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.
Matthew O. JacksonProfessor
Kevin Leyton-BrownProfessor
Yoav ShohamProfessor
