>> All right, the next concept that we're going to
need to understand the folk theorem is the notion
of a minmax profile. So a minmax profile is
going to be a pair of payoffs, one for each
player. And the value for player represents the payoffs
that that player can achieve by defending itself from
a malicious adversary. So what do you suppose a
malicious adversary would mean in a game theory context?
>> Someone who's desperately trying to hurt you.
>> And what does hurt mean?
>> Gives
you the lowest score.
>> Yeah, and what does that remind you of from your lesson?
>> My grad students.
>> You think they're malicious?
>> It would explain a few things.
>> Yeah, I don't think they're malicious.
>> They're sweet.
>> [LAUGH]
Yeah, I know a lot of them and they're, they're wonderful people.
>> Well, what it reminds me of is, they
are wonderful people. It reminds me of zero-sum games.
>> Exactly. So you can imagine thinking about the game
that we're playing, now, no longer as being I get my payoff and
you get yours, but I get my payoff and you get the negative of
my payoff. So you don't, you don't really care about yourself anymore. All you
care about is hurting me. And that's, that's the idea of a malicious adversary.
>> I have some ex-girlfriends like that.
>> I'm so. Oh. [LAUGH].
It is. People do get into this mode sometimes. And that,
that's actually going to be important in understanding the folk there.
>> Hmm.
>> So what
I'd like to do is figure out what the min-max profile is for this game. So this
is a very famous Game theory, game example.
Sometimes goes by the name battle of the sexes.
>> That what the b and the s stand for?
>> Sometimes it stands for Bach and Stravinsky.
>> Blech.
>> Those are like composers, I think.
>> You mean like the Backstreet Boys and Sting.
>> Ahh. Alright, that works for me. So,
so, let me explain this story. It turns out that
Smooth and Curly actually got away, they didn't make any kind
of deal, they actually just figured out a way of
escaping from the jail. So they're, they're back out on the
streets again, and they decided that they'd like to celebrate
their freedom by going out to see a concert. And they
both decided that in advance, but what they didn't know was
which concerts were available. Once they escaped out into the world,
they couldn't communicate with each other, they
discovered that there's in fact two concerts
in the city that night. The Backstreet Boys are playing, and Sting is playing.
>> Okay.
>> Now as it turns out, each of them is now going
to have to choose, whether to go to the concert with Backstreet
Boys or Sting, and they're choosing independently. Now, if they end up
going to different concert's they're both going to be unhappy and get zero's.
>> I see.
>> If they end up at the same concert, then they're going to be happier,
but in fact, as it turns out, Smooth really likes
the Backstreet Boys and would prefer that they both end up
at the Backstreet Boy concert. But Curly really likes Sting
and would prefer that they end up at the Sting Concert.
>> That's not realistic.
>> Which part?
>> The fact that I prefer the Backstreet Boys to Sting.
>> What, what do you mean you? I mean this is Smooth. He's a criminal.
>> Mm, that's a fine point that you
make there. There is no connection between these
characters and ourselves.
>> Real life characters, living, dead
or fictional, or mathematical, or instructional.
>> If so, otherwise purely coincidental.
>> Yeah. I could switch these around if you'd prefer.
>> No, no. I'll go with your fantasy.
>> [LAUGH] All right. I, yeah, I think that payoff matrix may look
something like we both have twos in, in the s, the same place.
>> Mhm.
>> But anyway, but let's say for the purposes of this example,
there's a little bit of a disagreement. Okay, so now what we
need to figure out is what the minmax profile is for this game.
>> Okay.
>> Alright, so that's going to be a pair of numbers.
>> Mm-hm.
>> One number corresponds to the payoff for Curly and one number
corresponds to the payoff for Smooth. And it should be, the payoff
for Curly should be the payoff that Curly can guarantee himself even
if Smooth is trying to get him to have a low score.
>> Okay.
>> And vice versa. Smooth's score is going to be the score that it
can guarantee, he can guarantee himself even
if Curly is trying to minimize Smooth's score.
>> All right.
>> So let's do this as a quiz. So,I want you
to find the min-max profile for this game, this Bach, Stravinsky
game or Backstreet, Sting game, and put the, the number for
Curly in the first box and Smooth in the second box.
>> Okay.
>> Go.