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 choose, 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, that 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, 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

Equilibria of this game, we're doomed to either an unfair outcome where one member

of the couple always gets their preferred activity or miscoordination,

where sometimes, the, 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.