 So, let us define this. An extensive form is said to be nested if each player has access to the information by all its predecessors. So, what does this mean? So, you take a game like this which is, so I will just draw this something like this. So, take player 1, then you have player 2, then you have player, so of course this is player 3. Now, what you have to check is, does each player have access to all the information that is known to its predecessors. Now, the information that a player would know depends on the node that he is on. So, the information set that is on. So, what you have to ask is in each information, this has to be checked when you say each player, it really has to be checked at each information set of that player. Now, that information set has some parent and then grandparent and so on some predecessors corresponding to that. You see what information do the predecessors have along the, you know, for the predecessors of that information set have. What information do they have at their information sets? And check if this player has all the information that is predecessors had. So, let us do this as an example first. Now, does player 3 for example, so let us look at this information set of player 3, the yellow one. Does player 3 have all the information that his predecessors have? Does he have all the information that his predecessors have at this information set? So, what does he know at the left information set? Yeah, he just knows that P1 has played this arm and then P2 has played. So, he knows that. Now, what does P2 know? So, P2 is the predecessor here at this. So, what does P2 know at this information set? He just knows P1 has played. So, P3 does know that P, what P2 knows. So, P3 knows all the information that P2 had at his information set, at P2's information set. So, P3 does know, say similarly here, here again P3 knows whatever information that P2 had. Now, what about P2? Does P2 know whatever its predecessors knew? Obviously, because predecessor is P1, P1 started with null information, P2 knows that P1 has played. So, he actually knows more than P1. So, that is ok. A player can know more than the predecessor, but cannot lose the information that predecessors already know. Is this clear? So, that is a nested form. Now, so let us take this one. So, this is player 1, this is now player 2, this is player 3. So, let us ask ok, is this nested? Does player 3 know what its predecessors know? So, we have to go information set wise. He has only one information set which is this one. At this information set, what does player 3 know? P1 and P2 have played. He does not know anything else, what they have played. He just knows that P1 and P2 have played. Then, what does P2 know? He knows what P1 has played. So, if P1 has, if this was L and R, he knows whether P1 has played L or P1 has played. So, here he knows that P1 has played R. And here he knows that P1 has played L. So, P2 now knows something which P3 does not. So, therefore this is, so this one is nested. This one is not nested. But you see here is the interesting thing and this is something that comes up because of the, there is a little bit of variability or some leeway we have when we are writing information, when we are writing extensive forms. Now, this is an extensive form of some physical situation and the physical situation is player 1 has played. Then player 2 can knows what player 1 has played and then player 3 plays without the knowledge of what player 1 has played or player 2 has played. That is the situation. Now, this we know is strategically equivalent to the case where player 3 plays like this. So, suppose player 1 plays, then player 3 plays and then player 2 plays. Is this the same as this problem? The problem on the left and the problem on the right. Are these the same? Why are these the same? See, let us ask what does each player know at this? Player 1 is starting in both cases, he starts with the null information set. I am of course going to put the same payoffs at the leaf nodes. So, player 1 starts with null information in both cases, same set of actions in both. Player 3 here, what does player 3 know here? Player 1 has played but he does not know what he has played and player 2 has not yet played chronologically. Player 2 has not yet played. So, he again does not know what player 2 has played. I mean this is because that has not even happened. So, at this information set, player 3 actually does not, player 3 does not know what player 1 has played or what player 2 has played and that is the same as what he knew here. Now, here you may say, well he knows player 2 has played but knowing that player 2 has played is not payoff relevant. His payoff remains the same regardless of his knowledge of whether player 2 has played or not because the payoff just depends on the finally the leaf node that he reaches. That way he may know a whole lot of other things. He may know if player 2 is wearing a hat or not. The question is whether that is payoff relevant. So, this is a trick essentially. What has happened is what we have done is we have although yes it is true that player 3 knows something here on the left additional to what he knows on the right but that additional thing is not payoff relevant. So, essentially strategically it is the same as player 3 knowing the same thing in both cases. He does not know what player 2 and player 1 have played. Now, it could happen I mean in this particular extensive form it does not happen but it could happen that that knowledge of whether someone has played or not itself is embedded in the definition of the game in the formulation of the game and so on. But then that is not happening in this particular setting. So, if for example there could you had information sets where the exact difference was whether between so player 3 knew what player 2 had played he would get one piece of information and add another one part of the tree and whether he did not know that player 2 had played then he would get another tree then that would be a different situation altogether. But essentially the in the kind of games you see that is a much more exotics in a situation it leads to you know non-sequential because of different problems and so on where the order of play actually affects the strategic actions of players. But in this case that is not the case because what the actions available to player 3 are the same and the payoffs are the same regardless of what the player 2 has played before or not. Now, if you just want to see an example where this whether player 2 has played or not matters right is say for example if you have say some kind of a resource constraint you do not know how much player 2 has played but that he has been there tells you something right that he has consumed some amount of the resource or something like that that tells you something. So, that is not present in this game. So, therefore essentially what we have done is player 3 now knows the same and likewise player 2 also knows the same player 2 here does not know what player 3 has played but was player 1 what player 1 has played. So, if what you can the the the important thing is so this is nested and now these two are actually the same right. So, therefore this is this is also nested and equivalent equivalent equivalent to this. So, what this also means is that whether something is nested or not is a matter of the extensive form not not necessarily the physical situation in the game. So, extensive form therefore is a modeling device you may want to model games in various ways some kind of models will help you do analysis better some kind of model will not ok. So, this is a modeling technique and so you know it is part of I mean how you model will define decide how the eventually the analytical is that you have ok. So, an extensive form so no definition. So, but we this by itself nested being nested by itself is not enough to help us decompose because you see what happens is as I said you cannot go further from here ok because these are these two are in the same information set of player 2 ok. So, you can refine this further an extensive form only difference between the information of a player let us say player I and its immediate precedent player I minus 1 is the actions of player I minus 1 and only nodes corresponding to branches only at corresponding to branches emanating from player I minus 1's singleton information sets. So, sorry I said to be ladder nested if it is nested this is a further definition I forgot to mention that if it is nested and the only difference ok. So, it has to be nested means that every player must have access to all the information that its precedent had ok. And if there is a difference in the information then that difference in information has to be only about the action of its immediate precedent and moreover that action has to be something that was taken at a singleton information set of that precedent ok. So, that basically kind of nails down this scenario where so you cannot have something like this. So, here player 3 did have more information than player 2 ok, but that information is not about the actions of player 2 ok. So, it is actually about the actions of player 1 alright. Whereas in this scenario you could have it is ok because here player 3 actually does not have any additional information about player 2 ok. So, I will give a more detailed example now. So, here for example, so you could have something like this player 1 and this then player 2 plays this then player 3 or let us say here ok. Now is this nested? So, what does player 3 know at this information set? On the let us take the one on the left he just knows that P2 played and he knows what P1 has played ok. He knows that P1 played left for example ok. So, he knows what P1 has played and he knows that P2 has played ok. So, this so and what does P2 know? P2 also knows that P1 has played left. So, player in this information set player 3 has this has all the information that player 2 has ok. Now let us come to this information set. This is a singleton information set of player 3. Player 3 does know all the information that player 2 has here also clearly and here also he has all the information that player 2 has ok. Now so, this is definitely nested as a result ok. Now question is this ladder nested. So, for us to check if it is ladder nested firstly it has to be nested and any additional information that player has above its over and above it what its immediate precedent has ok should be about the actions of that precedent and those actions have to be taken at singleton information sets is this clear ok. So, here what does player 3 know about this thing? He basically knows that player 2 he knows the same as what player 2 knows ok. So, he has he has no additional information he just knows that player 1 has played L1 player 2 also knows that player 1 has played L1. At this information set player 3 knows player 1 has played L1 and he knows that player 2 has played something this particular one what is this let us call this left we will write ok. So, he knows that player 2 has played left ok. So, this is additional information that player 3 has which player 2 does not have ok. Now this additional information equation is this additional information about the actions of player 2 it is about actions of player 2. Have these actions been taken at a singleton information set of player 2? Yes this action has been taken at a singleton information ok. So, therefore, this is likewise at this one also here the additional information is that player 3 knows that either player 2 has played either M or R this is information about player 2's actions and it is information that and these actions were taken at a singleton information set this is clear. So, therefore, this is both nested and ladder nested. So, I am sorry I forgot to mention we are in the world of single act games ok. So, these are single act games. So, in the single once it is a single act game and this is then it has to be that you can do the following you start from the leaf node ok go above and look for a single information set. And you look for the parent nodes of that information set either those parent nodes are all going to be in one information set or they are going to be former they are going to form there is going to be a single parent node. So, in other words you take a information set take its parent node ok take the immediate parent node they will all be in one information set and then take its parent they will also be in one information set and so on. So, in other words what is going to happen is that you should be able to decompose the tree into either something like this which is a simultaneous which is a game of perfect information a sub tree of perfect information or something like this or this which is a game of which is a simultaneous movement right because of the very nature by the way we have defined this ok. So, what this means is that you can actually find the equilibrium algorithmically.