 And immediately they were separated, there is no information between both of them, there is no communication between both of them and it is then the choice were giving to them whether they should confess or whether they should not confess. So, they are arrested, they are immediately separated and how the pay off will come, if convicted they will get a term of 10 years in prison, if the if the crime is proved they are getting conviction and conviction they are getting 10 years in prison. The evidence is not sufficient to convict them more than crime of possessing stolen good which carries a sentence of only one year. If the evidence is not sufficient to convict them because it is a case of robbery, so in this case if the it is not getting proved they cannot get the 10 years of prison. And they will just carry a sentence of only one one year because they have one crime left that they have a position of the stolen goods there in the with them. So, if it is it if you look at it is two different activity they are caught for being one, but still they have some stolen goods and for them they will get the punishment for one year. But if they are getting convicted for bank robbery they will get the punishment of 10 years. The suspects are given for information from the authority, they are told the following if you confess if you confess you your your accomplice does not you will go free. If you do not confess then your accomplice does you will get 10 years in prison, if you both confess you will get both get get 5 years in prison. So, these are the options given to the suspect, if you confess then you will go free because you have confessed that you have done the crime. If you do not confess, but your other one other one confess other partner that confess then you will get 10 years and you will go free, if both of you are confessing then you will get both get 5 years in prison. Now, from there we get they get this is the pay off matrix and how this pay off matrix, how the pay off matrix we can construct now this is for prisoner 1, this is for prisoner 2. So, in this case is getting 10 years, both of them they are getting there, so both of them get 10 years when both of them they confess then prisoner 2 if so let us call it this is confess, this is not confess, this is confess, this is not confess, if both of prisoner 1 and prisoner 2 both of them they are confessing they are getting the sentence of 10 years. If prisoner 1, prisoner 1 not confessing prisoner 2 confess then prisoner 1 here get 10 years and prisoner 2 gets, prisoner 2, prisoner 2 generally goes free because he has confessed both of them they are not confessing, prisoner 1 confess prisoner 2 not confessing prisoner 1. So, if we can call it is 1 not confess then we can call it prisoner 1 goes free. So, we get 0 prisoner 2 is get 10 years, both of them they are not confessing they get 1 1. Now, what is the best option or may be we can just change this on the basis of our pay off. So, if you confess and your accomplice does not you will go free and your accomplice will get 10 years. So, in this case there is a small change over here. So, this is 5 and 5. So, when both of them they are confessing they are just getting 5 years, when one is confessing the other one is not confessing who is confessing he is going freeing the other one is getting 10 and similarly if both of them they are not confessing they are getting 1 1. Now, what is the best option for them if you look at best option for them is to remain silent. If they are not confessing remain silent they just get 1 1, but practically how this will happen practically this is not going to take place. Since they are the rivals and since there is no communication between prisoner 1 and prisoner 2 they will feel that if I am not going to confess the other one is going to confess. So, in this case I am going to get 10 years the other one goes free and the same thought prisoner 2 also will think that if I am not going to confess the other one is anyway going to confess and in that case I am getting a prison of 10 years then the other one is going free. Here if you look at cooperation is beneficial if both of them they are remain silent if both of them they have the trust that the other one is not going to confess they will not they will remain silent that they would have got just 1 year 1 year, but ideally how this will happen both of them they will confess with the thought that if I am not going to confess the other one is going to get the confess and in that case he is going free and I am just getting I am getting more I am getting 10 years. So, in that case with the same line of thought both of them they will confess and finally, they will land in a they will land in a payoff which is not optimal rather this is sub optimal because the optimal one is here when both the prisoners they are remain both the prison they are remain silent, but they are not silent they both of them they are going to confess and that is the reason they will end into a sub optimal solution and which is may be not the Nash equilibrium for here you cannot get a Nash equilibrium and finally, they will end in a situation which is not optimal rather it is a sub optimal situation. Now, the same thing so, if you look at here again what is the dominant strategy the dominant strategy is the best strategy for a player to follow regardless of the strategy chosen by the other player. So, in this case can we say that when we confess that is the best strategy because a best strategy for both the prisoner because what is the dominant strategy dominant strategy is one where irrespective of whatever is the other one is doing that is the best strategy. If prisoner one decides to remain confess that should be the best strategy irrespective of what other is doing. So, in this case if you look at still confess is the best strategy for best strategy for the prisoner one because if the other one is not confessing other one is confessing he is just getting 5 years the other one is not confessing then he is going free and if the other one is may be remain silent that is an again another strategy. So, in this case the dominant strategy is the best strategy for the player follow the regardless, but if you look at it may be the dominant strategy but this is not best best payoff because for prisoner one what are the option if he remain silent if the other one remain silent it is that is one, but the other one confess then you get 10 years. So, he has to maximize the maximize or the minimize the whatever the worst payoff can happen in case of the rival section. So, he will prefer to confess because at least even if it is not optimal solution, but still it is better than if he is not confessing and the same thing will happen with prisoner two and both of them they will confess they will reach to a solution which is may be the best strategy at that point, but that is not the optimal solution and what is the problem over here? Problem over here is there is lack of cooperation and they find that cooperation is difficult and that is the reason they are getting into a suboptimal solution. So, cooperation is difficult to maintain because cooperation is not the best interest of the individual player. Then we will take this example in a revenue function or in a revenue payoff and we will understand how the price increase and how generally the oligopolist changes accordingly. So, there are two oligopolist Jack and Jill and they are into the business of they generally sell the oil in the market. So, in the first case they have different options when the price is 40 rupees for 40 dollar per gallon. So, if you look at if the price is 40 dollar per one gallon both of them they are selling 40 gallon each and they are getting 1600 as revenue. Now, if they both of them they are reducing the from 40 gallon to 30 gallon the price is going to 50 dollar and both of them they are getting 1800 as revenue. This is one case where 40 rupees for one gallon and both of them they are just selling 40 gallons. Similarly, when they are just selling 30 gallon the price will increase to 50 gallon and both of them they are getting a revenue of 1800. If Jack sell 40 and Jill sell 30 in this case what is the revenue if Jack sell 40 and Jill sell 30 in this case Jill will get Jack will get Jack sell 40 gallons. So, in this case Jack will get 2000 and Jill will get 1500. Similarly, if Jill is selling 30 and Jill is selling 40 and Jack is selling 30 then in this case it is getting 2000 and here it is 1500 the price is 50 dollar. Now, we will see what both of them they will do. So, now if you look at the slide when Jack is selling 40 Jill is selling 40 both of them they are getting 1600 as the revenue and they knows that if both of them they are selling 30 gallon the price will go up and they can get 1800 as the revenue because price will go for 60 rupees per gallon and they are getting a 60 dollar per gallon and they are getting 1800 as the revenue. But ideally what they will do they will not reduce both of them they will try to sell 40. Here what is the optimal the optimal strategy optimal strategy is to sell less. So, that the price will go up and they will get they will get a higher revenue. But what they will do both of them they will not sell 30 they will sell 40. So, in this case if you look at if Jack is selling 40 and Jill is selling 30 he is going to get a revenue Jill is going to get a revenue 1500 and Jill Jack is going to get a revenue of 2000. Price price goes up to because it is 70 in place of 80 it is 70 now. So, that in that case the price goes up to 50 dollar per gallon. Now, in the other case also if Jill is selling more and Jack is selling less in the same case the total in the first case if both of them they are selling both of them when they are selling 40 40 total is 80 gallon and the price is 40 dollar per gallon. Now, ideal solution is both of them they should just sell 30 30 gallons that comes to 60 gallon the price goes up to 60 dollar and in this case both of them they will get a revenue of 1800. What they will try to do ideal is this both of them if they are reducing they are getting it, but they will not try to reduce it both of them they are trying to just produce just sell 40 gallon and they will land in a revenue which is again not a optimal solution like if you look at here Jack gets 1600 Jill gets 1600 and why they get into this 40 gallon because if at any point of time Jill is selling 30 gallon he gets less revenue as compared to Jack because Jack is not going to reduce beyond 40 gallons and in some situation if Jack is Jack is reducing it to 30 gallons Jill is not going to reduce and in this case Jack get a revenue of 1500 and Jill get a revenue of 2000. So, if you look at the pay off in the fourth box this looks more profitable for them this should be the optimal strategy, but they will not follow here they will land in a situation where it is suboptimal or where they are getting less profit. This same example can be can be taken into again in a different context like you have two country, country one and country two and the options are different. So, the options are whether to keep arm and ammunition or whether to not to keep the arm and ammunition. So, the choice are if you look at whether to arm or to discern here again whether to arm or whether to discern. If country one is keeping arm company two is keeping arm then both country one and country two they are at the risk. If country one is disarm and country two is still keeping arm in this case country one is may be the risk and country two is country two is safe and powerful. Similarly, here if country one is disarm and country two is keeping arm in this case again country one is safe and country two is risk and when both of them they are not keeping the arm and ammunition both of them they are safe. Here in this case what is the optimal strategy optimal strategy is here where both country one and country two they are safe. But they are not going to this option they are going to exercise this option and they both the country one and country two they are going on the risk. So, if you look at what is what you can conclude from here on the basis of all this situation that even if the cooperation is difficult even if the cooperation is profitable still they go situation where may be they always and into a sub optimal strategy like whether you take a case of the prisoners whether you take the case of the oligopolist whether you take the case of the typical country whether it is keeping arm and ammunition. All these cases cooperation is always lead them to a strategy or lead them to a outcome which is best for both of them. But since there is no trust or there is lack of cooperation they always feel that the rivals is going in a different direction and rival will try to give us the worst payoff and that is the reason that will end into a situation which is sub optimal. So, if you if you remember from the case of prisoner the best outcome is to remain silent, but they will not remain silent both of them they will confess and they will land into a situation which is sub optimal. Similarly, about the two oligopolist Jack and Jill in both these cases if they are selling both of them they are selling just 30 gallons they are getting a profit of 1800, but still they are not doing that both of them they are selling 40 gallons and finally, they leads into a sub optimal situation. And similarly, in the country level also keeping arm and ammunition both the country they are at the risk, but still they are keeping it because there is a lack of trust rather is a lack of cooperation that the other firm is also other country is also going to deserve. But the best option is that both of them they deserve themselves when they become they become safe, but that is not going to happen in this case and that is why both of them both the country they keep it in the they keep their strategy as arm and they get into a situation where both the country are at the risk. So, prisoner's dilemma is particularly talks about a game where cooperation is profitable, but difficult to maintain and that is why we do not get into the optimal strategy rather we get into the sub optimal strategy. Then we will talk about some types of game like what are the different types of game on the basis of the outcome on the basis of the players and then we will see how this is linked into the different oligopoly model what we discuss in our oligopoly market structure. So, games are classified either on the basis of the relation between players or in the basis of the strategy or on the basis of the outcome. So, the first kind of game is cooperative and non-cooperative game. So, cooperative game are essentially those which enters cooperation among the players. In real business world such cooperation is considered to be illegal generally that is called as collusion it is not legal in the real world, but cooperative games are essentially those which enters the cooperation among the player and non-cooperative games are where there is no possible to tie up among players like in case of court throat competition. So, non-cooperative games there is no tie up between the player or there is no collusion between the player it generally happens in case of the court throat competition. Then we have a normal form and extensive form games. So, normal form games list each player strategy and possible outcome that they derive from each strategy of the opponents and outcome is revealed by the payoff matrix and each players payoff is denoted by the number to measure the utility derived from each strategy. So, in the previous case whatever the payoff we are finding out on the basis of the different strategy that is generally a normal form of the game. So, normal form of the game generally identify the list of the action taken by the players that is the strategy. What is the end outcome in term of the strategy and listing all this end outcome in term of a payoff matrix that is generally the normal form of a game. Whereas in case of extensive form of game or the typical game tree we call it is gives a complete plan of action of the player over a period of time and it is it gives a chronological order in which player take their action at that particular point of time depend on what they know at what point. So, generally game tree is gives a complete plan of the player over a period of time it is in a chronological order and here player takes whatever the particular point of time whatever the decision takes that generally if you look at the when you are deciding the one decision point that leads to the what is the previous decision point and it is dependent on the previous decision of the player. So, we will just take an example to understand the extensive form of game. So, for if you look at in the previous case again we will take where we take the case of the advertisement. So, firm one if there are two option either to advertise or do not advertise this leads to again two outcome that is for firm two. So, this leads to outcome for a firm two and here again two options advertisement or not advertisement and this leads to the payoff for both firm one and two and this comes as if you remember 50, 20 and if it is not advertising then it is 60 and 10. Similarly, if it is the firm one is do not advertise then this leads for firm two to take two action again advertise do not advertise and from here we get the payoff for both firm one and two if do not at firm one do not advertise firm two advertise we get a payoff of 40, 30 and in the case of firm one do not advertise firm two also do not advertise we get a payoff of 55 and 25. So, this is the extensive form of game which record the particular action at the different point of time and then depend on. So, if you look at why firm two is advertising it is depends upon because firm one is advertising firm two why it is not advertising again it is depend on what firm one is doing. Similarly, if you start from the payoff why the payoff is this because firm two is advertising because firm one is advertising. So, extensive form of the game or this is also known as the game tree in this case it gives a chronological order in which players take their action at that particular point of time dependent on what they know at that particular point. Then we will take a different kind of game types of game that is two portion games and n portion games this is classification is on the basis of the number of players. So, if it is two number is two it is a two portion games if it is more than two then it is a n portion games. Then we have a simultaneous move and sequential move. So, in simultaneous game both the players act at the same time even if players do not act at the same time the second player is informed about the first player move. So, in case of simultaneous move game both the players act at the same time even if the player do not act at the same time the second player is informed about the first player move. This game is used for generally understanding the behavior of the oligopoly firm and the typical example is cornered model. So, if you remember in case of cornered model it is the it is the reaction function and that decides that what will be the outcome of the other firm dependent on the output of the whatever the output decision of the previous firm. Then in case of sequential game one player acts followed by the other second player knows that the move adopted by the first player and take its decision contingent that taken by the first player and the typical example is the Stackelberg model what we discuss in our discussion during the previous oligopoly market. So, simultaneous move game is the example of the cornered model and sequential move game is the example of the Stackelberg model. Then we have constant sum zero sum and non zero sum game. So, in this case the classification is on the basis of the rivalry on the basis of the outcome. So, the extent to which goals of the player is coincide is the basis of the classification. So, in a constant sum game total benefit of players given each strategy is constant the players have to share the profit. It is a game of if you look at constant sum game is the game of the total conflict and also this is a game of the pure competition. The typical example is the game of poker where it is the combined wealth of players remain constant player of share A increases though share of player B must decrease. Then we have zero sum game here the total benefit has to be equal to zero. So, the sum of gain and loss is zero and whatever is gained by one player is lost by the other player. Then we have non zero sum game and in case of non zero sum game the total benefit of players added together given each strategy is more than zero and constant. So, both the players of the game ends up in win-win or lossless situation and the typical example is the strategic alliance and the joint venture. So, in case of non zero sum game total benefit of added together is more than zero or more than a constant and typical example of strategic alliance and the joint venture we take as the non zero sum game. Then we have symmetric and asymmetric game. So, in the symmetric game the payoff do not depends on the player of the game, but on the strategy of the game and typical example is the prisoner dilemma. So, this is the here the payoff is not on the player of the game rather it is what is the strategy taken by the game and typical example prisoner dilemma what we discussed before few minutes and asymmetric game do not have identical strategy for both the player because they are asymmetric and typical example is the market entry game. Then we will take two three situation to understand this application of game theory in economics. So, game of entry a potential firm in an industry which already has a monopoly firm and here the increment has to decide whether to enter the market or stay out and monopolist has two option collude or fight with the entered firm. So, we will just prepare a payoff matrix on this basis and we will see that how this game theory is also applicable on the basis of the on the basis of the decision of the firms when they enter into the market. And also we will see the application of this in the corner model and application of this in the Steckelberg model in our next session.