Alright, guys, so now we're here at the bottom of the page in our payoff matrix. Let's go ahead and take all that information that we just gathered in our different situations and put it into our payoff matrix. Okay, so let's start with the situation where they were colluding, right? When they both produced 30 gallons, Jack's decision was to produce 30 gallons, Jill's decision was to produce 30 gallons. Well, what was their profit? Jack had $1800 in profit, and Jill had $1800 in profit, right? So notice how we're filling out a payoff matrix using this information that we just came up with. We're going to have those decisions, how much they are going to produce, and the payoffs based on those decisions. Okay?

How about that second situation where Jack produces 30 and Jill produces 40? Well, when Jack produces 30, Jill produces 40, that was the situation where Jill's taking some of Jack's revenue, right? And coming out on top. So Jack's income or profit will be $1500 in that case. Jill's profit will be $2000, right? That's what we calculated up here for Jack and Jill's profit when Jack produces 30 and Jill produces 40. Well, it would be the opposite, right? What if Jack produced 40 and Jill produced 30? We would have a similar situation, it would just be flipped, right? In that case, when Jack produces 40 and Jill produces 30, Jack comes out with $2000, right? And Jill gets $1500 over here, right? Because we're just flipping who was the cheater.

And then last but not least, we've got the situation where they both cheat and both produce 40 gallons, right? So that's going to be this box right behind me in the bottom right corner, and we had profits over here, right? We calculated Jack and Jill's profit to be $1600 each, so that would be $1600 for Jack and $1600 for Jill, right? So we filled in our payoff matrix. I'm going to go ahead and get out of the way, and let's use our check and X method to find dominant strategies and a Nash equilibrium. Okay? Let's check it out now.

Alright, so let's do this. Let's start with Jack, okay? So for Jack's decision, he has to think about what he would do based on Jill's decisions, right? So Jill decides to produce 30 gallons, Jack, what will Jack do? When Jill produces 30 gallons, well we saw, right? Jack wants to cheat. He's going to get more profit when he cheats, right? He'll produce 40 gallons and get $2000 rather than 30 gallons and get $1800. So we're going to put a check over here for Jack's decision when Jill produces 30. What about when Jill produces 40? If Jill produces 40, Jack either has to choose between $1500 or $1600, right? He can produce 30 and get $1500 or produce 40 and get $1600, so his better choice is to produce 40, right? So what do we see? We already see that Jack has a dominant strategy to produce 40, right? We have this column right here with two check marks, so we know that's a dominant strategy for Jack.

Okay, let's try Jill now. So Jill, she's first going to think what if Jack produces 30? So if Jack produces 30, I can produce 30 and get $1800 right here, or Jack can produce 30 and I'll produce 40 and get $2000. So Jill is going to want to cheat, right? Jill will cheat and produce 40, and that is why we're going to put an X in that box. What about if Jack produces 40? Again, the same thing. If Jack produces 40, Jill has to choose between making $1500 or $1600. Well, guess what Jill's going to pick? Jill's going to pick the $1600, right? Rationally, she's going to pick the one with more money. What do we see? We've got two X's in the same row, right? So now that we've got two X's in the same row, we know that that's also a dominant strategy, right? So Jack's dominant strategy is 40 gallons. Right? Jill's dominant strategy is also 40 gallons. And what about our Nash equilibrium? Our Nash equilibrium is a box that has both a check and an X, right? There's a box with a check and an X right here. That is our Nash equilibrium. Nash equilibrium is going to be this box right here, right? Where they're both earning $1600.

So I'm coming back in now. So what do we see? The Nash equilibrium was something like a prisoner's dilemma, right? If they had been able to cooperate, they would have both made $1800, but they both end up cheating and end up in this situation where they earn $1600, right? And that's because they're making their best choices based on what their competitors would do. So what does that do? It leads us to a situation where an oligopoly is producing somewhere in between the monopoly and perfect competition, right? Because of this interdependence and uncertainty of what your opponents are going to do. Cool? Alright. Let's go ahead and move on to the next video.