 In the last class, we are talking specifically about the group behavior of the oligopolist firms. And in that context, one methodology or the one tool immerse as to understand that how the firms they behave or how when they collude or when they are competing, how it can be routed into a typical group behavior. And what is the tool to understand this group behavior is generally known as game theory. In last class, as I was saying oligopoly is a market structure which talks about economic of cooperation either positively when they collude with each other and also negatively when they are competing with each other. So, today we will understand game theory, a specific tool to understand the group behavior and how the firms behave. And when it comes to specific application of game theory, generally we understand the firms behavior, we understand other different company behavior in a typical oligopoly market. So, game theory is a tool, it has application for variety of the topics or the variety of subject, but specifically in case of economic analysis, we understand that too or we use that to understand the relationship between the firms when they compete, typically when they compete and how they generally respond to rival's action, rival reaction to their price and output plan. So, to start with we will talk about the equilibrium situation of the oligopoly and how we will see the need and how there is a need for the game theory we will see from there. So, if when you talk about the equilibrium in many cases, equilibrium is absent in case of oligopoly because the interdependence, there is a interdependence between this firm when it comes to the action and reaction of the firms related to price and output decision. So, there is importance of interdependence in case of the oligopoly's firm and since there is interdependence, generally it leads to strategic behavior. And what is strategic behavior? Strategic behavior is the behavior that occurs when what is best for A depends upon what B does and what is best for B depends upon what A does. So, strategic behavior is where the end outcome or whether profit, price, output decision or whether the strategy of one firm is not dependent on their own price and output decision or the strategy decision, rather it is dependent on what is the strategy, what is the output price decision taken by the other firm. So, in layman understanding, strategic behavior is one when what is best for A depends upon what B does and what is best for B depends on what A does. And oligopoly's behavior, if you look at it, if you remember also in the last class what we discussed, oligopoly's behavior includes both ruthless competition and cooperation. So, when it comes to call oligopoly, it is about the cooperation and when it comes to non-college of oligopoly, it is generally the competition. And since it is cooperation, since it is competition, the behavior is strategic behavior because it is strategic behavior in the sense that the firm's well-being depends upon what the other firms touch. So, if there are two firms, it is a case about the oligopoly market, if there are two firms, what is best for one firm that depends upon how the other firm is doing in the market. But the other firm is increasing the price, decreasing the price, increasing the output, decreasing the output, what kind of advertising campaigning they are using, what is the after-sales service they are giving, based on that it depends that how is the, what should be the profit or what should be the output, what should be the price for the previous firm. So, if there are case of the oligopoly market, there are two firms, A and B, to simply put it, strategic behavior is one where what is A for, what is best for A depends upon what B does and what is best for B depends upon what A does. Now, what can be considered as the strategic behavior? Now, there is one evidence that there is limit pricing and what is limit pricing, when if you remember in case of the oligopoly market, we are discussing about the price leadership model, where the dominant firm or the low-cost firm, they set the price in such a low level that it is difficult to survive for the small firms or the inefficient firm and in that case they goes out of this market. So, in order to do and this here this is a kind of strategic behavior comes from the low-cost firm or the dominant firm, because in term of that they are restricting the entry, they are creating a barrier to enter to the small firm and that is best for the dominant firm, because it gives more market share if the small firm leaves the market. So, this is one of the activity that comes under strategic behavior is that when the price leaders price leader of the market, whether it is a dominant firm or the low-cost firm, when they charge such a low price that really difficult for the that makes difficult for the small firms to survive in the market. Similarly, we have the price retaliation like whatever the price decided by the market forces that will not accepted by the firm and they will they will charge a price where at least it is not going to make a equilibrium output or equilibrium price and they are going to charge a price and with that price maybe it leads to them to get a larger market share or larger profit. So, this is again a strategic behavior means the price is such that or the typical firm will charge a price who is having a largest market share, they will charge a price which is not conducive to the market. Then the capacity expansion. So, capacity expansion is where the large scale firm they generally operate do a scale operation and when they do a scale operation they always do at a they always do at a do at a lower price. So, that when the other firms they try to come into the market they cannot compete with a high cost low-cost firm and with a low price rather they have to operate in a high cost. So, capacity expansion is one where the large firm is not leaving the scope for the other firms to expand in the market and also they always charge a price which gives them less profit. So, that is not incentive for the other firms to operate in the market and that is why they do a they do a entry restriction through the capacity expansion and similarly for the market saturation also. So, that if you look at if the large firm is continuously going on producing a product and they when the new firm enter into the market they also change their product style. So, the new firm has to compete with the existing product of the large firm and also the new product of the new product of the large firm. So, in that way that creates a barrier to entry that it is not about the existing product also the new product which is given by the by the same brand name. So, if the large scale firm is operating in the market for a longer period of time and also whatever the new product comes from their market obviously people they knows the brand they knows the company and they will have more affinity for that typical product rather than new product in the market. So, whether to compete with a new firm the existing firm go for a new product or about the capacity expansion or about the price return or about the limit price. These are all comes under the strategic behavior and why this is called a strategic behavior because all these activities not only to only get more market share more profit for this typical firm rather all these activities are done. So, that the other firm should not get into the market or the other firm should not get more market share or more profit. So, here the activity is not for only the firm itself rather for the how to restrict the market share how to restrict the profit of the other firm and that is why this is known as the strategic behavior. So, in this case all this firm what is best for them is not dependent on the whatever the activity is taken by them rather what is the best for that firm depend also on the how the other firms they are behaving in the market. So, since it is the case of economics of typically in the oligopoly firm it is the economics of competition, economics of cooperation the strategic behavior is important because the well-being of the one firm is dependent on the how the other firms they are doing in the market. So, here it comes game theory to analyze this strategic behavior. So, game theory is a method which is generally being used to analyze the strategic interaction of the strategic behavior. It is concerned it is concerned with how individual make decision when they are ever that their action affects each other and when each individual takes this into account. So, when one individual firm takes a decision they know that whatever the decision they are going to take it is not only affecting their own firm also affecting the other firms. So, in this case game theory is generally analyze the situation when the individual firm is concerned or the game theory is concerned with the analysis that how individual firm takes their action or how individual firms react to the situation when they know that this particular action is not only affecting their own firm also it is affecting the other firm there in the market. So, it is a mathematical tool that generally helps to study the strategic situation or the strategic behavior. So, game theory is a mathematical tool to put it simply game theory is a mathematical tool which used to understand the firm's behavior in a oligopoly market structure. So, it helps to study the strategic situation in which players optimize a variable not only on the basis of their own preferences, but also on the other player decision and the reaction. So, here the optimization situation is it is not on the basis of their own opportunity in own constant also what is the opportunity of the other firm or what is the constraint of the other firm. So, here we can call it that here this tool is getting used by the individual players or tool is getting used by the economics to analyze that how firms they optimize their outcome and outcome not on the basis of their own opportunity and constant also the other firms present in the market their opportunity and their constant. So, games typically in case of the game theory here the games are characterized by the number of player or the decision makers who interact and even threaten each other at times establish the coalition take action under uncertain condition. So, generally here in the game theory games are characterized by the number of players or the players may be the decision makers players may be the firm and who interact with the other firms who even threaten each other at time to establish the coalition typically if you talk about price leadership model it is about the bargaining strength right. So, in this case bargaining strength also one firm generally puts the pressure that if you are not getting agreed to the price I am going to charge a price independently which is no way going to give you the benefit. So, in sometimes the players or the decision makers they threaten each other to establish the coalition and take take also the action under the uncertain condition. So, the price leader has also take the action when there is uncertainty in the market what is the price to be followed what is the output to be produced. Now, what is the outcome the players or the so called decision makers they interact they interact in a different way in a positive also in the negative when the positive they come into a collision when it is negative they get into the competition. Now, what is the end outcome the end outcome is they get some benefit or they get some loss. So, if it is output they get revenue profit share if it is. So, this if there is a decrease in the profit that is loss, if there is a increase in the profit that is gain or the benefit if there is a decrease in the market share it is loss if there is a increase in the market share its benefit or its gain it is if it is maybe we can call it revenue or profit. Again when it is go for the increasing direction its benefit when it goes in the the direction it is a loss. So, players they get into a situation where they compete with each other, cooperate with each other in a specific situation with the set of constant and the outcome is positive, positive leads to benefit, the outcome is negative, negative leads to loss. So, there are different types of moves taken by the different players in various games that is systematical also, that is systematic and also structurally designed and they take different moves, they take the moves can be in the simple way we can call it the activity, they take different actions, different moves which are systematically and structurally used to explain the economic theory specifically to understand the firm's behavior. So, different types of moves taken by different players in various games are systematically and structurally used to explain economic theory specifically to understand the firm's behavior. 1950 John Nash demonstrated the idea of an equilibrium situation in which all players in a game chose a strategy or action which are best for them given the opponent's choice. So, this game theory specifically when it is applied to economic analysis, the first development here using the game theory to economic analysis, the first development or the first concept development came from Nash in 1950 and later on he got a Nobel Prize for his contribution to this economic theory in the form of the Nash equilibrium. And what is Nash equilibrium? This is the kind of equilibrium the market using the game theory typically analyzing the firm's behavior. Here John Nash generally he developed this concept of Nash equilibrium and here all players in the game chose the strategy or the action which are best for them given the opponent's choice. So, what is best for one firm depends on whatever the action taken by the opponents or whatever the reaction are going to happen by the opponents due to this specific action. So, game theory is typically a study how people behave in the strategic situation. So, to make it understand very simply or from the layman understanding game theory is a study of how people behave in the strategic situation. And what is strategic decision? Strategic decision are those in which each person in deciding what actions to take must consider how others might respond into that action. So, strategic decision are those in which each person in deciding what action they have to take they must consider how the other they have might respond to that typical action. So, as the number of firms is in an oligopoly market is small each firm has to act strategically one is small number and also secondly they are interrelated one firm is related to the other firm either they are competing with each other or they are colluding with each other to maximize the joint profit. So, since the number of firm is small and also they are interdependent to each other they have to act strategically and each firm knows that its profit depends not only how much it produces, but also how much the other firm produces. So, if you narrow down the strategic action in case of the interdependence between two firm what is the profit of the firm it is not dependent only what it produces or how much it is selling rather it is also dependent on the fact that how much others they are producing how much the other firms they are producing in the market and how much they are selling. So, each decision makers or the each firm has two or more well specified choice or the sequence of the choices and every possible combination of the place available to the player leads to a well defined end state either it is win or it is loss or it is draw to terminate the game. So, when it comes to a specific game what are the assumption we need to take each decision maker has two or more well defined choice or the sequence of choice either they have to go for choice one choice two or in a sequence that first I will go for choice one first I will go for choice two. So, that is well defined and whatever defined that has to be only taken by the player not the other choices. Then whatever the possible combination of place are available it will lead to some kind of outcome when it is positive it is win what is negative it is loss and when it is a mix of rather when there is no definite outcome of this then it leads to the draw kind of situation. So, specified payoff or the specified outcome from the game for each player associated with each end state either it leads to zero sum or it leads to constant sum or it leads to non zero sum. We will talk about this zero sum constants of a non zero sum game when you talk about the types of game in details, but for the understanding here let us understand that whatever the specified payoff for each player associated with some kind of end state. So, there is some end outcome when the payoff is associated with each of this player it is assumed that the players they have the perfect knowledge about the game and the outcome generally the end outcome what we are calling as the payoff. They have to be the rational because if you remember all economic agents they have to be rational if they are they want to optimize their end outcome or they want to maximize their profit. And the player has to be in this case the player has to be rational or the decision makers have to be the rational. They have to always make the rational choice they cannot go for a biased choice. Now, we will come to the structure of the game. So, previously we are discussing about the assumption what are the assumptions to be followed about the game. Now, we will discuss what should be the structure of the game. The first structure of the game is that about the players individual firms they can be the players. So, firm may be the decision maker individual may be the decision maker. So, individual can be the players also the firms can be the players over here. Strategy now what is strategy? It is the precise course of action with a clearly defined objective either having a complaint knowledge about the other players or predicting its behavior. So, strategy is the course of action taken by the firm with a clearly defined objective that if they are taking this action what is the end outcome or what is the end output. Either to take this action either they have complete knowledge about the other players or at least they can predict what will be the behavior of the firms when they are taking this action. Strategy profile it is a set of strategy for each player that fully specify all the action in a game. So, it is not about only one strategy taken by the player in the entire game rather may be the player is taking four strategy or the other player is taking six strategy or the third player is taking five strategy. They have they are having a strategy profile profile and which specifying whatever the strategy taken by the players in the game and that generally known as a strategy profile. The action taken by the player in the game looking at what is the objective and at least assuming that how the players they are going to behave with the when this action is being taken there is a strategy profile that is least of action taken by the firm. Then payoff now what is payoff this is the net utility or the gain to a player for any given counter strategy of the other player. So, net utility generally this is the outcome or the utility or the gain to a player for any given counter strategy of other players and this gain is major in term of the objective of the player defined in number. So, generally in the payoff we get it in term of the number and this is the utility or the gain due to any action or due to any strategy by the player. This gain is in term of the objective of the player. So, suppose if the action is taken either there will be increase in the market share increase in the profit increase in the output or the revenue and again what is the rival's action on that basis again whether there is a increase in the share or the decrease in the share increase in the profit or the decrease in the profit or what has to be the on the basis of the revenue. If goal is to maximize profit payoff will be in term of profit. So, if the goal is maximize to maximize the profit the payoff will be also in the same terminology we have to do it in term of profit. If the goal is to increase the market share the payoff will be also measured by the share that the strategy will yield to firm opting for it. So, if it is to maximize the profit the payoff will be in term of profit if it is maximize market share the payoff will be in term of market share. If it is maximize revenue the payoff will be in term of the revenue. So, depends upon that what is the goal of the firm for taking this action that will decide what will be the payoff what will be the measurement of payment or what will be the measurement unit of the payoff matrix. So, payoff matrix generally given strategy of all the players in the game payoff matrix will represent the set of outcome for the game and what is outcome? Outcome is the end result occurring to the different player by opting for a different strategy. So, whatever the strategy they take what is the outcome that is generally known as the end outcome that is the end result whatever is coming to the player by opting a specific strategy or specific action. Some of that will give us the payoff matrix. Equilibrium a specific outcome if no players in the game can take any actions to make its payoff better and when all player continue to follow their optimal strategy. So, how we will get the equilibrium? This is the specific outcome if no player in the game can take any action to make it better. So, finally, when both the player they reach to a specific outcome and after that whatever the mean is taken by any of this player if it is not going to give any benefit to them that is the equilibrium. So, it is a kind of state of balance beyond which whatever the action taken by the firm it is not going to increase the share market share increase the revenue or increase the profit. Then we will talk about the kind of strategy. So, the first strategy comes here is PO strategy and what is PO strategy? When a strategy specify one and the same particular action for each decision point in the game that is generally known as the PO strategy. So, if the strategy specify whether it is about taking a decision on output, taking a decision on sales, taking a decision on maximizing profit, taking a decision on advertising whatever the strategy whatever the decision point if the same particular action is going to follow or the strategy specify the same particular action for each decision point this is generally known as the PO strategy. Then we have a dominant and dominated strategy. Optimum strategy taken by a player which maximize its outcome whatever the strategy of its opponent. So, what is dominant strategy? The optimum strategy that is taken by the player which maximize its outcome irrespective of whatever may be the strategy of the opponent. So, whatever the optimum strategy taken by one firm keeping in the view whatever may be the strategy by the other firm if that is giving the best outcome that is generally known as the dominant strategy. So, we will just take an example to understand this dominant strategy. Suppose given all combination strategy of the other player the outcome derived by a player from strategy A is better than the strategy B, generally strategy A is the dominant strategy. So, given all possible combination of strategy of the other player if the outcome by a player from strategy A is better than strategy B in this case strategy A will be known as the dominant strategy and strategy B is the dominated strategy. Why strategy B is the dominated strategy? Because it is not the best looking at the whatever the strategy taken by the rivals or the whatever the strategy taken by the all possible strategy taken by the opponents. So, a dominant strategy equilibrium is one in which all the players have a dominant strategy. So, it is not about the Nash equilibrium it about the dominant strategy equilibrium and dominant strategy equilibrium is one where all the players they have the at least one dominant strategy and through that we reach to the dominant strategy equilibrium. So, suppose one player is having a dominant strategy other player is not having we cannot get a dominant strategy equilibrium in that particular game. Then we have a maximum strategy, maximum strategy is the one which maximize among the worst case payoff of the player and maximum value for the game for a player is that minimum amount payoff granted by the maximum strategy. So, maximum value of the game for a player that is at least minimum the player is getting if they are playing this particular strategy. Then min max strategy in which generally player minimize the best case payoff its rival. So, whatever the best case payoff the rivals this particular player try to minimize this and the min max value of two players for player one is maximum amount of payoff that the other player could achieve under the player one of the min max strategy. So, min max value of two players for a player one is maximum amount of payoff what that can be achieved under the player min max strategy. We will understand all this strategy by just taking the example we will start with the dominant dominant strategy, maximum min max strategy and also we will see whether we have a Nash equilibrium just taking this example. So, there is two mobile service provider in the market one is firm one second one is firm two they have their own advertising drive to enhance the market share. So, both have two strategy options either to advertise or not to advertise. So, two mobile service providers one is firm one another is firm two they have their own advertising drive to enhance the market share both have two strategy option either to advertise or not to advertise. Now, what would be the possible strategy combination if both firm one and firm two advertise firm one get a market share of 50 firm two get a market share of 20. So, if firm one and firm two both of them they are advertising the outcome is here is to maximize the market share by advertising. So, in this case if both of them they are advertising firm one get a market share of 50 and firm two get a market share of 20. If firm one advertises and firm two does not advertise the firm one get a market share of 60 and firm two get a market share of 10. So, when both of them they are advertising firm may get 50, firm two gets 20. When firm one only advertise and firm two does not advertise firm one get a market share of 60 and firm two get a market share of 10. If firm one is if firm one is not advertising firm two advertises then firm one get a market share of 40, firm two get a market share of 30. If both firm one and firm two does not advertise firm one get a market share of 55 and firm two get a market share of 25. Now, this is the payoff matrix on the basis of their strategy. Now, we will take this payoff matrix to understand whether the what is their dominated strategy, what is their dominant strategy, what is the maximal strategy, what is their min-max strategy and whether they are reaching the equilibrium or not, whether they are reaching the Nash equilibrium or not. So, we will just take this payoff to understand this different strategy. So, let us call this is firm two, this is firm one, this is firm one, this is advertise, this is not going for advertise, this is again advertise, this is not going for advertisement. So, when both the firms they get the, when both the firms they are advertising then firm a get a market share of 50, firm b get a market share of 20. When firm one is advertising and firm two is not advertising then firm one get 60, firm two get 10. When firm two is advertising, firm one is not advertising then firm a get 40, firm two get 30. When both of them they are not advertising firm one get 55 and firm two get 25. Now, we will understand what is the max min, what is the min-max, what is the dominant strategy or whether they are reaching equilibrium or not. We are assuming that firm one and firm two both have to be rational. Now, we will understand this from the firm two point of view now. If firm one advertising, firm two will choose a strategy advertising and here they are getting 20 rather than 10. So, if firm one is advertising, firm two has two option, either they have to advertise or they have to not advertise. If they are advertising they are getting 20, if they are not advertising they are getting 10. So, since 20 is greater than 10, if firm two is going for advertising they are getting a better pay off by advertising. Now, we will analyze the case for firm two, when firm two one is not advertising. So, here if firm one is not advertising then it gets 20. So, if firm one is advertising he gets 30, but if he is not advertising he is getting 25. So, in this case again 30 is greater than 25. So, what is the strategy, what is the dominant strategy for here? Because whatever firm one does whether advertise or not advertise always advertising is the best option for firm two. And since advertising is the best option for firm two to advertise is the dominant strategy for firm two. Now, how it is a dominant strategy? Because when firm one is advertising and firm two is also advertising they are getting a pay off of 20 rather than not advertising. When firm two is not advertising it is getting a pay off of 30 by advertising which is more than the pay off which is not advertising. So, whether firm one advertise or not advertise always the pay off is maximum for firm two when they are advertising like 20 and 30 and that is why to advertise is the dominant strategy for firm two. Now, we will analyze this from firm one perspective. Now, suppose firm two advertise what firm one will do? If he is advertising he is getting 50, if he is not advertising he is getting 40. So, if firm two is advertising if firm one is advertising he is getting a better pay off rather than not advertising. And when firm two is not advertising and firm one is advertising he is getting a pay off of 60, firm two is not advertising firm one is not advertising he get a better pay off of 55. Since, 60 is greater than 55 and in both these cases whether firm two advertise or not advertise firm one is getting a better pay off in advertising. So, when firm one is firm two is advertising the when firm two is advertising this is the pay off when firm two is not advertising this is the pay off when firm one is advertising that is why for firm one is also to advertise is the dominant strategy for firm one also because and how to interpret this dominant strategy irrespective of the whatever the action not taken by the other firm to advertise is the best possible action or the best strategy by the firm. So, in this case we have dominant strategy for both the firm. What is the dominant strategy for firm one to advertise? What is the dominant strategy for firm two to advertise? Since, both the firms they have the dominant strategy we get a equilibrium and the equilibrium gives us a strategy that is advertise this is the pay off or this is the strategy advertise by both the firms and this gives us the equilibrium and since both of them they have the dominant strategy this is generally the dominant strategy equilibrium. Then we will understand the max mean and min max strategy taking this specific example. So, to start with we will do the max mean we will just do the pay off matrix once again to understand this. So, advertise not advertise advertise not advertise. So, this is firm two is the dominant strategy for firm this is firm one. So, this is 50, 20, 40, 30, 60, 10, 55, 25. Now, to understand max mean what is the max mean? Players will try to players will try to maximize the pay off the worst pay off maximize the worst pay off. Now, how this worst pay off will come? That will come from the strategic behavior. What worst can happen for firm one? If they advertise they get 50 if they are not advertising they get 40. They will try to maximize that they should advertise because they are getting a highest pay off. So, for them what is the max mean strategy? The max mean strategy is max mean strategy is advertise. Similarly, when the other firms is not advertising what is the pay off for them? If they are advertising they get 60 if they are not advertising they are getting 55. So, for them what is best? Again if they are advertising when the firm two is not advertising also. So, this is the pay off that is 50, 40, 60, 55 related to the two kind of strategy when they are advertising and when they are not advertising. They will try to maximize the value they are trying to maximize the pay off. So, the worst pay off can be 40 if they are not advertising and firm two is advertising and if they are not advertising when firm two is not advertising. But, since they have to maximize the profit they will take always the highest pay off and that is why the max mean strategy for firm one is to advertise. Similarly, we will understand for firm two. Now, for firm two if the firm two is advertising they get 20 they are not advertising they are getting 30. Similarly, if they are not advertising they get 30 or 10 and if they are not advertising again they are getting 25. So, what is the what is the maximum they have to maximize the pay off here and what is the maximize here between this advertising and not advertising it is 20 and 10. So, if they are advertising they are getting 20 if they are not advertising they are getting 10 and since they have to maximize the outcome since they have to maximize the pay off they will always check this this is because this 20 is the highest pay off. Similarly, when it comes to firm two and firm one is not advertising if they are advertising they are getting 30, if they are not advertising they are getting 25 and since 30 is more than 25 they have to maximize the value and they will take 30. So, from them it is always the maximum strategy for firm two is also to advertise. Then, we will understand the min-max strategy and min-max strategy is what what is the logic for min-max strategy the player will try to minimize the pay off for the opponents by their own strategy or by their own action. So, to put it simply when firm one will decide whether to advertise or not advertise they will look at which one will give give the minimum pay off to the opponents because that will be chosen by them and that is why they look for that how to minimize the pay off of the opponents rather than how to maximize the pay off their own firm what generally they look it in the maximum strategy. So, min-max strategy their focus is to minimize the pay off of the rivals or the minimize the pay off of the opponent. So, looking if we will take now about the min-max we will take for firm one. Now, what can be the min-max for when it comes to firm two when they are advertising what is best to firm when it is best to firm two they have to also that is 20. When they are not advertising what is best for firm two that is that is 30, but if they are not advertising the other one is getting 25. So, now what what he will do firm one will try to advertise so that firm two is also advertising and they are getting a less pay off rather than not advertising because if firm one is not advertising it is getting a highest pay off in both the cases whether firm two advertise or not advertise, but if firm one is advertising whether firm two advertise or firm two is not advertising still they get a pay off which is lower than their counterpart and that is why the min-max strategy for firm one has to be to advertise. Similarly, we will now understand from firm two perspective. Now, for firm two if they are advertising what is the pay off for firm one that is 50 and if they are not advertising that is 40. When firm two is not advertising the firm one is advertising they are getting 60 and not advertising they are getting 55. So, since 50 is less than 60 and 40 is less than 55 firm two will feel that it is better to advertise because they are getting a lower pay off whether they are advertising or not advertising. So, in that case the min-max strategy for firm two will be also to advertise because if they are advertising that gives us the less pay off to the firm two rather than not advertising. So, this is how we understand this dominated strategy, dominant strategy and max min and min-max strategy. Now, in this case in the particular case if you look at all the strategy whether it is dominant whether it is max min or whether it is min-max all the strategy they are the to advertise is the all the strategy is to advertise for both the firm. This may not happen in all these cases there may be also whatever the dominant strategy of A that may not be the dominant strategy of B or it may happen that there is a dominant strategy for one player, but there is no dominant strategy for the other player. So, in this case the possibilities that will not get a dominant strategy equilibrium where there is a dominant strategy for both the players. Then we will talk about Nash equilibrium and Nash equilibrium generally propose a strategy for each player such that no player has the incentive to change its action unilaterally given that the other player follow the proposed action. Because again equilibrium is a state of balance equilibrium is a state of rest beyond this there is no incentive for the other firm to go of this equilibrium because that is the place where they get the maximum profit or maximum positive outcome. So, generally Nash equilibrium propose a strategy for each player such that no player has changed incentive to change its action unilaterally given the other players to follow the proposed action. And it is a optimal collective strategy in a game involving two or more player where no player has anything to gain by changing his or her strategy. So, we will understand this Nash equilibrium taking our previous example we will take up the payoff matrix, but it is a case of two firms that is firm one and firm two and they have two options to advertise or not advertise. And the final output is in term of the payoff that is whatever the outcome they are getting. So, here we will add one more new assumption and the new assumption is here that firm one uses a typically expensive advertising agency. And since the advertising agency is doing advertisement for them that increase their cost of production. And here the firm would try to shift the burden to the consumer in term of increase in the price of the product. So, that the company gets lesser markets here when it advertise as compared to when it does not advertise. So, since they are shifting the burden of the increasing cost to the consumer it is obvious that the market share will decrease because when price increases even if it is a good product still some amount of the quantity demanded decreases. So, that will increase the market that will increase the price of the product that will increase the market share and company gets less market share when it advertise compared to what when it does not advertise. So, accordingly our payoff matrix will change and if firm two in this case does not advertise then it is better for firm one not to advertise and get a larger share of market. Now, here in one case firm one is doing a expensive advertising and they are passing the cost to the consumer and second case and in continuation to that they are getting a less market share. But if firm two does not advertise here then it is better for firm one not to advertise and get a larger share of market. So, here what is the best action for firm two they are doing the advertising because firm two is also doing the advertising. If firm two is not doing the advertising now what is the best choice for firm one best choice for firm one is not to advertise because if they are not advertising they do not have to spend for a advertising agency. There is no increase in the cost of production there is no increase in the market price there is no decrease in the market share and if there is no decrease in the market share this is the best possible action or the best possible strategy for firm one. So, we will continue our discussion on Nash equilibrium taking this specific example. We will talk about the different types of game we will talk about the prisoner's dilemma and we will talk about that how this game theory is applied specifically to few of the oligopolist model in our next session.