Hello everyone, in this video we are going to learn about application of game theory to oligopoly. First thing, game theory is basically a method that we use to analyze strategic behavior. When it comes to oligopoly, there is few large firms, that means they have to engage in strategic behavior in order to maximize their profits.
Some oligopolies have only few large firms, sometimes only two firms. Okay, so game theory... application actually makes perfect sense to analyze firms choices.
Now to see an example of this let's take a scenario of duopoly that means assuming only two competitors are two firms let's consider them as rare air and uptown and they have two strategies here of course price can be a continuous variable but we are assuming that as if if they have to choose only two types of prices which is high price and low price. price. In that case you can see in this payoff matrix there are four possible outcomes.
If both firms chooses high price you will end up in one outcome. If both firm chooses low price another outcome and you can see if one firm chooses low price and other chooses high price and vice versa two more outcomes. Now in this payoff matrix the blue area is going to represent the profits or payoffs to rare air.
because it is on the other side whereas the yellow area or light gray area is going to represent the payoffs to uptown price strategy so when you have four combinations i'm going to call them as just for the reference this a b c d is not required i'm going to present it as there are four possible outcome if both choose high and high the outcome will be a if both choose low and low the outcome will be d and it is different ones C or B can happen now if you have something like this then firms has to decide thinking from the other firm side what is the strategy other firm is making based on that this firm need to figure it out now let's give a try suppose if rare air price strategy is high in that case we are going to end up only in this first column that's the case uptown is going to decide which strategy to choose. If uptown goes for high price, it can get 12,000 of profit. If it goes for low price, it can get 15,000 of profit given if rare air goes for high price.
So that means whenever rare air goes for high price, the best strategy for uptown is going for low price, which gives the higher profit. Now let's see the other side. Suppose if rare air goes for the low price strategy in that case what happens will end up in this column and Uptown has to make a choice whether to go for high price to get Six as profit or go for low price as eight as profit as you can see low price gives them higher profit It will choose eight here. So in this case the uptown is basically making a choice based on the strategy of rare air price.
Now you can do the opposite. Suppose if Hufftown has to choose high price that means you'll end up in this particular row. Rare air can make a choice of high price to get 12 as a profit or low price 15 as a profit. Since 15 is better it's going to choose 15. As you can see I'm comparing blue areas when rare air has to make a choice.
Suppose if Hufftown goes for low price we'll end up in the second column. In that case What Rarer will do is if it goes for high price, it will get six. If it goes for low price, it will get eight. Eight is better.
I'm just connecting these things. Now you can see, doesn't matter what other firm is doing, for first firm, choosing the low price is always a better strategy. That kind of scenario, we call it as dominant strategy.
That means in this case, both the... firms have a dominant strategy to go for low price that gives them the best outcome. Now, since both of them are going to choose the same strategies, the outcome you'll end up with is this particular one, D, because both of them always choose low price.
If both are always choosing low price, obviously we'll end up with outcome of D. This is where the application becomes useful, although that's not the best outcome. So, Let's look at the possibility to explain these things.
So first one we want to explain, first terminology I want you to know is dominant strategy. A strategy that always yields best results regardless of the strategies of other players. In this example, that strategy is choosing low price. Second thing is outcome. So John Nash, a mathematician, actually came up with this equilibrium concept.
The outcome that results from all players having one and choosing their dominant strategy. That means if everybody is choosing dominant strategy, well, you'll end up or you'll stuck with that outcome. Not necessarily that that's the best outcome.
What could be the best outcome? Best outcome in this case is if they cooperate, if you go back to the previous slide, if they cooperate, they can actually end up with the outcome of A, where both can get actually 12 and 12 profit. Since they are making independent choices, they are ending up with the outcome of D in this case. Now, what does game theory suggest? That when players cooperate, it may actually increase their collective payoff or collective profits.
What do we call that scenario? That one we actually call it as collusion. What is collusion means? Collusion is an agreement among the firms in the industry in two ways. One is either to fix the price saying that you choose low high price sorry and I'll choose high price.
Consumers don't have other option. They'll come to either you or me as a firms then we can make the profits. Our second possibility is dividing the market.
So how do they divide market? It could be like one side of consumer line you can manage, the other side I'm going to manage. Easy example is, let's say there are two airlines. One is running their flights from San Francisco to LA. The other one is running flights from San Francisco to Las Vegas.
Now, each of them can collude saying that you don't come in my way. I will be the only one available service from San Francisco to LA. And you don't come in, I won't come in your way.
where you can manage the other route. That way consumers will have only single option, it becomes almost like monopoly. But one we need to recognize is collusion is not a legal thing in the United States, it is illegal. So what does firms do?
They want to reach that collusion, but not necessarily that they want to be explicit about it. So they have to do either non-collusive things. If they're not doing explicitly, there is other difficulties they will actually face. Let's look at the difficulties in collusion other than not being legal.
That means when it is not legal, you don't have an agreement. There is no legal system protects your agreement. You are fixing the price or dividing the market here. What could be the difficulties here? One could be difference in cost of production among the firms.
If one firm is able to produce at a lower cost, it will be looking at like, well, I can surely lower the price and gain more market. power without losing my profits. Why should I bother about other firm?
That could be one difficulty. Second could be obviously legal system that is preventing them. Third one is difficulties in production quantities.
What happens is when you have to collude, you have to control the amount of output. Controlling the output, you need to communicate with the other firm. But if there are plenty of firms in the market, when I say plenty, Six, seven, something like that. Still, it could be oligopoly. Reaching out who is going to produce how much can be a difficulty.
That can also prohibit collusion. Sometimes could be potential entry of new firms. That means three firms reach the agreement. You produce this much, I'll produce this much.
But suddenly the fourth firm enters into the market. It becomes a challenge to accommodate the fourth firm. Other thing is potential for cheating. Okay, so. What happens is every firm will be looking at like, I want to gain a little bit market share by lowering the price.
If others can't detect me, I'm obviously going to do that one. And there is no system that can protect other firms. Next thing that you want to look at is what could be the possible non-collusive strategies? That means without entering into the, what do you say, actual agreement or communicating, bothered about the government maybe looking at.
applying antitrust laws, without communication, can we reach that collusion outcome? So that's what we call non-collusive strategies. Strategies to increase collective payoffs without directly fixing the price or dividing the market.
First possibility is matching prices. So what firms do is they don't communicate, but they will have an informal understanding. So if one firm changes the price or increases the price, other firm kind of follows that particular thing. OK, so the other firm will say, I will match the price if one firm reduces the price.
This will actually help them informally reaching an agreement. Second thing could be price leadership. Sometimes it is inevitable to increase the price.
But when there is a Nash equilibrium, any firm. wants to increase will be losing the profits. So they don't take any initiative. In that case, they may actually come up with something called as price leadership. That means there is an informal understanding among the oligopolist to follow any price changes initiated by the dominant or a leader firm in the industry.
That means if that firm increases the price, the other firms automatically increase the price. Third possibility is infrequent price changes. That means certain goods firms try to keep the prices constant. By doing so, they will actually divide the market. Classic example comes in grocery stores.
Some grocery stores, few goods, they'll keep the price kind of constant. Whenever a consumer thinks of that particular good to purchase, they may choose to go to that particular store. By doing so, they will actually make the profit on other goods, not necessarily making the profit on the good that they're keeping the price constant. All these strategies actually help the firm to reach the collusion outcome without directly communicating.
And that way they can actually increase the profits of the firm.