 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 is specified 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 is specified 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 is specified 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 maximized its outcome whatever the strategy of its opponent. So, what is dominant strategy? The optimum strategy that is taken by the player which maximized 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 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 dominated 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 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 what is their dominated strategy, what is their dominant strategy, what is the maximum 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 advertised, this is not going for advertised, this is again advertised, 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 payoff 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 30, if he 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 payoff of 20 rather than not advertising. When firm two is not advertising it is getting a payoff of 30 by advertising which is more than the payoff which is not advertising. So, whether firm one advertise or not advertise always the payoff 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 payoff rather than not advertising and when firm two is not advertising and firm one is advertising he is getting a payoff of 60, firm two is not advertising firm one is not advertising he get a better payoff 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 payoff in advertising. So, when firm one is firm two is advertising the when firm two is advertising this is the payoff when firm two is not advertising this is the payoff when firm one is advertising that is why for firm one is also to advertise is the dominant strategy, dominant strategy for firm one also because and how do you 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 dominate both the firms. 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 payoff or this is the strategy advertised 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 payoff matrix once again to understand this. So, advertise not advertise advertise not advertise. So, this is firm two 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 payoff, the worst payoff maximize the worst payoff. Now, how this worst work pay off will come that will come from the strategic behavior. What worst can happen for firm 1? 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 maximum strategy? The maximum strategy is, maximum strategy is advertised. 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 2 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 2 is advertising and if they are not advertising when firm 2 is not advertising. But since they have to maximize the profit they will take always the highest pay off and that is why the maximum strategy for firm 1 is to advertise. Similarly, we will understand for firm 2. Now for firm 2, if the firm 2 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 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 2 and firm 1 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 for them it is always the maximum strategy for firm 2 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 1 will decide whether to advertise or not advertise they will look at which one will 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 1. Now what can be the min-max for when it comes to firm 2 when they are advertising what is best to firm, when it is best to firm 2 they have to also that is 20. When they are not advertising what is best for firm 2 that is 30 but if they are not advertising the other one is getting 25. So now what he will do firm 1 will try to advertise so that firm 2 is also advertising and they are getting a less pay off rather than not advertising because if firm 1 is not advertising it is getting a highest pay off in both the cases whether firm 2 advertise or not advertise. But if firm 1 is advertising whether firm 2 advertise or firm 2 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 1 has to be to advertise. Similarly we will now understand from firm 2 perspective. Now for firm 2 if they are advertising what is the pay off for firm 1 that is 50 and if they are not advertising that is 40. When firm 2 is not advertising the firm 1 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 2 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 2 will be also to advertise because if they are advertising that gives us the less pay off to the firm 2 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 to 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 proposes 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 for this equilibrium because that is the place where they get the maximum profit or maximum positive outcome. So generally Nash equilibrium proposes strategy for each player such that no player has change 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 market share 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.