 We will continue our discussion on the theory of a game and particularly its application on economic analysis. So, last class, if you remember, we discussed about different types of game and we will pick up specifically few types of game, which is more applicability in the case of the economic analysis. So, in that context, the first discussion will be on the market entry game and here we will analyze that how the when the firm plans to enter into the market, generally how he uses the game theory and from the other point of view, the existing firms who those who are there in the market, how they use game theory to create a barrier to entry or to if the firm is coming into the market, how they are going to maximize the profit. So, game of entry or potential firm in an industry which is already a monopoly firm. So, we will take a case where the existing industry set up is there is only one monopoly firm and there is a potential firm who is trying to enter into the market and compete with the monopolist firm to maximize the profit or get the market share. The incumbent has to decide whether to enter the market or stay out. So, incumbent has two choices or the two options at this point of time, whether he has to enter the market or he will stay out, he will not enter into the market and in the other hand, the existing firm typically the monopolist firm has also two options whether to collude if the firm is entering into the market, whether to collude with the entrant firm or whether to fight with the entrant firm. So, there are four options that is there with the taking the incumbent firm of the existing firm. For the incumbent firm, the options are whether to enter into the market or stay out and to existing firm whether to whether to fight or collude with the new entrant in the market. So, on that basis now we will try to do a payoff matrix for on the basis of the options available to the existing firm and also to the incumbent firm. So, to draw this payoff matrix, we need the payoff for the all these four options. So, here we will take this the case of the entrant and the two options are either to enter or to enter. Stay out, this is for the incumbent and what is the options for them collude or fight. Now the outcome is in term of market share. So, how we can construct the payoff matrix? Suppose the entrant is deciding to enter and the incumbent firm is collude once the new entrant comes the payoff will be 40 and 50. The market share will be 40 for entrant and 50 for the monopolist firm. If the entrant decides to stay out obviously his outcome is 0, he is not going to any market share and the incumbent firm they are going to get the they are going to get 100. So, let us change this is the existing monopolist. Now if the entrant decides to fight and the existing monopolist entrant decide to enter and the existing monopoly decide to fight. In that case if you look at then we take into a case where maybe we can get minus 10 for the payoff and 0 for the monopolist. Why it is minus 10 and why it is 0? Because if the entrant is entering and the existing monopolist is fighting may be no one is getting a market share and it goes to goes to someone else we can do it may be 90. Then if entrant is entering stay out and obviously there is no choice this fight. So, this comes again to 0 and 100. Now the basic purpose of doing a payoff matrix is to evaluate the options. When the firm is trying to enter into the market basically these evaluating options that if he is entering what will be the market share what will be the outcome and if he is not entering what will be the market share and what will be the outcome. Similarly, the monopolist has two options if the entrant is getting into the market what should be the what should he do whether he should collude whether he should fight. So, one payoff will come if the entrant comes into market and if he is going to fight what should be the market share and if the entrant is entering to the market he is going to collude what should be the market share. So, collude fight two options for monopolist enter into the market stay out from the market two options for the new firm. So, in this case we get four payoff in term of four market share and among them now they will decides that whether it is a dominant what should be the dominant strategy for both of them whether they are getting a Nash equilibrium or whether they are getting two Nash equilibrium if there is a absence of the dominant strategy in both these cases. Now, in this case what should be the strategy of the rational monopolist because we assume that the monopolist has two rational and what should be the strategy of the rational monopolist and where the Nash equilibrium generally occurs. So, Nash equilibrium occurs when entrants enter and the increment firm collude with it. So, in this case if you remember your payoff matrix that is the case where both of them they are getting a market share. In all these three options either of them is getting a zero or them getting a minus, but in this case when if the new firm is entering into the market and existing firm colluding with it then that is whatever the market share is getting that is more preferable for both from the monopolist point of view and the new firm point of view if they are acting rational. So, when it comes to the Nash equilibrium, Nash equilibrium typically occurs when the entrant enters and the increment firm collude with it because this is the point actually where both of them they are getting some amount of the market share. So, before going to this, this is what this is which this is also a types of game and we will see what is the game tree over here because this is also a sequential game and in this case sequential game how I will see how the game tree looks like. So, this is for the entrant it has two options one is enter another is stay out if it is enter then the existing monopolist has two options one is collude another is fight. So, in that case we get two columns of our monopoly both for the entrant and the second column and for the monopoly. So, in this case we get 40, 50. So, if entrant enter monopolist collude with it we get a market share we get a payoff matrix 40, 50 where the share of entrant is 40 where the share of the monopolist is 50. If entrant enter monopolist fight then we get a share of minus 10 for entrant because you cannot compete with the monopolist and 0 for the monopolist because the market share is not going to come to if it is fighting with the existing market or same thing can be analyzed in a different version also because it is getting a market share of 90 whereas the other entrant is getting a market share of 10. Then stay out then what is the option for the monopolist it is again collude it is again fight again we will get a payoff matrix for both the entrant and the monopolist and here we get the payoff as 0, 100, 0, 100 because if the entrant is staying out obviously the market share is 0 whether and the second part is not at all relevant because if it is staying out the question is not coming whether monopolist should collude or monopolist should fight. So, basically and the market share of entrant will be 0 and whether and the all these cases of market share of the monopolist will be 100. So, this is the case of a sequential game where the decision of one firm is always dependent on what is the decision of the other firms and in this case the decision is followed from whatever the market share what is the end outcome here the end outcome is to maximize the market share dependent on what is the outcome with respect to its decision points and also looking at to that what is the rival sections like if the entrant is trying to get into the market now what should be the what should be the decision point of the monopolist. So, the entrant will evaluate option in term of two things that whether the monopolist is going to collude or whether the monopolist is going to fight. Similarly, the monopolist is going to take the options that what would be the market share if he is going to fight and if he is going to collude on that basis he will decide what is the dominant strategy for him. So, typically in case of a market entry situation in case of a situation when the market is trying to enter into the market where there is a monopolist firm generally this game theory is relevant typically sequential game theory where it gives us the sequence that what should happen if one firm behaves in this direction and the other firms behave in the following action. Then we will talk about the application of game theory in case of a cornered model. So, if you remember we discussed this cornered model in case of a non-collusive oligopoly and cornered models talks about a situation that where there are two firms they are sharing the market and they always assume that the whatever the previous output plan for the other firm that has to be follow in the revised period also, but practically it leads to a situation where they reach to a suboptimal solution or we can say top part of the market is still untapped by both of the monopolist firm because they always assume that the output plan whatever followed by the firm in the previous time period that has to that is going to be continued. So, the same thing we will see that how this game theory is applied to a cornered model. If both the firms they fight with each other then they earn the duopoly profit because they share the market and they earn a duopoly profit, but if they form a cartel each firm earns a greater profit, but given the structure of the game and the player's rivalry they end up in a suboptimal equilibrium. So, cornered model if you look at always they feel that the other one is going to take the half of the market. So, his decision point is on the basis of that the other firm is going to take half. So, let me take another half and in that process when the iteration takes place finally, in the revised period revised period and then the nth period if you look at the one-third is only taken care of and rest if you look at rest of the rest of the market is not taken care of neither of this firm, but the other option is that if they form a cartel if they cooperate with each other then then ideally they can decide on the basis of their productive capacity or on the basis of their cost function they can decide that who has to share how much of the market or who has to supply how much share of the market and on that basis they can tap the full market and they can reach to into a optimal equilibrium, but practically the structure of the game is such the cornered model is such that there is a rivalry and they always believe that the output plan is not going to revise by the other player and that is why they go on consider the same output plan and they accordingly they devise their price and output plan and that is why they lead to a sub-optimal equilibrium rather than optimal equilibrium. So, here how we can conclude we can conclude that even if the cooperation is profitable still the firms they are not cooperating with each other rather they are competing with each other and going into a sub-optimal equilibrium rather than a optimal equilibrium. Then we will see the Stackelberg model. So, if you remember in case of Stackelberg model it is a leader follower model generally one follow generally one take a lead and the other one is follow. So, we will see that generally the sequential kind sequential types of game is used in case of the Stackelberg model. So, sequential move game is different from the cornered game and typically in case of there is also a difference in case of a cornered model and Stackelberg model even if Stackelberg model is the extension of the cornered model in case of Stackelberg model the significant feature is that one firm acts as the leader and the other firms act as the follower. So, sequential move game is that is how it is different from the cornered game here one firm known as the leader chooses his output second firm chooses after observing the first quantity of the output. So, one is as the leader firm second one is the follower firm one firm generally chooses this is the output I am going to produce and the second firm after looking at or after observing that what is the output plan for the first firm generally the second firm decide his quantity. So, this is generally known as a follower leader game and here the leader firm always sets a higher quantity of output and earns more profit than the follower firm and by doing or this they get because they have the first mover advantage. Since they are the leader they are the first one to decide what should be the output generally they get a greater advantage in term of the share in market share in term of the profit because they are the first one to decide what is the share of them and this is generally known as the first mover advantage and always in case of a Stackelberg model the leader or leader firm get a first mover advantage because they are the first one to choose the output and in that way they can maximize the market share and they can maximize the profit also. So, in case of Stackelberg model the equilibrium is decided on the basis of the backward induction in the game theory and how we say this the backward induction in the game theory because this technique first consider the optimal strategy of the player and its best response which takes the move that are last in the game. So, the equilibrium whatever the method is follow generally known as the backward induction in the game theory. So, in the previous case also in the market entry if you look at the decision of decision point is based on that what is the last decision point of the rivals or what is the last decision point of the opponent. So, this is the part of the backward induction in the game theory where the decision is dependent on the what is the previous decision taken by the opponent and this technique first consider the optimal strategy of the player and its best response with which it takes the move and that is the previous or previous time period that is the last in the game. Predicting the future action of the last player the second last player proceeds taking the best move. So, in the when it is coming to take above the last player or the predicting about the future action here the second last player proceeds taking the best move and the process continues backward in time determining for each player the best response until the beginning of the game is reached. So, when we identify the best of best what is the best option for each player they go in a backward direction till the time they are reaching the the reaching the beginning of the game because that way they just go on evaluating what is the best response with respect to the previous time period or with respect to the action taken in the previous time period and in that way they decide the optimal strategy. So, in the game theory typically to conclude the game theory we can say in the game theory we discuss about the structure of the game we discuss about what are the assumptions to be taken to use the game theory and then we talked about the types of game and how this game is being used in the case of the economic analysis. So, to sum up we can say that game theory is a tool which is used typically in the economic analysis to understand the group dynamics to understand the group behavior specifically in case of a oligopoly market structure.