 Now let us look at a slightly different example. Suppose there is one cake and there are two kids and their mother wants to divide the cake in such a way that both these individuals, both these kids, are happy with his or her portion. What do we mean by happy? That they do not envy each other. So one way of defining that is that after the division is done, kid one will think they got at least half of this cake. And the other kid will also think that she also got at least half of that cake. I would like to emphasize that this view that they are getting half of that is according to their own view. And the mother does not know, nobody essentially knows what they actually like. So maybe some of them like the cherry on top, some of them like the chocolate part more than the other parts. And this is completely unknown. If the mother knew everything, every choice or every preference of these individuals, then she could have actually made the division herself and given the pieces to them. Now this at least half as we have mentioned, this notion is subjective. And this is also a private information of each of these kids. Now without this information, if the mother cuts this cake and gives the pieces to each of this child, then there could be a possibility that one child will say that the piece of the other child is actually larger. And that will create a situation of an envy. Now the question that we are going to ask in this context is how can you make or can you at all make this kind of a division to be envy free so that nobody essentially envies each other's pieces? Now this is a kind of a classical problem, very age world problem. And therefore it also has an age world solution. So how does it do? Before that, let's list down the challenges. So the mother wants to achieve what we will call a fair division, fair as in envy free, but it does not have, the mother does not have enough information to do that fair division. In other words, it does not even know that what is a fair division. So how can you still do a fair division without knowing this information? So this is naturally bringing us to the situation of mechanism design. Can she design a mechanism that with this incomplete information the mother can achieve a fair division? And people who had siblings might have come across the situation very often. And here is one solution, one very interesting and quite a well-known solution. Let us call this mechanism, I cut you choose mechanism. So what the mother says is that it identifies one of this case, let's say kid one to cut the cake, but kid two to choose her favorite piece. So it will not allow the person who is cutting the cake to pick the first piece, the remaining piece will be picked by kid one. This is the I cut you choose mechanism. So let us try to understand why this mechanism works. So the first thing is that you would see that kid one when this mechanism is designed and the rules are told to this kids, the kid one will know that it will get the second piece after kid two has picked her piece. So kid one will try to make the division as equal as possible in his view. So his view might be different from the other kid's view, but he will divide it exactly in half according to his view so that he is indifferent between these two things. Because he knows that if he cuts it unequally the other kid might pick the bigger piece and he will be envious. So he will do it in exactly the halfway and he will be happy with any of the pieces that he gets. Kid two will also be happy because he got exactly the first piece to pick. I mean, if in his view, in kid two's view, one of the pieces were larger then she gets to pick that larger one and she will not be envying the piece that kid one gets. So this will solve the problem for both these people. Nobody will envy each other's pieces and that will solve this problem for the mother even without knowing what is a fair division. So isn't that a classic mechanism? So that is exactly what mechanism design is all about. We are going to discuss that and quite naturally it is the inverse of the game theory. We started with an objective to do a fair division and we designed the game and this mechanism is essentially that designed game which gave you the desirable or the reasonable outcome in this case the fair division outcome as the equilibrium and nobody will like to deviate from it. So this is essentially giving you a prescription. So this is why it is called the prescriptive approach mechanism design. Why should we care to design a game in practice? And there are many such examples. So this is certainly a toy example but you can extrapolate that example for various other kind of fair division problems. Just imagine the division of some other resources when there are various other kind of influences or constraints. So one example that I'm going to talk about specifically which really happens in practice is about sports tournaments. So imagine the cricket tournaments or football tournaments, any other kind of sporting tournaments. Typically those tournaments have the teams are being partitioned into different groups and the first round is a round robin where every team in that particular group plays against each other. And then finally the top two qualifies to the next round. Now we are going to ask whether this is a really good tournament design. And I'm going to argue that it is not. And here is one example. Let us go back a little bit. In fact, there are various such examples in the recent past, in particular the 2012 London Olympics in the badminton tournament. Very similar thing had happened. You can search for it. But let me keep my attention focused on this specific example. The World Cup footballer soccer of 1982. So and this happened in group two. So at that point, there were various teams and Austria was one of the very strong teams at that point. It was much stronger, presumably on paper than most of the other teams. And Chile was the weakest team in this group. There was no doubt that Chile has very little chance to qualify to the next round. The only contest is between Algeria and West Germany who are kind of quite close to each other. Now in the first game, some shock happened. I mean, even though West Germany was slightly better than Algeria, Algeria actually beat West Germany in 2-1. This was a shock defeat for West Germany. And that essentially started this whole event of how game theory can come in or mechanism design can come in into this situation. So the rest of the games until the last game was very uneventful. Austria beat Algeria, which was expected. Algeria also beat Chile. So essentially everybody beat Chile. But what happened was Algeria beat Chile but by only a goal difference of one while West Germany beat Chile with a larger goal difference. So in goal difference way, West Germany was ahead of Algeria. Now all that depends is on the last game between West Germany and Austria. So the final game was between Austria and West Germany and almost everybody assumed because Austria is a much stronger team. West Germany has no chance to win against it. So if they draw or even if they lose or make a draw, Algeria is going to qualify. But that is where the whole game theory part started. This essentially West Germany and Austria made a pact for whatever reason. They made a contract that they will essentially get will be losing. So Austria will be losing to West Germany. So in the first 10 minutes of the game, West Germany was very aggressive and scored one goal. And then in the rest of the game, they both these teams just stopped playing. They did not, they were doing some passes around and there were no competition among them. And both the spectator account and all the other documents essentially point to the fact that they decided the outcome. What happens in that case is because Austria has already qualified, it doesn't really matter for them whether they lose or win at the last game. But for West Germany, because of its win, it gets the points which equals Algeria. But because it has a larger goal difference than Algeria, it actually qualifies. So Algeria gets eliminated and West Germany and Austria qualifies. So if you want to dig deeper into it, you can search with disgrace of Gijon. Gijon is the place in Spain where this tournament took place in 1982 and you can get more information. Now, if we have to say what was the reason, it is not about the players, like the teams. In fact, FIFA's final ruling was that none of these teams have actually broken any rule. It was the rule that was imperfect, the mechanism in which these tournaments were designed was imperfect and these teams just took advantage of that. So similar things happened, as I mentioned in 2012 in London Olympics. So the point here that I'm trying to make is that your tournament design should be some sort of truthful in some sense so that none of these teams have any incentive to do such kind of a malpractice in the game. Later on, after this incident, FIFA has changed its tournament design slightly by making the last two matches which are quite a deciding factor among these teams simultaneously. But that also does not completely solve this problem. So you can think of a completely different tournament design as happens in most of the tennis tournaments where it is knockout from the very beginning, but that gives very little chance for anything to come back. So for instance, if there was just due to some other reason, they did not perform well in the first game itself, they have no chance to come back into the tournament. So there is a kind of a disparity and maybe it's a very interesting mechanism design problem, how you can keep both these chances of coming back to the tournament as well as not doing this kind of strategic manipulations. So that is what we will be discussing in the second part of this course in mechanism design. So the broad outline of this course is that first we'll be talking about non-cooperative game theory. That is what I meant by game theory. We'll not be discussing another component aspect of game theory, which is cooperative game theory. And in the second part we'll be discussing in mechanism design in more detail. And that is the focus of this course. The first part is essentially a preparatory phase for the second part. And in between we'll be giving various applications where both this game theory and mechanism design could be useful. So at the end we will be able to apply the principles of economic theory and computation to understand incentives in social systems and that on the internet. And we'll get test for mathematical description of the social problems. And if you are interested, you can also transform this understanding into deployable AI system that does all this decision-making automatically. So this course will be mostly self-contained and we'll share the lecture notes and also these videos will be available. But if you really want to read some of the books and do problems, there is a game theory book by Mashla, Solan and Zameer and a multi-agent systems book by Shoham and Lettendran and several other references which are also given on the course webpage.