21:14SPEAKER_03: Now uh I found that uh you know I should try out whatever I whatever little I know on Indian agriculture.
- 1:21:23SPEAKER_03: The reason for that is that uh you know when I was reading some papers, it turns out that 85% of uh farmers in India are smallholder farmers or marginal farmers.
- 1:21:40SPEAKER_03: These are farmers you know who hold less than five acres of land, and for a variety of reasons, the kind of I think the greatest risk in India is faced by the farmers.
- 1:21:55SPEAKER_03: There is risk because of nature, there is risk because of government, there is risk because of middlemen, there is risk because of market fluctuations and so on.
- 1:22:07SPEAKER_03: So I'm trying to work on some problems which will possibly help the farmers.
- 1:22:15SPEAKER_03: And this is one area where you know I want to inspire my students and also work with startups and develop two or three mobile apps for the farmers, which will help them in whatever they do.
- 1:22:32SPEAKER_03: I think one mobile app will be for estimating the price of whatever they are growing right now reasonably accurately.
- 1:22:44SPEAKER_03: The second mobile app is to recommend a portfolio of crops for the next one year based on a variety of conditions, fine, and taking into account even cultural factors.
- 1:22:59SPEAKER_03: See, when I when I go to the farmer and then tell him, right, I'm trying to develop uh some of these things, they will say, Sir, you don't know anything, right?
- 1:23:09SPEAKER_03: We we know for for centuries we have been doing this, we know what to do and so on.
- 1:23:15SPEAKER_03: It's not very easy to convince.
- 1:23:17SPEAKER_03: So all the algorithms that I develop, uh you know, I want them to be explainable and explainable in a language that will be understood by the farmers.
- 1:23:26SPEAKER_03: So that's the second mobile app.
- 1:23:29SPEAKER_03: The third mobile app I'm trying to do is using cooperative game theory, former collectives.
- 1:23:38SPEAKER_03: In fact, right now in India there are more than 6,000 plus uh so-called uh you know former producer organizations, FPOs they are called.
- 1:23:47SPEAKER_03: These are former collectives, they are these are former cooperatives, right?
- 1:23:52SPEAKER_03: And you know the super success of Amul, for example, right?
- 1:23:57SPEAKER_03: That is that is very well known, very well documented, right?
- 1:24:01SPEAKER_03: And I know that there are many people who have tried to replicate the Amool model in the farming sector and they have not been very successful, right?
- 1:24:09SPEAKER_03: For whatever it is worth, I really want to choose at least one aspect of agriculture and uh see whether the Amool model can be repeated there using some principles of cooperative game theory.
- 1:24:21SPEAKER_03: So these are the three things that I'm trying to do over the next three years.
- 1:24:24SPEAKER_03: As I said, uh you know, whatever whatever little I'm able to do, if it is if if it can create even an epsilon impact, I would consider that as a smashing success.
- 1:24:37SPEAKER_03: Because I know that even epsilon, when you multiply by the volumes of the farmers, it will be a huge number.
- 1:24:45SPEAKER_01: That's a great answer, Professor.
- 1:24:47SPEAKER_01: My next question is uh what's the best piece of advice anybody has ever given you?
- 1:24:53SPEAKER_01: Oh, okay.
- 1:24:54SPEAKER_03: I think that's a very, very interesting question.
- 1:24:58SPEAKER_03: Okay, I I will I will tell you that.
- 1:25:01SPEAKER_03: Um I was uh doing my third year BSc.
- 1:25:06SPEAKER_03: I was doing my third year BSc, and my brother's marriage was taking place, and uh then my brother's uh future father-in-law, he asked his name is uh Sri Anandra, he asked me the question, what are you going to do after BSc?
- 1:25:29SPEAKER_03: So I was studying in National College Gavari Bindnur.
- 1:25:32SPEAKER_03: My vision for myself was because I'm reasonably good in maths, I wanted to do MSc maths and then come back to the college as a lecturer in the college.
- 1:25:44SPEAKER_03: That is what I precisely told him.
- 1:25:47SPEAKER_03: Right?
- 1:25:47SPEAKER_03: I want to do MSc maths in Central College, uh, Bangalore, right?
- 1:25:52SPEAKER_03: And then get a good percentage, and then get a job as a lecturer in National College, Gauribidnur.
- 1:26:00SPEAKER_03: And that is where I would like to teach my mathematics.
- 1:26:04SPEAKER_03: He said, Do you know that you can do your MSC in Indian Institutes of Technology?
- 1:26:13SPEAKER_03: Then I told him I don't know what are IITs.
- 1:26:18SPEAKER_03: He also told me, do you know that there is a BE program, three E or BE program after your BSE in what is called Indian Institute of Science.
- 1:26:30SPEAKER_03: I said I do not know anything about IASC.
- 1:26:34SPEAKER_03: Frankly, I did not know much about IAS, and this happened in my early third year BSE because I think the level of awareness was very low at that point of time, right?
- 1:26:46SPEAKER_03: He said, you know, my first son has done his BE in IASC after finishing his BSE, and after finishing BE, he is now working as a manager in BHEL.
- 1:27:00SPEAKER_03: So why don't you try getting into a BE program in IASC?
- 1:27:07SPEAKER_03: So that's the first time I came to know about IISC, and uh I think they will say rest is history, they will say I applied to I applied to IISC knowing about IASC just three months before applying to IASC and I got a selection here.
- 1:27:24SPEAKER_03: This was in 1979, and from 1979 I am only in IASC.
- 1:27:30SPEAKER_03: I was a student here, I'm a faculty member here.
- 1:27:33SPEAKER_03: So I became a scientific, so I finished my PhD in 87, I became a scientific officer, then I became a lecturer, I became an assistant professor, then an associate professor, then a full professor, then I was chairman of the computer science department for four years, then I was actually chairman of the entire division of uh EECS for seven years.
- 1:27:58SPEAKER_03: That's where I am.
- 1:28:00SPEAKER_03: Right?
- 1:28:00SPEAKER_03: I think that was a turning point.
- 1:28:04SPEAKER_00: And uh my last question to you is what is one thing that you believe in that others disagree with you?
- 1:28:14SPEAKER_03: This is others my view of life uh is to be very positive about everything.
- 1:28:26SPEAKER_03: And anybody and everybody you know makes mistakes, right?
- 1:28:34SPEAKER_03: Just ignore the mistakes and then move on.
- 1:28:38SPEAKER_03: This is something that I firmly believe in.
- 1:28:42SPEAKER_03: I don't think anybody in this world agrees with me on this.
- 1:28:46SPEAKER_02: Nobody agrees with me in this.
- 1:28:49SPEAKER_03: Because they don't want to, they don't want to not punish.
- 1:28:53SPEAKER_03: They don't want to not punish people who have done mistakes.
- 1:28:56SPEAKER_03: And they think that is my greatest weakness.
- 1:29:00SPEAKER_01: Thank you for that answer, Professor.
- 1:29:02SPEAKER_01: My final question to you is if you could invite or if you would like to see another guest feature on countermines, who would it be and why?
- 1:29:12SPEAKER_03: Please get uh Narendra Bodhi.
- 1:29:18SPEAKER_03: If you can manage to get Narendra Modi on this, I think Counter Minds will be in a different plane altogether.
- 1:29:25SPEAKER_03: So that would be that would be very nice.
- 1:29:30SPEAKER_03: But um, you know, if you really uh ask me that question, then you should certainly get uh you know I really love this person, Professor Vivek Borkar from uh IT Bombi.
- 1:29:44SPEAKER_03: So he's my role model, and he has shown to the entire world that uh you know um India India can actually produce brilliant individuals, and uh the kind of publications and the kind of uh training that he has given to his own students is something he's like a role model for me, Professor Vivek Borkir from IIT Bombay.
- 1:30:09SPEAKER_03: Very, very simple, humble, uh, but you know, absolutely brilliant and uh you know scholar for excellence in mathematics.
- 1:30:20SPEAKER_03: He's actually uh he was uh you know President's Gold Medal winner in IIT Bombay.
- 1:30:27SPEAKER_03: Then he went to University of California, Berkeley, and did his PhD with Professor Praveen Varaya, and ever since he has actually been India and wonderful, wonderful.
- 1:30:39SPEAKER_00: Thanks a lot, Professor.
- 1:30:40SPEAKER_00: Uh it was a fantastic conversation, and uh I'm not even uh you know able to really look at the time and say, you know, about one and a half hours has passed with such interesting and deep topic as game theory.
- 1:30:57SPEAKER_00: You have made it so easy and uh extremely lucid in terms of explanations, and uh I really thank you for your time and it was fantastic talking to you.
- 1:31:11SPEAKER_03: Thank you very much.
- 1:31:12SPEAKER_03: I should say that I also really enjoyed uh you know the conversation.
- 1:31:16SPEAKER_03: I see that it's already 19 uh 745 or something like that.
- 1:31:20SPEAKER_03: I think it has almost uh crossed one hour, one hour, uh one and a half hours.
- 1:31:25SPEAKER_03: So I thoroughly enjoyed.
- 1:31:27SPEAKER_03: And uh, you know, some of the questions were absolutely I think uh you know enjoyable to me.
- 1:31:33SPEAKER_03: Very nice interacting with uh both of you.
- 1:31:36SPEAKER_03: Wonderful experience for me.
- 1:31:38SPEAKER_03: Something that I will remember for a long, long time.
- 1:31:40SPEAKER_00: Thanks a lot, Professor.
- 1:31:43SPEAKER_00: Thanks for listening to this episode.
- 1:31:46SPEAKER_00: For selected links and detailed show notes, visit www.contramines.com slash blog.
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