 feedback Nash equilibrium is said to be of delayed commitment type, if it is appropriate restriction stage is a delayed commitment type for the corresponding single act game. So, obviously this tells you how much structure is needed before we even start analyzing and even after you put in so much structure, we can still get many different exotic equilibria and so on. And so for there we are therefore now looking for feedback Nash equilibria and in that feedback Nash equilibrium you can further restrict and say well we will look for equilibria of delayed commitment type. So, one of the main lessons that you see once you start looking at multi act games is how complicated the strategic analysis can become where you know even with a small number of stages like if you have two or three stages also you know the kind of variety that you can get variety of outcomes that you can get is tremendous okay. Let me draw one game and you tell me if this is in feedback form or not. So, let us say so and now I will write draw the information sets. So, is this in feedback form? You cannot I mean if this is not you can see actually you cannot may divide this into stages where each player is playing once and yet have you know information sets not going across stages okay that is not possible. So, this is not in feedback form not feedback form is not even stage wise form okay. If you so let us see is this allowed so player one. So, generally what we do is this is again as I said it is a part of it is more of a modeling device you specify the stages okay. You can there are more than one way of specifying the stages but you fix the stages first and then start drawing the information sets that is a that is a more that is a much more effective way of otherwise you could have of course there are more than one way of creating stages and then you could have complications because of that not necessarily not necessarily okay. Now here let me see say for example suppose I take so this is player one this is player two at this now here suppose I have this now is this okay. So, this is stage wise but it is not in feedback form and that is because of this information set that I drew which is going across two nodes which are in two different sub-trees right. So, this is not allowed so you cannot do this this is not in feedback form okay. But this kind of thing is not a problem okay remember it is there is no problem with having an information set like this because it is part of one the single act game in that starting from this particular node here okay likewise this is also not a problem see player two is not the first acting player at this stage. So, player two can have imperfect information at that you cannot similarly you cannot have something like this because then player then this at this stage player one is confused about you know what had happened in the previous stage okay. Now it may be possible for you to do to play around with this in some way by you could potentially you know depending on the problem you could potentially exchange these two make player two the first acting player in this and player one first acting player there but be careful again you cannot violate the other requirement where player one's information set should not go across two different branches of player the first acting player who is now player two okay. So, depending on the problem you may be or may not be able to do this so just be aware by not having it well you cannot see this thing right the if you so this when we write for all this effectively what we are saying is that regardless of what has happened in the previous stage you should be able to get an equilibrium which means that your strategy the equilibrium here is the what you are playing in every subtree is a function of what has happened along that subtree alone and not across and does not depend on the other parts of the subtree. So, if you have an information set like this this starts breaking down. So, what you essentially what will happen is now how to play in this tree and how to play in this tree become coupled and that in turn depends on what has happened in the previous stage because because you do not know what happened at the previous state I mean at least player two does not know no no it is not physical it is more analytical I would say it is an analytical thing which we are trying to you know yeah make you just it just makes the analysis is easier okay. Now again the informational inferiority as a concept again extends but here we talk of informational inferiority at each stage okay you cannot make create information you could but again it leads to becomes way more complicated you cannot create in I mean informationally inferior games by putting information sets across games across stages into one into one information set right then a player has forgotten which stage he is at which everything he forgets and that sort or he does not remember any of that that is also an inferior game but then results are much harder to prove for those kind of things. So, we talk of infinitional inferiority at a stage wise level okay. So, you take the information sets combine them at the stage wise level but still retain the feedback form and so on then you can you can potentially you know use the whatever results we had from before again I mean there is not once a game is multi-act game without putting structure we cannot analyze much more okay. So, this is pretty much all you know one can say sort of systematically otherwise the only approach to finding all all equilibria and or for finding any equilibrium is to just write out the normal form and then that is going to be you know a huge normal form with vast number of strategies for each player. So, we will stop here and so what we will do in the next class is we will go in a different direction and start talking about the use of randomness in a dynamic game okay ways of randomizing in a dynamic game.