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1. Game Theory: Introduction: five first lessons
Poziom:
Temat: Edukacja
Professor Ben Polak: So
this is Game Theory Economics
159.
If you're here for art history,
you're either in the wrong room
or stay anyway,
maybe this is the right room;
but this is Game Theory, okay.
You should have four handouts;
everyone should have four
handouts.
There is a legal release
form--we'll talk about it in a
minute--about the videoing.
There is a syllabus,
which is a preliminary
syllabus: it's also online.
And there are two games labeled
Game 1 and Game 2.
Can I get you all to look at
Game 1 and start thinking about
it.
And while you're thinking about
it, I am hoping you can
multitask a bit.
I'll describe a bit about the
class and we'll get a bit of
admin under our belts.
But please try and look
at--somebody's not looking at
it, because they're using it as
a fan here--so look at Game 1
and fill out that form for me,
okay?
So while you're filling that
out, let me tell you a little
bit about what we're going to be
doing here.
So what is Game Theory?
Game Theory is a method of
studying strategic situations.
So what's a strategic situation?
Well let's start off with
what's not a strategic
situation.
In your Economics - in your
Intro Economics class in 115 or
110, you saw some pretty good
examples of situations that were
not strategic.
You saw firms working in
perfect competition.
Firms in perfect competition
are price takers:
they don't particularly have to
worry about the actions of their
competitors.
You also saw firms that were
monopolists and monopolists
don't have any competitors to
worry about, so that's not a
particularly strategic
situation.
They're not price takers but
they take the demand curve.
Is this looking familiar for
some of you who can remember
doing 115 last year or maybe two
years ago for some of you?
Everything in between is
strategic.
So everything that constitutes
imperfect competition is a
strategic setting.
Think about the motor industry,
the motor car industry.
Ford has to worry about what GM
is doing and what Toyota is
doing, and for the moment at
least what Chrysler is doing but
perhaps not for long.
So there's a small number of
firms and their actions affect
each other.
So for a literal definition of
what strategic means:
it's a setting where the
outcomes that affect you depend
on actions,
not just on your own actions,
but on actions of others.
All right, that's as much as
I'm going to say for preview
right now, we're going to come
back and see plenty of this over
the course of the next semester.
So what I want to do is get on
to where this applies.
It obviously applies in
Economics, but it also applies
in politics, and in fact,
this class will count as a
Political Science class if
you're a Political Science
major.
You should go check with the
DUS in Political Science.
It count - Game Theory is very
important in law these days.
So for those of you--for the
half of you--that are going to
end up in law school,
this is pretty good training.
Game Theory is also used in
biology and towards the middle
of the semester we're actually
going to see some examples of
Game Theory as applied to
evolution.
And not surprisingly,
Game Theory applies to sport.
So let's talk about a bit of
admin.
How are you doing on filling
out those games?
Everyone managing to multitask:
filling in Game 1?
Keep writing.
I want to get some admin out of
the way and I want to start by
getting out of the way what is
obviously the elephant in the
room.
Some of you will have noticed
that there's a camera crew here,
okay.
So as some of you probably
know, Yale is undergoing an open
education project and they're
videoing several classes,
and the idea of this,
is to make educational
materials available beyond the
walls of Yale.
In fact, on the web,
internationally,
so people in places,
maybe places in the U.S.
or places miles away,
maybe in Timbuktu or whatever,
who find it difficult to get
educational materials from the
local university or whatever,
can watch certain lectures from
Yale on the web.
Some of you would have been in
classes that do that before.
What's going to different about
this class is that you're going
to be participating in it.
The way we teach this class is
we're going to play games,
we're going to have
discussions,
we're going to talk among the
class, and you're going to be
learning from each other,
and I want you to help people
watching at home to be able to
learn too.
And that means you're going to
be on film, at the very least on
mike.
So how's that going to work?
Around the room are three T.A.s
holding mikes.
Let me show you where they are:
one here, one here,
and one here.
When I ask for classroom
discussions, I'm going to have
one of the T.A.s go to you with
a microphone much like in
"Donahue" or something,
okay.
At certain times,
you're going to be seen on
film, so the camera is actually
going to come around and point
in your direction.
Now I really want this to
happen.
I had to argue for this to
happen, cause I really feel that
this class isn't about me.
I'm part of the class
obviously, but it's about you
teaching each other and
participating.
But there's a catch,
the catch is,
that that means you have to
sign that legal release form.
So you'll see that you have in
front of you a legal release
form, you have to be able to
sign it,
and what that says is that we
can use you being shown in
class.
Think of this as a bad hair day
release form.
All right, you can't sue Yale
later if you had a bad hair day.
For those of you who are on the
run from the FBI,
your Visa has run out,
or you're sitting next to your
ex-girlfriend,
now would be a good time to put
a paper bag over your head.
All right, now just to get you
used to the idea,
in every class we're going to
have I think the same two
people, so Jude is the
cameraman;
why don't you all wave to Jude:
this is Jude okay.
And Wes is our audio guy:
this is Wes.
And I will try and remember not
to include Jude and Wes in the
classroom discussions,
but you should be aware that
they're there.
Now, if this is making you
nervous, if it's any
consolation, it's making me very
nervous.
So, all right,
we'll try and make this class
work as smoothly as we can,
allowing for this extra thing.
Let me just say,
no one's making any money off
this--at least I'm hoping these
guys are being paid--but me and
the T.A.s are not being paid.
The aim of this,
that I think is a good aim,
it's an educational project,
and I'm hoping you'll help us
with it.
The one difference it is going
to mean, is that at times I
might hold some of the
discussions for the class,
coming down into this part of
the room, here,
to make it a little easier for
Jude.
All right, how are we doing now
on filling out those forms?
Has everyone filled in their
strategy for the first game?
Not yet.
Okay, let's go on doing a bit
more admin.
The thing you mostly care about
I'm guessing,
is the grades.
All right, so how is the grade
going to work for this class?
30% of the class will be on
problem sets,
30% of the grade;
30% on the mid-term,
and 40% on the final;
so 30/30/40.
The mid-term will be held in
class on October 17^(th);
that is also in your syllabus.
Please don't anybody tell me
late - any time after today you
didn't know when the mid-term
was and therefore it clashes
with 17 different things.
The mid-term is on October
17^(th), which is a Wednesday,
in class.
All right, the problem sets:
there will be roughly ten
problem sets and I'll talk about
them more later on when I hand
them out.
The first one will go out on
Monday but it will be due ten
days later.
Roughly speaking they'll be
every week.
The grade distribution:
all right, so this is the rough
grade distribution.
Roughly speaking,
a sixth of the class are going
to end up with A's,
a sixth are going to end up
with A-,
a sixth are going to end up
with B+, a sixth are going to
end up with B,
a sixth are going to end up
with B-,
and the remaining sixth,
if I added that up right,
are going to end up with what I
guess we're now calling the
presidential grade,
is that right?
That's not literally true.
I'm going to squeeze it a bit,
I'm going to curve it a bit,
so actually slightly fewer than
a sixth will get straight A's,
and fewer than a sixth will get
C's and below.
We'll squeeze the middle to
make them be more B's.
One thing I can guarantee from
past experience in this class,
is that the median grade will
be a B+.
The median will fall somewhere
in the B+'s.
Just as forewarning for people
who have forgotten what a median
is, that means half of you--not
approximately half,
it means exactly half of
you--will be getting something
like B+ and below and half will
get something like B+ and above.
Now, how are you doing in
filling in the forms?
Everyone filled them in yet?
Surely must be pretty close to
getting everyone filled in.
All right, so last things to
talk about before I actually
collect them in - textbooks.
There are textbooks for this
class.
The main textbook is this one,
Dutta's book Strategy and
Games.
If you want a slightly tougher
book, more rigorous book,
try Joel Watson's book,
Strategies.
Both of those books are
available at the bookstore.
But I want to warn everybody
ahead of time,
I will not be following the
textbook.
I regard these books as safety
nets.
If you don't understand
something that happened in
class, you want to reinforce an
idea that came up in class,
then you should read the
relevant chapters in the book
and the syllabus will tell you
which chapters to read for each
class,
or for each week of class,
all right.
But I will not be following
these books religiously at all.
In fact, they're just there as
back up.
In addition,
I strongly recommend people
read, Thinking
Strategically.
This is good bedtime reading.
Do any of you suffer from
insomnia?
It's very good bedtime reading
if you suffer from insomnia.
It's a good book and what's
more there's going to be a new
edition of this book this year
and Norton have allowed us to
get advance copies of it.
So if you don't buy this book
this week, I may be able to make
the advance copy of the new
edition available for some of
you next week.
I'm not taking a cut on that
either, all right,
there's no money changing
hands.
All right, sections are on the
syllabus sign up - sorry on the
website, sign up as usual.
Put yourself down on the wait
list if you don't get into the
section you want.
You probably will get into the
section you want once we're
done.
All right, now we must be done
with the forms.
Are we done with the forms?
All right, so why don't we send
the T.A.s, with or without
mikes, up and down the aisles
and collect in your Game #1;
not Game #2, just Game #1.
Just while we're doing that,
I think the reputation of this
class--I think--if you look at
the course evaluations online or
whatever,
is that this class is
reasonably hard but reasonably
fun.
So I'm hoping that's what the
reputation of the class is.
If you think this class is
going to be easy,
I think it isn't actually an
easy class.
It's actually quite a hard
class, but I think I can
guarantee it's going to be a fun
class.
Now one reason it's a fun
class, is the nice thing about
teaching Game Theory - quieten
down folks--one thing about
teaching Game Theory is,
you get to play games,
and that's exactly what we've
just been doing now.
This is our first game and
we're going to play games
throughout the course,
sometimes several times a week,
sometimes just once a week.
We got all these things in?
Everyone handed them in?
So I need to get those counted.
Has anyone taken the Yale
Accounting class?
No one wants to - has
aspirations to be - one person
has.
I'll have a T.A.
do it, it's all right,
we'll have a T.A.
do it.
So Kaj, can you count those for
me?
Is that right?
Let me read out the game you've
just played.
"Game 1, a simple grade scheme
for the class.
Read the following carefully.
Without showing your neighbor
what you are doing,
put it in the box below either
the letter Alpha or the letter
Beta.
Think of this as a grade bid.
I will randomly pair your form
with another form and neither
you nor your pair will ever know
with whom you were paired.
Here's how the grades may be
assigned for the class.
[Well they won't be,
but we can pretend.]
If you put Alpha and you're
paired with Beta,
then you will get an A and your
pair a C.
If you and your pair both put
Alpha, you'll both get B-.
If you put Beta and you're
paired with Alpha,
you'll get a C and your pair an
A.
If you and your pair both put
Beta, then you'll both get B+."
So that's the thing you just
filled in.
Now before we talk about this,
let's just collect this
information in a more useful
way.
So I'm going to remove this for
now.
We'll discuss this in a second,
but why don't we actually
record what the game is,
that we're playing,
first.
So this is our grade game,
and what I'm going to do,
since it's kind of hard to
absorb all the information just
by reading a paragraph of text,
I'm going to make a table to
record the information.
So what I'm going to do is I'm
going to put me here,
and my pair,
the person I'm randomly paired
with here,
and Alpha and Beta,
which are the choices I'm going
to make here and on the columns
Alpha and Beta,
the choices my pair is making.
In this table,
I'm going to put my grades.
So my grade if we both put
Alpha is B-, if we both put
Beta, was B+.
If I put Alpha and she put a
Beta, I got an A,
and if I put Beta and she put
an Alpha, I got a C.
Is that correct?
That's more or less right?
Yeah, okay while we're here,
why don't we do the same for my
pair?
So this is my grades on the
left hand table,
but now let's look at what my
pair will do,
what my pair will get.
So I should warn the people
sitting at the back that my
handwriting is pretty bad,
that's one reason for moving
forward.
The other thing I should
apologize at this stage of the
class is my accent.
I will try and improve the
handwriting, there's not much I
can do about the accent at this
stage.
So once again if you both put
Alpha then my pair gets a B-.
If we both put Beta,
then we both get a B+;
in particular,
my pair gets a B+.
If I put Alpha and my pair puts
Beta, then she gets a C.
And if I put Beta and she puts
Alpha, then she gets an A.
So I now have all the
information that was on the
sheet of paper that you just
handed in.
Now there's another way of
organizing this that's standard
in Game Theory,
so we may as well get used to
it now on the first day.
Rather then drawing two
different tables like this,
what I'm going to do is I'm
going to take the second table
and super-impose it on top of
the first table.
Okay, so let me do that and
you'll see what I mean.
What I'm going to do is draw a
larger table,
the same basic structure:
I'm choosing Alpha and Beta on
the rows,
my pair is choosing Alpha and
Beta on the columns,
but now I'm going to put both
grades in.
So the easy ones are on the
diagonal: you both get B- if we
both choose Alpha;
we both get B+ if we both
choose Beta.
But if I choose Alpha and my
pair chooses Beta,
I get an A and she gets a C.
And if I choose Beta and she
chooses Alpha,
then it's me who gets the C and
it's her who gets the A.
So notice what I did here.
The first grade corresponds to
the row player,
me in this case,
and the second grade in each
box corresponds to the column
player,
my pair in this case.
So this is a nice succinct way
of recording what was in the
previous two tables.
This is an outcome matrix;
this tells us everything that
was in the game.
Okay, so now seems a good time
to start talking about what
people did.
So let's just have a show of
hands.
How many of you chose Alpha?
Leave your hands up so that
Jude can catch that,
so people can see at home,
okay.
All right and how many of you
chose Beta?
There's far more Alphas - wave
your hands the Beta's okay.
All right, there's a Beta here,
okay.
So it looks like a lot of -
well we're going to find out,
we're going to count--but a lot
more Alpha's than Beta's.
Let me try and find out some
reasons why people chose.
So let me have the Alpha's up
again.
So, the woman who's in red
here, can we get a mike to the -
yeah, is it okay if we ask you?
You're not on the run from the
FBI?
We can ask you why?
Okay, so you chose Alpha right?
So why did you choose Alpha?
Student: [inaudible]
realized that my partner chose
Alpha, therefore I chose
[inaudible].
Professor Ben Polak: All
right, so you wrote out these
squares, you realized what your
partner was going to do,
and responded to that.
Any other reasons for choosing
Alpha around the room?
Can we get the woman here?
Try not to be intimidated by
these microphones,
they're just mikes.
It's okay.
Student: The reason I
chose Alpha, regardless of what
my partner chose,
I think there would be better
outcomes than choosing Beta.
Professor Ben Polak: All
right, so let me ask your names
for a second-so your name was?
Student: Courtney.
Professor Ben Polak:
Courtney and your name was?
Student: Clara Elise.
Professor Ben Polak:
Clara Elise.
So slightly different reasons,
same choice Alpha.
Clara Elise's reason - what did
Clara Elise say?
She said, no matter what the
other person does,
she reckons she'd get a better
grade if she chose Alpha.
So hold that thought a second,
we'll come back to - is it
Clara Elise, is that right?
We'll come back to Clara Elise
in a second.
Let's talk to the Beta's a
second;
let me just emphasize at this
stage there are no wrong
answers.
Later on in the class there'll
be some questions that have
wrong answers.
Right now there's no wrong
answers.
There may be bad reasons but
there's no wrong answers.
So let's have the Beta's up
again.
Let's see the Beta's.
Oh come on!
There was a Beta right here.
You were a Beta right?
You backed off the Beta, okay.
So how can I get a mike into a
Beta?
Let' s stick in this aisle a
bit.
Is that a Beta right there?
Are you a Beta right there?
Can I get the Beta in here?
Who was the Beta in here?
Can we get the mike in there?
Is that possible?
In here - you can leave your
hand so that - there we go.
Just point towards - that's
fine, just speak into it,
that's fine.
Student: So the reason
right?
Professor Ben Polak:
Yeah, go ahead.
Student: I personally
don't like swings that much and
it's the B-/B+ range,
so I'd much rather prefer that
to a swing from A to C,
and that's my reason.
Professor Ben Polak: All
right, so you're saying it
compresses the range.
I'm not sure it does compress
the range.
I mean if you chose Alpha,
you're swinging from A to B-;
and from Beta,
swinging from B+ to C.
I mean those are similar kind
of ranges but it certainly is a
reason.
Other reasons for choosing?
Yeah, the guy in blue here,
yep, good.
That's all right.
Don't hold the mike;
just let it point at you,
that's fine.
Student: Well I guess I
thought we could be more
collusive and kind of work
together, but I guess not.
So I chose Beta.
Professor Ben Polak:
There's a siren in the
background so I missed the
answer.
Stand up a second,
so we can just hear you.
Student: Sure.
Professor Ben Polak:
Sorry, say again.
Student: Sure.
My name is Travis.
I thought we could work
together, but I guess not.
Professor Ben Polak: All
right good.
That's a pretty good reason.
Student: If you had
chosen Beta we would have all
gotten B+'s but I guess not.
Professor Ben Polak:
Good, so Travis is giving us a
different reason,
right?
He's saying that maybe,
some of you in the room might
actually care about each other's
grades, right?
I mean you all know each other
in class.
You all go to the same college.
For example,
if we played this game up in
the business school--are there
any MBA students here today?
One or two.
If we play this game up in the
business school,
I think it's quite likely we're
going to get a lot of Alpha's
chosen, right?
But if we played this game up
in let's say the Divinity
School, all right and I'm
guessing that Travis' answer is
reflecting what you guys are
reasoning here.
If you played in the Divinity
School, you might think that
people in the Divinity School
might care about other people's
grades, right?
There might be ethical
reasons--perfectly good,
sensible, ethical reasons--for
choosing Beta in this game.
There might be other reasons as
well, but that's perhaps the
reason to focus on.
And perhaps,
the lesson I want to draw out
of this is that right now this
is not a game.
Right now we have actions,
strategies for people to take,
and we know what the outcomes
are, but we're missing something
that will make this a game.
What are we missing here?
Student: Objectives.
Professor Ben Polak:
We're missing objectives.
We're missing payoffs.
We're missing what people care
about, all right.
So we can't really start
analyzing a game until we know
what people care about,
and until we know what the
payoffs are.
Now let's just say something
now, which I'll probably forget
to say in any other moment of
the class, but today it's
relevant.
Game Theory,
me, professors at Yale,
cannot tell you what your
payoff should be.
I can't tell you in a useful
way what it is that your goals
in life should be or whatever.
That's not what Game Theory is
about.
However, once we know what your
payoffs are, once we know what
your goals are,
perhaps Game Theory can you
help you get there.
So we've had two different
kinds of payoffs mentioned here.
We had the kind of payoff where
we care about our own grade,
and Travis has mentioned the
kind of payoff where you might
care about other people's
grades.
And what we're going to do
today is analyze this game under
both those possible payoffs.
To start that off,
let's put up some possible
payoffs for the game.
And I promise we'll come back
and look at some other payoffs
later.
We'll revisit the Divinity
School later.
All right, so here once again
is our same matrix with me and
my pair, choosing actions Alpha
and Beta, but this time I'm
going to put numbers in here.
And some of you will perhaps
recognize these numbers,
but that's not really relevant
for now.
All right, so what's the idea
here?
Well the first idea is that
these numbers represent utiles
or utilities.
They represent what these
people are trying to maximize,
what they're to achieve,
their goals.
The idea is - just to compare
this to the outcome matrix - for
the person who's me here,
(A,C) yields a payoff of--(A,C)
is this box--so (A,C) yields a
payoff of three,
whereas (B-,B-) yields a payoff
of 0, and so on.
So what's the interpretation?
It's the first interpretation:
the natural interpretation that
a lot of you jumped to straight
away.
These are people--people with
these payoffs are people--who
only care about their own
grades.
They prefer an A to a B+,
they prefer a B+ to a B-,
and they prefer a B- to a C.
Right, I'm hoping I the grades
in order, otherwise it's going
to ruin my curve at the end of
the year.
So these people only care about
their own grades.
They only care about their own
grades.
What do we call people who only
care about their own grades?
What's a good technical term
for them?
In England, I think we refer to
these guys - whether it's
technical or not - as "evil
gits."
These are not perhaps the most
moral people in the universe.
So now we can ask a different
question.
Suppose, whether these are
actually your payoffs or not,
pretend they are for now.
Suppose these are all payoffs.
Now we can ask,
not what did you do,
but what should you do?
Now we have payoffs that can
really switch the question to a
normative question:
what should you do?
Let's come back to - was it
Clara Elise--where was Clara
Elise before?
Let's get the mike on you again.
So just explain what you did
and why again.
Student: Why I chose
Alpha?
Professor Ben Polak:
Yeah, stand up a second,
if that's okay.
Student: Okay.
Professor Ben Polak: You
chose Alpha;
I'm assuming these were roughly
your payoffs,
more or less,
you were caring about your
grades.
Student: Yeah,
I was thinking - Professor
Ben Polak: Why did you
choose Alpha?
Student: I'm sorry?
Professor Ben Polak: Why
did you choose Alpha?
Just repeat what you said
before.
Student: Because I
thought the payoffs - the two
different payoffs that I could
have gotten--were highest if I
chose Alpha.
Professor Ben Polak:
Good;
so what Clara Elise is
saying--it's an important
idea--is this (and tell me if
I'm paraphrasing you incorrectly
but I think this is more or less
what you're saying):
is no matter what the other
person does,
no matter what the pair does,
she obtains a higher payoff by
choosing Alpha.
Let's just see that.
If the pair chooses Alpha and
she chooses Alpha,
then she gets 0.
If the pair chooses Alpha and
she chose Beta,
she gets -1.
0 is bigger than -1.
If the pair chooses Beta,
then if she chooses Alpha she
gets 3, Beta she gets 1,
and 3 is bigger than 1.
So in both cases,
no matter what the other person
does, she receives a higher
payoff from choosing Alpha,
so she should choose Alpha.
Does everyone follow that line
of reasoning?
That's a stronger line of
reasoning then the reasoning we
had earlier.
So the woman,
I have immediately forgotten
the name of, in the red shirt,
whose name was -
Student: Courtney.
Professor Ben Polak:
Courtney,
so Courtney also gave a reason
for choosing Alpha,
and it was a perfectly good
reason for choosing Alpha,
nothing wrong with it,
but notice that this reason's a
stronger reason.
It kind of implies your reason.
So let's get some definitions
down here.
I think I can fit it in here.
Let's try and fit it in here.
Definition: We say that my
strategy Alpha strictly
dominates my strategy Beta,
if my payoff from Alpha is
strictly greater than that from
Beta, [and this is the key
part of the definition],
regardless of what others
do.
Shall we just read that back?
"We say that my strategy Alpha
strictly dominates my strategy
Beta, if my payoff from Alpha is
strictly greater than that from
Beta,
regardless of what others do."
Now it's by no means my main
aim in this class to teach you
jargon.
But a few bits of jargon are
going to be helpful in allowing
the conversation to move forward
and this is certainly one.
"Evil gits" is maybe one too,
but this is certainly one.
Let's draw out some lessons
from this.
Actually, so you can still read
that, let me bring down and
clean this board.
So the first lesson of the
class, and there are going to be
lots of lessons,
is a lesson that emerges
immediately from the definition
of a dominated strategy and it's
this.
So Lesson One of the course is:
do not play a strictly
dominated strategy.
So with apologies to Strunk and
White, this is in the passive
form, that's dominated,
passive voice.
Do not play a strictly
dominated strategy.
Why?
Somebody want to tell me why?
Do you want to get this guy?
Stand up - yeah.
Student: Because
everyone's going to pick the
dominant outcome and then
everyone's going to get the
worst result - the collectively
worst result.
Professor Ben Polak:
Yeah, that's a possible answer.
I'm looking for something more
direct here.
So we look at the definition of
a strictly dominated strategy.
I'm saying never play one.
What's a possible reason for
that?
Let's - can we get the woman
there?
Student: [inaudible]
Professor Ben Polak:
"You'll always lose."
Well, I don't know:
it's not about winning and
losing.
What else could we have?
Could we get this guy in the
pink down here?
Student: Well,
the payoffs are lower.
Professor Ben Polak: The
payoffs are lower,
okay.
So here's an abbreviated
version of that,
I mean it's perhaps a little
bit longer.
The reason I don't want to play
a strictly dominated strategy
is, if instead,
I play the strategy that
dominates it,
I do better in every case.
The reason I never want to play
a strictly dominated strategy
is, if instead I play the
strategy that dominates it,
whatever anyone else does I'm
doing better than I would have
done.
Now that's a pretty convincing
argument.
That sounds like a convincing
argument.
It sounds like too obvious even
to be worth stating in class,
so let me now try and shake
your faith a little bit in this
answer.
You're somebody who's wanted by
the FBI, right?
Okay, so how about the
following argument?
Look at the payoff matrix again
and suppose I reason as follows.
Suppose I reason and say if we,
me and my pair,
both reason this way and choose
Alpha then we'll both get 0.
But if we both reasoned a
different way and chose Beta,
then we'll both get 1.
So I should choose Beta:
1 is bigger than 0,
I should choose Beta.
What's wrong with that argument?
My argument must be wrong
because it goes against the
lesson of the class and the
lessons of the class are gospel
right,
they're not wrong ever,
so what's wrong with that
argument?
Yes, Ale - yeah good.
Student: Well because
you have to be able to agree,
you have to be able to speak to
them but we aren't allowed to
show our partners what we wrote.
Professor Ben Polak: All
right, so it involves some
notion of agreeing.
So certainly part of the
problem here,
with the reasoning I just gave
you--the reasoning that said I
should choose Beta,
because if we both reason the
same way, we both do better that
way--involves some kind of
magical reasoning.
It's as if I'm arguing that if
I reason this way and reason
myself to choosing Beta,
somehow I'm going to make the
rest of you reason the same way
too.
It's like I've got ESP or I'm
some character out of the X-Men,
is that what it's called?
The X-Men right?
Now in fact,
this may come as a surprise to
you, I don't have ESP,
I'm not a character out of the
X-Men,
and so you can't actually see
brain waves emitting from my
head, and my reasoning doesn't
affect your reasoning.
So if I did reason that way,
and chose Beta,
I'm not going to affect your
choice one way or the other.
That's the first thing that's
wrong with that reasoning.
What else is wrong with that
reasoning?
Yeah, that guy down here.
Student: Well,
the second that you choose Beta
then someone's going - it's in
someone's best interest to take
advantage of it.
Professor Ben Polak: All
right, so someone's going to
take advantage of me,
but even more than that,
an even stronger argument:
that's true,
but even a stronger argument.
Well how about this?
Even if I was that guy in the
X-Men or the Matrix or whatever
it was, who could reason his way
into making people do things.
Even if I could make everyone
in the room choose Beta by the
force of my brain waves,
what should I then do?
I should choose Alpha.
If these are my payoffs I
should go ahead and choose Alpha
because that way I end up
getting 3.
So there's two things wrong
with the argument.
One, there's this magical
reasoning aspect,
my reasoning is controlling
your actions.
That doesn't happen in the real
world.
And two, even if that was the
case I'd do better to myself
choose Alpha.
So, nevertheless,
there's an element of truth in
what I just said.
It's the fact that there's an
element of truth in it that
makes it seem like a good
argument.
The element of truth is this.
It is true that by both
choosing Alpha we both ended up
with B-'s.
We both end up with payoffs of
0, rather than payoffs of 1.
It is true that by both
choosing, by both following this
lesson and not choosing the
dominated strategy Beta,
we ended up with payoffs,
(0,0), that were bad.
And that's probably the second
lesson of the class.
So Lesson 2,
and this lesson probably
wouldn't be worth stating,
if it wasn't for sort of a
century of thought and economics
that said the opposite.
So rational choice [in
this case, people not choosing a
dominated strategy;
people choosing a dominant
strategy]
rational choice can lead to
outcomes that - what do
Americans call this?--that
"suck."
If you want a more technical
term for that (and you remember
this from Economics 115),
it can lead to outcomes that
are "inefficient,"
that are "Pareto inefficient,"
but "suck" will do for today.
Rational choices by rational
players, can lead to bad
outcomes.
So this is a famous example for
this reason.
It's a good illustration of
this point.
It's a famous example.
What's the name of this
example, somebody?
This is called Prisoner's
Dilemma.
How many of you have heard of
the Prisoner's Dilemma before?
Most of you saw it in 115,
why is it called the Prisoner's
Dilemma?
Yes, the guy here in orange.
That's okay;
he can just point at you that's
fine.
Student: I think it's
whether or not the prisoner's
cooperate in the sentence they
have,
and if they kind of rat out the
other person,
then they can have less;
but if both rat out,
then they like end up losing
large scale.
Professor Ben Polak:
Good, so in the standard story
you've got these two crooks,
or two accused crooks,
and they're in separate cells
and they're being interviewed
separately--kept apart--and
they're both told that if
neither of them rats the other
guy out,
they'll go to jail for say a
year.
If they both rat each other
out, they'll end up in jail for
two years, But if you rat the
other guy out and he doesn't rat
you out,
then you will go home free and
he'll go to jail for five years.
Put that all down and you
pretty quickly see that,
regardless whether the other
guy rats you or not,
you're better off ratting him
out.
Now, if you have never seen
that Prisoner's Dilemma,
you can see it pretty much
every night on a show called
Law & Order.
How many of you have seen
Law & Order?
If you haven't seen Law
& Order,
the way to see Law &
Order is to go to a random
TV set,
at a random time,
and turn on a random channel.
This happens in every single
episode, so much so that if any
of you actually - I mean this
might actually be true at
Yale--but if you any of you or
the TV guys: if any of you know
the guy who writes the plots for
this,
have him come to the class (so
I guess to see the video now)
and we get some better plot
lines in there.
But, of course,
that's not the only example.
The grade game and this is not
the only example.
There are lots of examples of
Prisoner's Dilemmas out there.
Let's try and find some other
ones.
So how many of you have
roommates in your college?
How many of you have roommates?
Most of you have roommates
right?
So I'm guessing now,
I won't make you show your
hands, because it's probably
embarrassing,
but what is the state of your
dorm rooms, your shared dorm
rooms, at the end of the
semester or the end of the
school year?
So I'm just guessing,
having been in a few of these
things over the years,
that by the end of the
semester,
or certainly by the end of the
school year, the state of the
average Yale dorm room is quite
disgusting.
Why is it disgusting?
It's disgusting because people
don't tidy up.
They don't clean up those bits
of pizza and bits of chewed
bread and cheese,
but why don't they tidy up?
Well let's just work it out.
What would you like to happen
if you're sharing a dorm room?
You'd like to have the other
guy tidy up, right?
The best thing for you is to
have the other guy tidy up and
the worst thing for you is to
tidy up for the other guy.
But now work it out:
it's a Prisoner's Dilemma.
If the other guy doesn't tidy
up, you're best off not tidying
up either, because the last
thing you want is to be tidying
up for the other guy.
And if the other guy does tidy
up, hey the room's clean,
who cares?
So either way,
you're not going to tidy up and
you end up with a typical Yale
dorm room.
Am I being unfair?
Are your dorm rooms all perfect?
This may be a gender thing but
we're not going to go there.
So there are lots of Prisoner's
Dilemmas out there,
anyone got any other examples?
Other examples?
I didn't quite hear that, sorry.
Let's try and get a mike on it
so we can really hear it.
Student: [inaudible]
Professor Ben Polak:
Okay, in divorce struggles,
okay.
You're too young to be worrying
about such things but never
mind.
Yeah, okay, that's a good
example.
All right, hiring lawyers,
bringing in big guns.
What about an Economics example?
What about firms who are
competing in prices?
Both firms have an incentive to
undercut the other firm,
driving down profits for both.
The last thing you want is to
have the other firm undercut
you, in an attempt to push
prices down.
That's good for us the
consumers, but bad for the firm,
bad for industry profit.
What remedies do we see?
We'll come back to this later
on in the class,
but let's have a preview.
So what remedies do we see in
society for Prisoner's Dilemmas?
What kind of remedies do we see?
Let me try and get the guy here
right in front.
Student: Collusion.
Professor Ben Polak:
Collusion;
so firms could collude.
So what prevents them from
colluding?
One thing they could do,
presumably, is they could write
a contract, these firms.
They could say I won't lower my
prices if you don't lower your
prices, and they could put this
contract in with the pricy
lawyer,
who's taking a day off from the
divorce court,
and that would secure that they
wouldn't lower prices on each
other.
Is that right?
So why wouldn't that work?
Why wouldn't writing a contract
here work?
It's against the law.
It's an illegal contract.
What about you with your
roommates?
How many of you have a written
contract, stuck with a magnet on
the fridge, telling you,
when you're supposed to tidy
up.
Very few of you.
Why do you manage to get some
cooperation between you and your
roommates even without a written
contract?
Student: It's not
legally enforceable.
Professor Ben Polak:
Well it probably is legally
enforceable actually.
This guy says not,
but it probably is legally
enforceable.
He probably could have a
written contract about tidying
up.
The woman in here.
Student: Repetition;
you do it over and over.
Professor Ben Polak:
Yeah, so maybe even among your
roommates, maybe you don't need
a contract because you can
manage to achieve the same ends,
by the fact that you're going
to be interacting with the same
person, over and over again
during your time at Yale.
So we'll come back and revisit
the idea that repeating an
interaction may allow you to
obtain cooperation,
but we're not going to come
back to that until after the
mid-term.
That's way down the road but
we'll get there.
Now one person earlier on had
mentioned something about
communication.
I think it was somebody in the
front, right?
So let's just think about this
a second.
Is communication the problem
here?
Is the reason people behave
badly--I don't know
"badly"--people choose Alpha in
this game here,
is it the fact that they can't
communicate?
Suppose you'd been able to talk
before hand, so suppose the
woman here whose name
was…?
Student: Mary.
Professor Ben Polak:
…Mary,
had been able to talk to the
person next to her whose name
is…?
Student: Erica.
Professor Ben Polak:
Erica.
And they said,
suppose we know we're going to
be paired together,
I'll choose Beta if you choose
Beta.
Would that work?
Why wouldn't that work?
Student: There's no
enforcement.
Professor Ben Polak:
There's no enforcement.
So it isn't a failure of
communication per se.
A contract is more then
communication,
a contract is communication
with teeth.
It actually changes the payoffs.
So I could communicate with
Alice on agreements,
but back home I'm going to go
ahead and choose Alpha anyway;
all the better if he's choosing
Beta.
So we'll come back and talk
about more of these things as
the course goes on,
but let's just come back to the
two we forgot there:
so the collusion case and the
case back in Law &
Order with the prisoners in the
cell.
How do they enforce their
contracts?
They don't always rat each
other out and some firms manage
to collude?
How do they manage to enforce
those contracts?
Those agreements,
how are they enforced?
Student: They trust each
other.
Professor Ben Polak: It
could be they trust each other,
although if you trust a crook
that's not…
What else could it be?
The guy here again with the
beard, yeah.
Student: Could be a zero
sum game.
Professor Ben Polak:
Well, but this is the game.
So here's the game.
Student: No,
but the pay,
the way they value,
the way of valuing each--
Professor Ben Polak:
Okay, so the payoffs may be
different.
I have something simpler in
mind.
Suppose they have a written
contract, or even an unwritten
contract, what enforces the
contract for colluding firms or
crooks in jail?
Yeah.
Student: Gets off Scott
free in five years when the
other guy gets out,
he might run into a situation
where [inaudible]
Professor Ben Polak:
Yeah,
so a short version of that is,
it's a different kind of
contract.
If you rat someone out in jail,
someone puts a contract out on
you.
Tony Soprano enforces those
contracts.
That's the purpose of Tony
Soprano.
It's the purpose of the mafia.
The reason the mafia thrives in
countries where it's hard to
write legal contracts--let's say
some new parts of the former
Soviet Union or some parts of
Africa--the reason the mafia
thrives in those environments,
is that it substitutes for the
law and enforces both legal and
illegal contracts.
So I promised a while ago now,
that we were going to come back
and look at this game under some
other possible payoffs.
So I wasn't under a contract
but let's come back and fulfill
that promise anyway.
So we're going to revisit,
if not the Divinity School,
at least in people who have
more morality than my friends up
in the business school.
We're going to ask for the same
grade game we played at the
beginning.
What would happen if player's
payoffs looked different?
So these are "possible payoffs
(2)."
I'll give these a name..
We called the other guys "evil
gits." We'll call these
guys "indignant angels."
I can never spell indignant..
Is that roughly right?
Does that look right?
I think it's right.
In-dig-nant isn't it: indignant.
Indignant angels,
and we'll see why in a second.
So here are their payoffs and
once again the basic structure
of the game hasn't changed.
It's still I'm choosing Alpha
and Beta, my pair is choosing
Alpha and Beta,
and the grades are the same as
they were before.
They're hidden by that board
but you saw them before.
But this time the payoffs are
as follows.
On the lead diagonal we still
have (0,0) and (1,1).
But now the grades here are
-1--I'm sorry--the payoffs are
-1 and -3, and here they're -3
and -1.
What's the idea here?
These aren't the only other
possible payoffs.
It's just an idea.
Suppose I get an A and my pair
gets a C, then sure I get that
initial payoff of 3,
but unfortunately I can't sleep
at night because I'm feeling so
guilty.
I have some kind of moral
conscience and after I've
subtracted off my guilt feelings
I end up at -1,
so think of this as guilt:
some notion of morality.
Conversely, if I chose a Beta
and my pair chooses an Alpha,
so I end up with a C and she
ends up with an A,
then you know I have a bad time
explaining to my parents why I
got a C in this class,
and I have to say about how I'm
going to be president anyway.
But then, in addition,
I feel indignation against this
person.
It isn't just that I got a C;
I got a C because she made me
get a C, so that moral
indignation takes us down to -3.
So again, I'm not claiming
these are the only other
possible payoffs,
but just another possibility to
look at.
So suppose these were the
payoffs in the game.
Again, suspend disbelief a
second and imagine that these
actually are your payoffs,
and let me ask you what you
would have done in this case.
So think about it a second.
Write it down.
Write down what you're going to
do on the corner of your
notepad.
Just write down an Alpha or
Beta: what you're going to do
here.
You're not all writing.
The guy in the England shirt
isn't writing.
You've got to be writing if you
are in an England shirt.
Show it to your neighbor.
Let's have a show of hands,
again I want you to keep your
hands up so that Jude can see it
now.
So how many of you chose Alpha
in this case?
Raise your hands.
Come on, don't be shy.
Raise your hands.
How many chose Beta in this
case?
How many people abstained?
Not allowed to abstain:
let's try it again.
Alpha in this case?
No abstentions here.
Beta in this case?
So we're roughly splitting the
room.
Someone who chose Alpha?
Again: raise the Alpha's again.
Let me get this guy here.
So why did you choose Alpha?
Student: You would
minimize your losses;
you'd get 0 or -1 instead of -3
or 1.
Professor Ben Polak: All
right, so this gentleman is
saying - Student: There's
no dominant strategy so -
Professor Ben Polak:
Right,
so this gentleman's saying,
a good reason for choosing
Alpha in this game is it's less
risky.
The worst case scenario is less
bad, is a way of saying it.
What about somebody who chose
Beta?
A lot of you chose Beta.
Let's have a show of hands on
the Beta's again.
Let me see the Beta's again.
So, raise your hands.
Can we get the woman here?
Can we ask her why she chose
Beta?
Student: Because if you
choose Alpha,
the best case scenario is you
get 0,
so that's - Professor Ben
Polak: Okay good,
that's a good counter argument.
So the gentleman here was
looking at the worst case
scenario, and the woman here was
looking at the best case
scenario.
And the best case scenario here
looks like getting a 1 here.
Now, let's ask a different
question.
Is one of the strategies
dominated in this game?
No, neither strategy is
dominated.
Let's just check.
If my pair chooses Alpha,
then my choosing Alpha yields
0, Beta -3: so Alpha would be
better.
But if my pair chooses Beta
then Alpha yields -1,
Beta yields 1:
in this case Beta would be
better.
So Alpha in this case is better
against Alpha,
and Beta is better against
Beta, but neither dominates each
other.
So here's a game where we just
change the payoffs.
We have the same basic
structure, the same outcomes,
but we imagine people cared
about different things and we
end up with a very different
answer.
In the first game,
it was kind of clear that we
should choose Alpha and here
it's not at all clear what we
can do--what we should do.
In fact, this kind of game has
a name and we'll revisit it
later on in the semester.
This kind of game is called a
"coordination problem."
We'll talk about coordination
problems later on.
The main lesson I want to get
out of this for today,
is a simpler lesson.
It's the lesson that payoffs
matter.
We change the payoffs,
we change what people cared
about, and we get a very
different game with a very
different outcome.
So the basic lesson is that
payoffs matter,
but let me say it a different
way.
So without giving away my age
too much--I guess it will
actually--when I was a kid
growing up in England,
there was this guy - there was
a pop star--a slightly post-punk
pop star called Joe Jackson,
who none of you would have
heard of, because you were all
about ten years old,
my fault.
And Joe Jackson had this song
which had the lyric,
something like,
you can't get what you want
unless you know what you
want.
As a statement of logic,
that's false.
It could be that what you want
just drops into your lap without
you knowing about it.
But as a statement of strategy,
it's a pretty good idea.
It's a good idea to try and
figure out what your goals
are--what you're trying to
achieve--before you go ahead and
analyze the game.
So payoffs matter.
Let's put it in his version.
"You can't get what you want,
till you know what you want."
Be honest, how many of you have
heard of Joe Jackson?
That makes me feel old,
oh man, okay.
Goes down every year.
So far we've looked at this
game as played by people who are
evil gits, and we've looked at
this game as played by people
who are indignant angels.
But we can do something more
interesting.
We can imagine playing this
game on a sort of mix and match.
For example,
imagine--this shouldn't be hard
for most of you--imagine that
you are an evil git,
but you know that the person
you're playing against is an
indignant angel.
So again, imagine that you know
you're an evil git,
but you know that the person
you're playing against or with,
is an indignant angel.
What should you do in that case?
What should we do?
Who thinks you should choose
Alpha in that case?
Let's pan the room again if we
can.
Keep your hands up so that you
can see.
Who thinks you should choose
Beta in that case?
Who's abstaining here?
Not allowed to abstain in this
class: it's a complete no-no.
Okay, we'll allow some
abstention in the first day but
not beyond today.
Let's have a look.
Let's analyze this combined
game.
So what does this game look
like?
It's an evil git versus an
indignant angel and we can put
the payoff matrix together by
combining the matrices we had
before.
So in this case,
this is me as always.
This is my pair,
the column player.
My payoffs are going to be what?
My payoffs are going to be
evil-git payoffs,
so they come from the matrix up
there.
So if someone will just help me
reading it off there.
That's a 0, a 3,a -1, and a 1.
My opponent or my partner's
payoffs come from the indignant
angel matrix.
So they come from here.
There's a 0,
a -3, a -1, and a 1.
Everyone see how I constructed
that?
So just to remind you again,
the first payoff is the row
player's payoff,
in this case the evil git.
And the second payoff is the
column player's payoff,
in this case the indignant
angel.
Now we've set it up as a
matrix, let's try again that
question I asked before.
Suppose you're the row player
here.
You're the evil git.
Those are your payoffs.
You're playing against an
indignant angel,
what would you do?
So once again,
no abstentions this time:
who would choose Alpha?
Let's have a show of hands
again, keep your hands up a
second.
Who would choose Beta?
Very few Beta's,
but mostly Alpha's.
Alpha, I think,
is the right answer here but
why?
Why is Alpha the right answer
here?
Yeah, can we get this guy here?
Student: It's the
dominant strategy.
Professor Ben Polak:
Good.
Actually nothing has changed
from the game we started with.
The fact that I changed the
other guy's payoffs didn't
matter here.
Alpha was dominant before--it
dominated Beta before--and it
still dominates Beta.
Let's just check.
If my opponent chooses Alpha
and I choose Alpha,
I get 0;
Beta, I get -1.
So Alpha would be better.
If my opponent chooses Beta and
I choose Alpha,
I get 3;
Beta, I get 1.
Once again Alpha is better.
So as before,
Alpha does better than Beta for
me, regardless of what the other
person does.
Alpha dominates Beta.
What was the first lesson of
the class?
Shout it out please.
Right, so you should all have
been choosing in this game,
you all should have chosen
Alpha.
So the one person who didn't
we'll let him off for today.
So Alpha dominates Beta here.
Let's flip things around.
Suppose now--harder to imagine,
but let's try it--suppose now
that you are an indignant angel
and you're playing against,
and you know this,
you're playing against an evil
git.
You're an indignant angel,
so you have the payoffs that
are still there and you're
playing against an evil git,
which is the payoffs we covered
up but we'll reproduce them.
Let's produce that matrix.
By the way, if this is
beginning to sound like a
wrestling match,
I don't mean it to.
Let's try here:
Alpha, Beta,
Alpha, Beta,
pair, me.
So my payoffs this time,
are the indignant angel
payoffs.
So mine are 0, -1, -3, and 1.
And my opponent's payoffs are
what would have been my payoffs
before.
They come from the other matrix.
Let's just show you it.
They come from this matrix.
So they're going to be 0,
-1,3, 1.
I took the second payoff from
that matrix and made it the
second payoff in this matrix.
Everyone see how I did that?
Once again, the row player is
the first payoff and the column
player is the other payoff.
What should you do in this case?
You're the indignant angel.
You're playing against this
evil git.
What should you do?
Write down on your notepad what
you should do.
Show it to your neighbor so you
can't cheat, or you can cheat
but you'll be shamed in front of
your neighbor.
Raise your hands.
Let Jude see it.
Raise your hands and keep them
up if you chose Alpha now.
How about if you chose Beta now?
So one or two Beta's,
mostly Alpha's.
Well let's see.
Let's reason this through a
second.
Does my Alpha dominate my Beta?
No, in fact,
Alpha doesn't dominate Beta for
me.
It doesn't dominate Beta.
If my pair chooses Alpha then
Alpha gets me 0;
Beta -3.
So Alpha does better.
But if my pair chooses Beta,
then Alpha gets me -1;
Beta gets me 1.
In this case Beta is better.
As we saw before,
Alpha is better against Alpha.
Beta is better against Beta.
There's no dominance going on
here.
Nevertheless,
at least 90% of you chose Alpha
here, and that's the right
answer.
Why?
Why should you choose Alpha
here?
Somebody …
can we get the guy with the
beard here?
Wait for the mike, great.
Student: We had
acknowledged that Alpha is a
dominant strategy for my
opponent so we must choose based
upon,
or knowing that my partner is
going to choose Alpha.
Professor Ben Polak:
Good, and your name is?
Student: Henry.
Professor Ben Polak:
Henry.
So Henry is saying sure I don't
have a dominated strategy.
My Alpha doesn't dominate my
Beta.
But look at my opponent.
My opponent's Alpha dominates
her Beta.
If I choose Alpha and she
chooses Alpha to get 0;
Beta she gets -1.
Alpha is better.
If I choose Beta,
if she chooses Alpha she gets
3;
Beta 1.
Again Alpha is better.
For my opponent,
Alpha dominates Beta.
So by thinking about my
opponent, by putting myself in
my opponent's shoes,
I realize that she has a
dominant strategy,
Alpha.
She's going to choose Alpha and
my best response against Alpha
is to choose Alpha myself.
So here, this time,
my Alpha does not dominate Beta
but my pair's choice of Alpha
dominates her choice,
her possible choice of Beta.
So she will choose Alpha.
And once I know that she's
going to choose Alpha,
it's clear that I should choose
Alpha and get 0 rather than Beta
and get -3.
So I should choose Alpha also.
Okay, so now we've seen four
different combinations.
We've seen a case where an evil
git was playing an evil git;
where an indignant angel was
playing an indignant angel;
and we've seen both the flips
of those: the evil git versus
the indignant angel;
and the indignant angel against
the evil git.
Why are we doing this?
Because there's an important
lesson here.
What's the lesson here?
The lesson is--comes from this
game--that a great way to
analyze games,
a great way to get used to the
idea of strategic thinking,
perhaps even the essence of
strategic thinking,
is the ability to put yourself
in someone else's shoes,
figure out what their payoffs
are, and try and figure out what
they're going to do.
So the big lesson of this game
is--I forgot what number we're
up too--I guess this is Lesson 4
I think.
Lesson 4 is:
put yourself in others' shoes
and try to figure out what they
will do.
In a sense, this is the first
difficult lesson of the class.
It's easy to spot when a
strategy is dominant,
more or less.
It's pretty easy to figure out,
you have to know about your own
payoffs.
But the hard thing in life,
is getting you to come out of
your own selves a bit,
realizing it's "not all about
you."
You've got to put yourself in
other people's shoes to figure
out what they care about and
what they're going to try and
do,
so you can respond well to that.
While we're here,
let's just mention that things
will get more complicated in a
world where I don't actually
know the payoffs of my opponent.
It's much easier to figure out
my own payoffs than to figure
out my opponent's payoffs.
I might not know whether I'm
playing someone who's an evil
git or an indignant angel.
So I'm going to have to figure
out what the odds are of that in
doing this exercise.
And we're going to come back to
that idea too way at the end of
the class, but that's getting a
bit ahead of ourselves,
but we'll get there.
Now, it turns out that this
game, this Prisoner's Dilemma,
with the Alpha's and Beta's,
or essentially the same game,
has been played many,
many, many times in
experiments.
So out there in the real
world--I think we can do this
here--out there in the real
world when they do these
experiments,
they find out that roughly 70%
of people choose Alpha and
roughly 30% choose Beta.
Roughly, almost a third choose
Beta.
What do we think is going on?
That's a third of the people
who seem to be choosing a
dominated strategy …
or is it?
What's going on there?
Why do you think 30% of people
are choosing Beta?
Anybody?
Can we catch this guy here?
Student: They might be
motivated by the fact that every
person who chooses Beta raises
the average score.
Professor Ben Polak:
They could be moral people.
So one possibility is:
this 30% of people in the real
world who choose Beta are just
nice people.
What else could it be?
Yeah?
Student: I know this
might be changing the game a
little bit, but if you ever
expected to play the same game
with the partner you have more
[inaudible]
Professor Ben Polak: All
right,
they could be thinking they're
going to play again.
Student: [inaudible]
long run payoffs are greater if
you choose Beta every time.
Professor Ben Polak: So
it could be that they think that
this is actually--they haven't
understood the experiment and
they think this is a multi shot
game,
not a one shot game, good.
What else could it be?
What's the simplest explanation?
What's the other obvious
explanation?
They could just be stupid,
right?
It could be.,
Are we allowed to say that in
class?
Let's be honest here,
when we say experiments in the
real world in Game Theory--or
the ones you read about in The
New York Times--the real world
when it comes to experiments in
Economics really means
undergraduates at the University
of Arizona.
I mean, I'm not making it up.
It just does.
They all are.
I don't know anything about
… are any of you from
Arizona, I don't know.
I don't know whether the
average undergrad at the
University of Arizona just has a
sunny personality or whether
they "spent too long in the
sun."
I just don't know which it is,
right?
We can't really distinguish
from this.
How about at Yale.
What's our numbers here.
How about in this class?
Do you want to mike your
colleague here?
So 238 at Yale--this is
Yale--versus 36.
So even at my level of
arithmetic that's a lot less
than 30%.
That's more like less than 15%.
It's about 15% I guess.
So 236--I'm sorry 238--chose
Alpha, and 36 chose Beta.
Now there's one more lesson in
this class and this is going to
be it.
This isn't the end of the class
but one more lesson to take
home.
You guys are going to be
playing games among each other
today and until--whatever it
is?--December 7,
whatever is the end of term.
Look around each other.
You better get to know each
other a bit.
And what did we learn today
about you guys?
The lesson here,
Lesson 5, is "Yale students are
evil." Be aware of that
when you're playing games.
I want to play one more game
today in the remaining minutes.
It doesn't matter if we finish
a little bit early,
but I want to try to get this
game at least started.
So do you all have Game #2 in
front of you?
Just while you're reading that
over, can I also make sure
you've all got your legal forms
and you're going to sign.
Don't walk away with your legal
forms, we need to get those
collected in.
So at the end of talking about
this game, I'm going to collect
in both the second game for the
class and also the legal form.
If you don't have a legal form,
if you've lost it or something,
it's online.
Let's have a look at that
second game.
I'll read it out for you.
Game 2: "pick a number."
Everyone got this?
Anyone not got this?
Everyone got it?
Good.
"Without showing your neighbor
what you're doing,
put in the box below a whole
number between 1 and a 100
[whole number between 1 and
100--integer.]
We will calculate the average
number chosen in the class.
The winner in this game is the
person whose number is closest
to two-thirds times the average
in the class."
[Again: the winner is the
person whose number is closest
to two-thirds times the average
number in the class.]
The winner will win $5 minus
the difference in pennies
between her choice and that
two-thirds of the average."
Just to make sure you've
understood this,
let me do an example on the
board.
I've got one more board;
that's good.
So imagine there were three
people in the class,
and imagine that they chose
25,5, and 60.
So 25 plus 5 plus 60 is 90.
People should feel free to
correct my arithmetic because
it's often wrong;
90 right?
Two-thirds of 90,
whoops, what do I need,
start again.
I need to divide it by three to
get the average.
So the average is 30.
So the total is 90,
the average is 30,
am I right so far?
So two-thirds of the average is
20.
I'm looking desperately at the
T.A.
Is that right?
Okay, so the average is 30 and
two-thirds of the average is 20.
So who's the winner here,
which number would have won
here?
25 would have won.
25 would have been the closest,
and what would they have won?
They would have won five bucks
minus five cents for a total of
four ninety-five.
Now to make this interesting,
let's play this for real.
So this of course relies on me
having brought some money and
we'll have to do this without
dislodging the microphone.
So I'm going to see if I
have… sorry about that.
I'm going to see if I have
enough money to do this in class
for real.
When we played this game in the
old days, during the dot com
boom with the MBA students,
you had to put fifty dollars on
the table to get them
interested.
Graduate students:
five cents will do it.
Okay, so this is a--there's
some bloke with a beard on this
one.
Yeah this is Lincoln apparently.
Who knew, Lincoln?
Okay, so this is a five-dollar
note and I'm going to put
it--sorry about that again--I'm
going to put it in an envelope.
I'm not cheating anybody?
No magic tricks here.
And this is going to be the
prize for this game and we
better give this to someone we
trust.
It's the prize for 159.Who do
you guys trust?
The camera guy.
Okay Jude: we know Jude's going
to be there next week.
I'm giving it to Jude.
You can't see this on
camera.--people at home--but I'm
giving it to Jude okay.
I'm going to put it here,
and Jude has to show up next
week with the prize.
I thought we should give it to
the guy at the back,
who is the moral guy.
Who is our moral guy at the
back?
Well never mind,
we will give it to Jude.
We know Jude's going to be here.
All right, has everyone put a
number down?
Any questions?
Just shout them out to me.
Student: So given that
we only have one five dollar
bill does there have to be one
unique winner,
and if so, how is that
determined if we have multiple
people who are - Professor
Ben Polak: That's a good
question.
If there's multiple winners,
we'll divide it but we'll make
sure everyone has a positive
winning.
Good question.
Given the number of people in
the room there may be multiple
winners, I accept that
possibility.
Has everyone written down a
number now?
All right, so hand your numbers
to the end of the row,
but don't go yet.
Hand it on to the end of the
row.
Before you go I want five
things from you.
I want to know the five lessons
from this class.
Tell me what you learnt?
What were the five lessons?
Without looking at your notes,
what were the five lessons?
Anybody, shout out one of the
lessons, yes madam.
Student: Don't play a
strictly dominated strategy.
Professor Ben Polak:
Don't play a strictly dominated
strategy, anything else?
Yes sir.
Student: Yale students
are evil.
Professor Ben Polak:
Yale students are evil.
Two lessons down, three to go.
The guy over here.
Student: Rational
choices can lead to bad
outcomes.
Professor Ben Polak:
Rational choices can lead to bad
outcomes.
We put it more graphically
before but that's fine.
Two more outcomes.
Student: Put yourself in
other people's shoes.
Professor Ben Polak: Put
yourself in other people's shoes
and I'm missing one,
I can't recall which one I'm
missing now.
Student: You can't get
what you want so you -
Professor Ben Polak: You
can't get what you want.
You could but it's a good idea
to figure out what you want
before you try and get what you
want.
Five things you learnt today,
hand in your numbers and the
legal forms and I'll see you on
Monday.
