Now, let's talk about another game. This game, we're going to call the advertising game. And the advertising game is just what it says. We're talking about two firms who compete a lot by spending a lot of money on advertising. And so, we're going to say these two firms go by the names of Coke and Pepsi. Two big players, they spend a lot of money advertising their products, okay? And the game is going to be such that they have two choices. They can both spent high advertising or they can both spend low advertising. Or one can do a low and one can do a high. And so, the question here is what's the payoffs? Now, again, remember, for simplicity's sake I've divided the world into just two possible outcomes, low advertising budget and a high advertising budget. In the real world, their budget is a continuum. And so, to solve this type of game in the real world will require some much higher order mathematics because they'll have to have function one against function two and figure out what's the right play in these situations. But right now, we're just going to make life simple and say there's only two. If I was just make it clearer. There's only four possible cells that can be an outcome. This is an outcome possible. This is an outcome. This cell's an outcome. And this cell's an outcome. Each cell has a payoff for the side player, in this case Coke, and for the top player, Pepsi. If I wanted to be really mean, which I wouldn't, I could have three. I could they there's low, medium, and high. That way, there would be nine cells because there would be three across the top and three down the side. So there would be nine cells and then we cold evaluate all those cells and determine which one is the equilibrium in that. But we get a lot of gain, I'll just do a two. So I'm going to say that if these two can both stick to low advertising, I'm going to say that they're both going to get $5. And this could be five million, five thousand, whatever. We'll just put number five in there. If Pepsi stays with a low commercial and Coke goes high, then there's if Pepsi stays with low advertising but Coke goes high, then what's going to happen is that Coke is going to get 8 and Pepsi will get killed in the marketplace. On the other hand, if Pepsi is the one that decides to go ahead and go high, and Coke sticks at low, then in this case, we're going to make this game symmetric, and Coke will get 0. If they both do high advertising, they're going to get something out of the game, but not very much. So these numbers are relatively similar to what we've been looking at, and the solution to this is to think through, again, ask yourself the question what should Pepsi do. If Pepsi thinks Coke is doing hi, Pepsi has two possible outcomes. Pepsi can either go low and get 0 or it can go high and get 1. So if Pepsi thinks Coke is going high, it's always better for Pepsi to go high. Pepsi is better doing hi if Coke is doing hi. If Coke is going low, Pepsi can stay in low and get 5. Or it can go high and get 8. So once again, Pepsi always wants to go high. It's just like that earlier one where defect made them better off. In this case, Coke says I don't know what Pepsi's doing, but if Pepsi's doing hi, I can either do low and get 0 or I'll go high and get 1. So in this case, I want to go high. On the other hand, if I think that Pepsi's down there doing low, I can stick at low and get 5 or I can go up to high and get 8. So once again, hi is going to make me better off. And so, we have, again, a dominant strategy equilibrium. This is a typical model of defensive advertising. It's a typical model defensive advertising. If they both stick to low advertising, they're still going to get lots of customers, okay? But they're not going to be sending millions and millions and millions of dollars to advertising agencies to create those funny little commercials and also to the networks to run their Pepsi and Coke commercials non-stop during football games and and other events. But unfortunately, they feel that if they could just maybe even go just a few extra commercials, especially if my rival doesn't. If I have a blitz of three or four Coke commercials and it turns out that Pepsi didn't do any for that because they're trying to stick low like we thought we were going to do, well, I'm going to get a lot of customers away from them. And they're really going to suffer, okay? And everybody knows how this game works, and so they end up spending a lot in what we call defensive advertising. But it's just a typical prisoner's dilemma game. Now, we're going to end here by suppose I took that game, and suppose I were to do one thing. Just one thing. I know you're tired of me saying this, but I have the pen, I put those numbers in there. Because I have the pen and I wanted those numbers because they're showing certain outcomes. Suppose I had instead, suppose let's just cross this off. Suppose I just cross this 8 out and put it as 4. Notice what's happened here all of a sudden is that if Coke thinks Pepsi is going high, Coke can go low and get 0 or go high and get 1. So Coke is going to go high. Mark that strategy. But on the other hand, if Coke thinks that Pepsi is going low, Coke can go high and get 4 or low and get 5. So in this case, the right strategy for Coke is to go low. Notice what's happened here. All of a sudden there's no longer a dominant strategy equilibrium. Coke's optimal play depends crucially on which one Pepsi chooses. In the previous model, this one, it was always right for Coke to go high regardless of what Pepsi did. But now, just simply because Larry changed the numbers, Coke will want to go high if Pepsi is going high. But if Pepsi's going low, Coke says hey, I like low, if you're going low, I'm going to go low. If you're going hi, I'm going to go high. We don't have a model to solve that, do we? because right now, we've only worked with dominant strategies where it was simple game. People always went in some direction. Now, we got a problem. We have to figure out a solution to this problem. That'll come next.