In this module, we're going to move to considering another form of equilibrium, another market form. To give it some structure, let's go back to a little graphic that we've used in the past to give us an idea of what we're talking about here. This is a number line. At one extreme, we have just one supplier, and we looked at how that analysis worked. Those markets are called monopoly markets. A monopoly market has a very special type of outcome and we understand how it works and also some limitations of that. At the other polar example, we have enlarge that means there's just lots of firms out there and our polar example for that is something called the perfectly competitive market or perfect competition. We understand perfect competition, we understand the outcome, we know that there were some restrictive assumptions but that's okay, we set up this polar example, we set up monopolies as a polar example and now in this module we're going to venture into the middle end here this middle end sort of starts with two, three dot dot. So, this situations where there's more than one firm, and we don't really know how many it takes to actually get to the point where you've collapsed back into the competition, but there's this grey zone which we're calling Oligopoly. Oligopoly is Greek for competition amongst the few and that's what's happening in situations like this. Now it turns out we're going to think about doing this Oligopoly solution but it's really quite a bit harder than the earlier ones and the reason it's harder is because those two polar examples have what we call deterministic solutions. Think about perfect competition. We can take a look at the firm's costs, we can do that with oligopoly. We can take a look at the demand curve, we can do that with oligopoly but that's enough for us to actually find a solution because the firm in the competitive space will optimize based on its cost and the signal that comes from the market that's their price takers. They can make more or less output and it doesn't impact any of their rivals. Each firm is so small that their rivals are independent of each other. As I said before, you can take the largest corn farmer in Illinois and have her double her production and there wouldn't be an impact at all in Chicago Board of Trade. It's just like a little bitty bug landing on a lake, there's really no ripples out of that effect. Go to the other end, the monopoly case. The monopolist looks at demand, looks at its cost and just optimize. It doesn't have to worry about how its behavior is going to be responded to by our other rivals. Why? Because they're not there. By definition a monopoly is the only game in town whether it's because of a patent or because of control of a natural resource or whatever. They just make their own call. They are constrained by the demand curve and that's about it. We understood the demand curve meant that if they actually wanted to sell more units they have to lower the price that was a constraint on them but they can still optimize and we as analysts can do that pretty straightforward. Now we get in the middle. Life gets a lot harder. When Honda decides to say increase the production of its Accord by say 20 percent, Honda has a good idea that increasing the production of its Accords by 20 percent is going to have an impact on market price and it is because they are a big player in the industry and if they increased their Accords by 20 percent it's going to happen but we're neglecting to think about what's Toyota going to do. How do we model Toyota's response? If you're Toyota and you make the Camry head to head competitor with a Honda Accord and Honda increases the number of Accords, what are you going do? More importantly, what does Honda think you're going to do. If Honda thinks they could increase their production by let's say 20 percent, and you Toyota will back off by 20 percent because you kind of like the current market or they're going to do one thing. On the other hand, if they think they increase theirs by 20 percent and Toyota says well I'm putting mine up by 20 percent too because I don't want to have market share maintenance, I want to maintain my status in this industry. Well, how do we model that? How do you write mathematical equations? How do you put graphs to explain what's going on with this firm thinking that firm? It's really much more complicated than that. It's Honda has to have some sort of conjecture about what Toyota's going to do. Honda knows that if it throws its own extra output on the market the Honda can look at the demand curve for the mid-size automobiles and see what happens if they put a couple 100,000 more cars in the market but that's not enough for them to make that optimization decision because they got to have an idea about how Toyota will respond. But they also have to have an idea of how Toyota thinks Honda will respond to what Toyota does. Because if Toyota decides to increase more maybe we'll come back with a little bit more or maybe we'll back off a little bit. So, it's these conjectures get all intertwined. It's I have to know what you think, I think you think in this situation. These models can get quite complicated. The mathematics can get quite complicated as you can imagine. We call this the oligopoly problem and it has a long name. We have to worry about conjectures and in fact we have to understand that we have conjectural interdependence. My conjectures are dependent upon your conjectures which are dependent upon my conjectures. Again, modeling this can get quite complex to go through this. How do we model conjectures, how do we model response functions? Well, the number of courses that an economics department offers that dwell on these issues more than two or three courses. Four semester-long courses do it. We're going to cut down to just two. We're going to look at collusive arrangements. A collusive arrangement is just what it says. It's when a small group of oligopolists doesn't have to be small but it's small enough to be manageable in a room with people yelling at each other. A group of oligopolists get together and decide in some sort of mildly cooperative way to come up with a joint solution to their industry. Here's a price that we ought to live with. Now let's make it happen. Collusion happens all the time. The most famous one that's obviously opec cartel. The opec cartel everybody in the world knows about them. That was a collusion that we could watch on TV as the people who were the major producers of oil could get together and determine how much oil they're actually going to ship out. The headquarters they kept their own oil wells in an attempt to try to dry down the supply of oil and drive up the price. We'll talk about that. In the United States not so much. I've already sort of given you the hint that it's against the law to collude to fix prices and we'll talk a bit about that too. Then, we're going to talk about something called game theory. Game theory started out as a branch of mathematics, it's a way to mathematically model strategic interaction between players. That's why it's called game theory and the beginning they sort of set up ways to put algebraic notation to rules of games and see if you can put the rules and algebraic notation you could think about constrained maximization problems where you had something you want to maximize subject to these constraints which were the sort of alphas and betas and x's and y's of some notation. Lends itself very well to economics lends itself very well to thinking about oligopolistic interaction. How do Coke and Pepsi strategically compete not only on prices but on advertising is a very classic model and we'll spend some time thinking about how game theory allows us to push forward and get some very robust pretty accurate predictions and what we see happening in oligopoly markets.