 In this video, we're going to look at some additional solution concepts other than the Nash equilibrium. So these are different ways of talking about which outcomes of a game make sense from a game theoretic perspective. First of all, I want to talk about a solution concept called iterated removal of dominated strategies. And I want to illustrate this by the example of Grace, shown in this picture here, who decided to jump out of a plane to celebrate her 91st birthday. So I want to think about a game between Grace and the guy that she chose to strap herself to, who you can also see in the picture. And in particular, I want to think about his decision of whether to pack the parachute safely or not, and her decision about whether to jump out of the plane or not. Now, in principle, she might worry that he would choose not to pack the parachute safely, and she would choose to jump out of the plane. And if that were to happen, then she would never get to celebrate her 92nd birthday. But you can see, in fact, she did choose. And indeed, she landed safely, and her choice was a good one. So how was she able to reason that this was sensible? Well, if she looked at the payoffs of the game, she would see that this guy, let's call him Bruce, Bruce's action of not packing the parachute safely was very bad, not only for Grace, but also for himself. In fact, it was a dominated strategy. And knowing that he's rational, Grace reasoned that he would never play a dominated strategy. And so she was able to change the game by removing this dominated strategy, and instead to reason that she only had to care about the remainder of the game in which his dominated strategies didn't exist. This is the idea of iterated removal of dominated strategies, which you'll hear about more formally later. Secondly, I'd like to revisit our question of soccer goal kicking. And I'd like to ask, is it really the case that when a player prepares to take a penalty kick, he's really solving for the Nash equilibrium? Now, we did see experimental evidence that shows that the Nash equilibrium is a pretty good description of what actually happens in these situations. But is it the case that the players are really thinking about the idea of Nash equilibrium? That doesn't seem right. It seems like the players are thinking about how best to kick the ball into the goal in order to hurt the other guy as much as possible, or in order to do as well for themselves as possible. It turns out that this isn't an accident. In the case of zero-sum games, these three ideas, doing as well for yourself as possible, hurting the other player as much as possible, and being in Nash equilibrium, all turn out to coincide. Finally, I want to revisit the battle of the sexes and ask, is it really the case that, as we saw before with the Nash equilibrium of this game, we're doomed either to an unfair outcome where one member of the couple always gets their preferred activity or a miscoordination where sometimes the two members of the couple end up doing different activities. It doesn't seem like this is a good model of how people really do solve disputes like this between themselves. So I want to think about a new solution concept called correlated equilibrium, in which we don't have this problem and we're able to achieve fairness without miscoordination.