Original subtitles

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?

Uh 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 one and game two. Can I get you all

to look at game one and start thinking

about it? And while you're thinking

about it, I'm hoping you can multitask a

bit. I want 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 some of you are not looking at it cuz

they're using it as a fan here. All

right, so you look look at game one 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

what is game theory?

Game theory is a method of studying

strategic situations. Okay, so what's a

strategic situation? Well, let's start

off with what's not a strategic

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. Right? Firms in perfect

competition are price takers. They don't

particularly have to worry about the

actions of their competitors.

Right? 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. Right? Is

this looking familiar for some of you

who can remember doing 115 last year or

maybe 2 years ago for some of you?

All right. Everything in between is

strategic. So, everything that

constitutes imperfect competition is a

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 but for

for the moment at least what Chrysler is

doing, but perhaps not for long. All

right? Right? So, there's a small number

of firms, their actions affect each

other.

All right. So, for a literal definition

of what strategic means, it's a setting

where the outcomes that 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 it to to what where this applies. So,

obviously it 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

to check with the DUS in political

science.

Right? It count it

Game theory is very important in law

these days. So, for those of you for the

half of you who 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 is

applies to sport.

All right.

So, let's talk about a bit bit of admin.

How are you doing on the filling out

those games? Everyone managed to

multitask? Bringing in game one. 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 you some of you probably

know,

Yale is undergoing a

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 US

or places miles away, maybe in in in

Timbuktu, whatever, who find it

difficult to get educational materials

uh

from a local university or whatever, can

watch certain lectures from Yale on the

web.

All right. Some of you have been in

classes that do that before. What's

going to be different about this class

is that you're going to be participating

in it. Right? 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 among the class, and

you're going to be learning from each

other.

Right? 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 very least on mic.

All right. So, how's that going to work?

Around the room are three TAs holding

mics. Let me just 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 TAs go to

you with a microphone much like in you

know Donahue or something. Okay?

All right. And 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 cuz I really feel that

this class isn't about me. I'm I'm part

of the class, obviously, but it's about

you teaching each other and and

participating.

All right. 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 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.

Right? For those of you who are on the

run from the FBI, your visa's run out,

or you're sitting next to your

ex-girlfriend, you know, 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. Will you all wave

to Jude? This is Jude. Wave. Right.

Right. Okay? Okay? And Wes is our audio

guy. This is Wes. Right? 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.

All right. If this is making you

nervous, if it's any consolation, it's

making me very nervous. Okay? So,

All right. We'll try and make this class

work as smoothly as we can allowing for

this extra thing. And let me say, no

one's making any money off this. At

least I'm I'm hoping these guys are

being paid, but me and the TAs are not

being paid. This is a

The aim of this is I think it's a good

aim. It's an educational project, and

I'm hoping you'll help us with it. All

right. The one difference this is going

to mean is that at times I might hold

some of the discussions with the class

coming down into this part of the

of the of the room here to make it a

little easier for Jude.

All right. How are we doing now on

filling out this form? So, has everyone

filled in their strategy for the first

game?

Not yet. Okay, so 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 midterm, and 40% on the final. So,

30 30 40. The midterm will be held in

class on October 17th. That is also in

your syllabus. Don't Please don't

anybody tell me late anytime after today

you didn't know when the midterm was and

that you thought you it clashes with 17

different things. The midterm is on

October 17th, which is a Wednesday, in

class.

All right. The problem sets. There will

be

uh roughly 10 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 10 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 minus, a

sixth are going to end up with B plus, a

sixth are going to end up with B, a

sixth are going to end up with B minus,

and the remaining sixth, if I've added

that up right, are going to end up with

what I guess we're now calling the

presidential grade. Is that right?

Right? That's not literally true. I'm

going to squeeze the bit. I'm going to

curve it a bit. So, actually a slightly

fewer than a sixth will get straight A's

and fewer than a sixth will get you C's

and below. We'll squeeze the middle to

make the 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 plus. The

median will hit fall somewhere in the B

pluses.

All right. Now, just as a forewarning

for people who have forgotten what a

median is, that means half of you, not

not approximately half, it means exactly

half of you will be getting something

like B plus and below and half of you

will get something like B plus and

above.

Okay.

Now, how are you doing on filling in the

forms? Has everyone filled it in yet?

Surely it 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, Dixit'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. All right.

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 the

class. Right? But I will wouldn't I will

not be following these books religiously

at all. In fact, they're just there as

backup. 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.

This 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 advanced copies of it.

So, if you don't buy this book this

week, I may be able to make the advanced

copy of the new edition available for

some of you next week.

Uh I'm not taking a cut of that, either.

Right? There's no there's no money

changing hands there.

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 in 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. We're done with the forms?

All right. So, why don't we send the TAs

with or without mics up and down the

aisles and collect in your game number

one. Not not game number two, just game

number one.

Just when 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.

All right? So, I

I'm hoping that's what the reputation of

the class is. All right? So, you

shouldn't If you think this class is

going to be 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

Quiet down, folks. The nice 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.

You got all these things in? Everyone

hand them in?

So, I need to get those counted. Has

anyone taken the Yale accounting class?

No one wants to No one aspirations to be

One person has I'll I'll have a TA do

it. It's all right. We'll have a TA do

it. So, uh

Kai, can you count those for me? Is that

right?

Let me read out the game you've just

played.

Game one, a simple grade scheme for the

class.

Read the following carefully without

showing your neighbor what you are

doing. Put 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

your pair puts 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

minus. If you put beta and your pair

puts alpha, you'll get a C and your pair

an an A. And if you and your pair both

put beta, then you'll both get B plus.

All right? 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.

All right. We'll discuss this in a

second.

But, why don't we actually record what

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.

Okay? 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 in the columns, alpha and beta, the

choices my pair is making. And in this

table, I'm going to put my grades.

All right? So, my grades if I If we both

put alpha,

it's B minus. If we both put beta,

it was B plus. 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? Is that more or less

right?

Yep.

Okay. And while we're here, why don't we

do the same for my pair?

All right? So, this is my grades in the

left-hand table,

but now

let's look

at what my pair would do, what my pair

would get.

So, I should warn people sitting at the

back

that my handwriting is pretty bad.

That's one reason for moving forward.

The other thing I should apologize for

this 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.

All right. So, once again, if we both

put alpha, then my pair gets a B minus.

If we both put beta, then we both get a

B plus, or we say my pair gets a B plus.

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.

All right? So, I now have all the

information that was on the sheet of

paper that you just handed in.

All right?

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 than drawing two

different tables like this, what I'm

going to do is I'm going to take the

second table

and superimpose 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.

We both get B minus if we both choose

alpha.

We both get B plus

if we both choose beta.

All right? 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.

All right? So, notice what I did here.

The first grade corresponds to the row

player,

me in this case, and the second grade

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. All

right? And this is an outcome matrix.

This tells us everything that was in the

game.

It's an outcome matrix.

All right?

Okay. So, now seems a good time to start

talking about what people did. So,

uh let's just have a show of hands. How

many of you

uh chose alpha?

All right. Leave your hands up so that

you can catch that. So, just so people

can see at home, okay?

All right? And how many of you chose

beta?

That's far more

Be Be Wave your hands if you're okay.

All right. There's a beta here, okay?

So, a lot It looks like a lot of Well,

we're going to find out. We're going to

count, but a lot more alphas than betas.

Let me try and find out some reasons why

people chose. So, let me have the alphas

up again.

Uh so, uh the woman who's in red here,

uh can we get a mic to the Yeah.

Okay, we asked you Are you You're not on

the run from the FBI. We can ask you

what why you Okay. So, you chose alpha,

right? So, why did you choose alpha?

I then realized that my partner is going

to choose alpha, therefore

All right. So, so you wrote out the

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 can we can we

get the the woman in here?

Try not to be intimidated by these

microphones. They're just mics.

It's okay. Yeah. Yeah. Um

I think you're right that if I chose

alpha,

regardless of what my partner chose, I

think there would be better um outcomes

than choosing

All right. So, so let me see names a

second. So, your name was Courtney.

Courtney, and your name was Clara

Louise. Clara Louise. So, slightly

different reasons, same choice, alpha.

Clara Louise's reason

for the Clara Louise. So, she said, no

matter what the other person does, she

reckons she'd get a get a better grade

if she chose alpha. So, hold that

thought a second. We'll come back to Is

it Clara Clara Louise? Is that right?

We'll come back to Clara Louise in a

second. Let's talk to the betas a

second. Let me just emphasize at this

stage, there are no wrong answers. Later

on the class, there will be some

questions which have wrong answers.

Right now, there's no wrong answers. All

right. There may be bad reasons, but

there's no wrong answer. So, let's have

the betas up again. Let's let's see the

betas.

Oh, come on. There was There was a beta

right here. You were You were a beta,

right? Uh you've backed off the beta.

Okay.

So, how can I get a mic into a beta?

Let's let's stick in this aisle a bit.

Is that a beta right there? Are you Are

you a beta right there? There was There

was a beta Can Can I get the beta in

here? Who's the beta in here? Can we get

a Can we get the mic in there? Is that

possible? In here? Leave your hand up so

There we go. There we go. Just point

towards That's fine. That's fine. Just

just just just speak into it. That's

fine.

So, the reason I Yeah. Go ahead.

I personally don't like swings that

much, and it's the B minus B plus range,

so I'd much rather

prefer that to a swing from A to C.

All right. So, you're saying You're

saying it it compresses the range. I

don't know if it does compress the

range. I mean I mean, if you chose uh

alpha, uh you're swinging from A to B

minus, swinging from B You're choosing

from B plus to C. I mean, there's a

similar kind of ranges, but it's it's

it's it's certainly reasons. Other

reasons for choosing

Yeah, the the guy in blue here. Yep.

Yep. Here. Good.

Let's say just Don't hold the mic. Just

let it point at you. It's fine. Uh well,

I guess I thought we could be more

collusive and kind of work together, but

I guess not. Um

So, uh I chose beta.

Is it Is it kind of background, so I

missed the answer. Just Stand up and

then we just hear you. Yep. Sorry, did

you say again?

Sure. My name's Travis. Uh

I thought we could work together, but I

guess not. All right. All right. Good.

Good. Good.

chosen beta, we would all get B pluses,

but

I guess not. Good. So, so Travis is

giving us a different reason, right?

He's saying He's saying that maybe maybe

some of you in the room might actually

care about each other's grades, right? I

mean, you all know each other. You're in

class. You all go to the same college.

Uh for example, if we

if we played this game up in up in the

business school

Any MBA students here today? One or two,

right? We We played this game up in the

business school, I think it's quite

likely we're going to get a lot of

alphas chosen, right? But, if we played

this game up in let's say the divinity

school,

All right?

And I'm guessing that I'm guessing that

Travis's answer is reflecting what you

you guys are using here. If you played

in the divinity school, you might think

that people in 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 that's that's the the reason to

focus on. And perhaps the the lesson I

want to draw out of this is that right

now, this is not a game. Right now, we

have actions, strategies we want 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?

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, until we know

what the payoffs are. And let's let's

just say something now which I'll

probably forget to say at any other any

other moment of the class, but today

it's relevant. Right? Game theory, me

y- professors at Yale cannot tell you

what your payoffs should be. They should

not

We can't I can't tell you in a useful

way what it is that you your goals in

life should be or whatever.

Right? That's not what game theory is

about. However, once we know what your

payoffs are, once we know what your

goals are, perhaps we can game theory

can help you get there.

All right?

So, we've had two different kind of

payoffs mentioned here. We've had the

kind of payoff where we care about our

own grade, and Travis has mentioned the

kind of payoff when 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.

So, 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 we'll

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 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.

Right? They they represent what this

what these people are trying to

maximize, what they're trying to

achieve, their goals.

All right? And the idea is to just to be

just to compare this to the outcome

matrix is

for the person who's me here, AC yields

a payoff

of uh it's AC is this box. So, AC yields

a payoff of three, whereas

B minus

B minus

yields a payoff

of zero, and so on.

All right?

So, what's the interpretation?

This is the first interpretation which

the the 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 plus, they prefer a B plus to a B

minus, and they prefer a B minus to a C.

Right? I'm hoping I got the the grades

in order, otherwise it's going to ruin

my curve at the end of the year. All

right? All right? 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?

But in English, I think we'd refer to

these guys, whether it's technical or or

not, as evil gets.

I mean, these are not these are not

perhaps the most moral people in the

universe.

All right?

So, now we can ask a different question.

Suppose, whether these are actually your

payoffs or not, pretend they are for

now.

All right? Suppose these are your

payoffs. Now we can ask not what did you

do, but what should you do? Now we have

payoffs, I can really switch the

question to a normative question, what

should you do? And let's come back to

uh

uh to to Clarice. Where was Clarice

before? Let's get the mic on you again.

So, just explain what you did and why

again.

Why I chose alpha? Yeah, stand stand up

a second. Okay. If that's okay.

Right? You You chose alpha, and I'm

assuming these were roughly your

payoffs, more or less, right? You were

caring about your grades. Yeah, I was.

you choose alpha?

Um I'm sorry? Why did you choose alpha?

Just just repeat what you said before.

Like Because I thought the payoffs

the two um different payoffs that I

could have gotten were highest if I

chose alpha. Good. Good. So, what

Clarice is saying, and 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 zero.

If the pair chooses alpha and she chose

beta, she gets minus one. Zero is bigger

than minus one.

All right? If the pair chooses beta,

then if she chooses alpha, she gets

three, beta she gets one, and three is

bigger than one. So, in both cases, no

matter what the other person does, she

receives a higher payoff from choosing

alpha, so she should choose alpha.

Right? Everyone follow that that line of

reasoning? That's a stronger line of

reasoning than the reasoning we had

earlier. So, the one I've now

immediately forgotten the name of in the

red shirt,

uh

whose name was

Courtney. So, Courtney also gave a

reason for choosing alpha, and that was

a perfectly good reason for choosing

alpha, nothing wrong with it, but notice

that this reason is a stronger reason.

It kind of implies your reason. All

right?

All right? 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

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.

Regardless of what others do. So, let me

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. All right? But a few bits of

jargon are going to be helpful in in

allowing the conversation to move

forward, and this is certainly one. Evil

gets is maybe one, too, but this is

certainly one.

All right?

Let's draw out some lessons from this.

And actually, so so you can still read

that, let me bring down and clean this

board.

So, the first lesson of the class, and

there's going to be lots of lessons,

is a lesson that emerges immediately

from the definition

of a domin-

of a dominated strategy,

and it's this.

So, lesson one of the course is

do

not

play

a

strictly

dominated

strategy.

All right? So, I with apologies to

Strunk and White, this is in the passive

form, okay? This dominated.

Passive voice. Do not play a strictly

dominated strategy.

Why?

Someone want to tell me why?

Yeah, Ali, do you want to get this guy?

Yeah, yeah. Stand up. Yep. Is this

right?

Yeah?

Because

because everyone's going to pick the the

dominant outcome, and then everyone's

going to get the worst result, the

collectively worst result. I'm not sure

that's

Yeah, that's a possible answer. I'm

looking for something more direct here.

So, we we 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 let's Can we get the the

woman there?

You'll always lose. Well, I don't know.

It's not about winning and losing. What

else could we have? Can we get this this

guy in the pink down here?

The payoffs are lower. The payoffs are

lower. Okay. So, so here's a here's an

abbreviated version of that. I mean,

that's perhaps a little bit

That's not an abbreviation, it's longer.

The reason I don't want to play a

strictly dominated strategy is by if

instead I play the strategy that

dominates it,

I do better in every case.

All right? 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.

All right?

Now, that's a pretty convincing

argument. That sounds like a convincing

argument. It sounds like too obvious

even to worth be worth stating in class.

All right? So, let me now try and shake

your faith a little bit in this in this

answer.

All right? Is somebody 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 If we, me and my

pair, both reason this way and choose

alpha, then we'll both get zero."

But if we both reasoned a different way

and chose beta, then we'll both get one.

So, I should choose beta. One's bigger

than zero. I should choose beta.

What's wrong with that argument?

That argument must be wrong cuz it goes

against the lessons of the class, and

the lessons of the class are gospel,

right? They're not wrong ever. So,

what's wrong with that argument? What's

wrong with that argument?

Let's go just just just Yeah. Yeah.

Yeah. Good.

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. All right. So,

it involves some notion of agreeing. 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

What's it called? The X-Men. Is that

what it's called? X-Men, right? Right?

Now, in fact, this may come as a

surprise to you, I'm not I don't have

ESP and I'm not a character out of the

X-Men, and so you can't actually see

brain waves emanating from my head, and

my reasoning doesn't affect your

reasoning. Right? So, if I did reason

that way and chose beta, I'm not going

to affect your choice one way or the

other.

Right? That's the first thing that's

wrong with that reasoning. What else is

wrong with that reasoning?

Yeah, that guy down here.

Yeah?

Well, the second that you choose beta,

then someone's going It's in someone's

best interest to take advantage of you.

All right. Someone's going to take

advantage of me, but even more than

that, even stronger argument than that.

That's true, but even a stronger

argument. Well, how about this? Even if

I could Even if I was that guy in the

X-Men or the Matrix, whoever 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 cuz that way I end up getting

three.

All right. So, it it There's two things

wrong with the argument. One, there's

this magical reasoning aspect that I'm

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 to choose

alpha.

All right.

So,

nevertheless, there's an element of

truth in what I just said. It's It's the

fact there's an element of truth in it

that makes it very,

you know, it seems like a good a good

argument. The element of truth is this.

It is true that by both choosing alpha,

we both ended up with B minuses. We both

ended up with payoffs of zero

rather than payoffs of one.

Right? 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.

All right? And that's probably the

second lesson of the class.

So, lesson two,

and this lesson probably wouldn't be

worth stating if it wasn't for sort of a

century of thought in 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 uh what Americans call it that that

that suck. That suck.

All right?

If you want a more technical term for

that, and you remember this from from

Economics 115, it can lead to outcomes

that are inefficient, that are Pareto

inefficient. But suck will do for today.

Right? Rational choice by rational

players can lead to bad outcomes.

Okay?

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?

It's called prisoner's dilemma. How many

of you've heard of the prisoner's

dilemma before? Most of you heard in

115. Why is it called the prisoner's

dilemma?

Yeah, so the guy here in in in orange.

Uh

It's okay. Let's just just You can just

point to you. It's fine. I think it's

whether or not the prisoners cooperate

in

the 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. Good. 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 2 years. But if you

rat the other guy out and he doesn't rat

you out, then you'll go home free and

he'll go to jail for 5 years.

And you put that all down, you pretty

quickly see that regardless of whether

the other guy rats you out or not,

you're better off ratting him out.

All right? Now, if you haven't ever seen

that prisoner's dilemma, uh you can see

it uh

pretty much every night uh on a show

called Law & Order. How many of you have

seen Law & Order?

Right? 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 This This happens in every single

episode. So much so that if any of you

actually I mean, this may not be true at

Yale. If any of you or the TV guys, for

that matter. If any of you know the guy

who writes the plots for this, have him

come to the class, or I guess see the

video now, and we can get some better

plot lines in there. Right?

All right. But it's Of course, that's

not the only example. The grade game and

this is not the other only example.

There are lots of examples of prisoner's

dilemmas out there. Let's try and find

some other ones.

All right? So, how many of you have

roommates in your in your college? How

many of you have roommates?

Most of you have roommates, right?

Right? So, I'm guessing now, but I won't

make you show your hands cuz 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?

Right? 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.

All right? Why is this Why is it

disgusting?

Why is it disgusting? It's disgusting

cuz people don't tidy up, right? 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? 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, cuz 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?

Right? 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.

All right? Right? So, there are lots of

prisoner's dilemmas out there. Anyone

got any Any other examples?

Other examples?

I didn't quite hear that. Sorry. It's

going to get a mic on it so we can

really hear it.

The The hiring a lawyer and not paying

him a lot of money.

Uh And do And do Okay. And divorce And

divorce struggles. Okay. Okay. Yes.

Okay. You're too young to worry about

such things, but never mind.

Never mind. Yeah. Okay, that's a good

example. Okay. All right. Hiring lawyers

and getting bringing in big guns.

What about an economics example?

What about firms who are competing in

prices? Right? Both firms have an

incentive to undercut the other firm,

driving down profits for both. Right?

The last thing you want is to have the

other firm undercut you. And that tends

to push prices down. That's good for us

the consumers, but bad for the firms,

bad for industry profit.

What remedies do we see? We 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 we see?

Let me try and get get the the guy here

in right right in front of you.

Collusion.

Yeah, go ahead. Collusion. Collusion.

Okay, so firms can collude. All right?

So, uh what what prevents them from

colluding?

What prevents them from colluding?

So, 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 pricey lawyer who's taking his day

off from the divorce court, and that

would secure that they wouldn't lower

their prices on each other. Is that

right?

Right?

So, why wouldn't that work?

Why wouldn't writing a contract here

work?

Right? It's against the law, right? It's

an illegal contract. It's an illegal

contract. All right? What about you with

your roommates? How many of you have a

have a written contract stuck with a

magnet on the fridge telling you you're

supposed to when you're supposed to tidy

up?

Very few of you, right? Why Why do you

manage to get some cooperation between

you and your roommates even without a

even without a written contract? It's

not legally enforceable.

Well, it probably is legally

enforceable, actually. This case is not

It probably is legally enforceable. You

probably could have a written contract

about tidying up.

Yeah, the the the the the woman in the

in here. Yeah. Repetition. You do it

over and over. Yeah, so maybe Maybe even

among your roommates, maybe you don't

need a contract because you can manage

to achieve the same end 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 may allow you to obtain

cooperation, but we're not going to come

back to that till after the midterm.

That's way down the road, but we'll get

there.

All right? Now, one person earlier on

had mentioned something about

communication. I think it was the one in

the front, right? So,

let's just think about this a second. Is

communication the problem here? Is the

Is the reason people behave badly in

this Oh, badly. People choose alpha in

this game here? Is it the fact that they

can't communicate?

Suppose Suppose you Suppose you'd been

able to talk beforehand. So, suppose the

woman here whose name was

Mary had been able to talk to the person

next to her whose name is

Erica, and they'd said, you know,

"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?

Yeah.

There's no enforcement.

enforcement, all right? So, it isn't a

failure of communication per se. Right?

A contract is more than communication. A

contract is communication with teeth.

Right? It actually changes the payoffs.

So, I could communicate with Alice some

agreement, but back home I'm going to go

and go ahead and choose alpha. Anyway,

all the better if he's choosing beta.

All right. 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

to two we forgot there. So, the

collusion case and the case back in Law

& Order with the with the prisoners in

the cell. How do they enforce their

contracts? And 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?

Yeah. They trust each other.

It could be they trust each other.

Although, if you trust a crook, that's

not What What else could it be? Yeah,

the guy the guy here again with the with

the beard, yeah.

It's a zero-sum game. Well, but this is

the game, right? So, here's the game.

So, we're going but the the way they

value the way they value each other.

So, the payoffs may be different. They

may have been different. I have

something simpler in mind. How Suppose

they have a written contract or even an

unwritten contract. What enforces the

contract for colluding firms or crooks

in jail?

Yeah? Even if the crook gets out

scot-free, in 5 years when the other guy

gets out, he might run into a situation.

Yeah. Yeah. So, 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. All right?

All right? 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 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.

All right. 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, let's know I 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 some people

who have more morality than my friends

up in the business school.

I'm going to ask for the same grade game

we played at the at the beginning, what

would happen if players' payoffs looked

different?

So, these are possible payoffs, too.

All right? And I'll give these a name.

We called the other guys evil gets. So,

we'll get we'll call these guys

indignant

angels. I can never spell indignant. Is

that roughly right?

That look right? I think it's right.

Indignant, isn't it? Indignant. All

right. Indignant angels. 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. All right? But this

time, the payoffs are as follows. On the

lead diagonal, we still have zero zero

and one one, but now the grades here are

minus one and

they're sorry, the payoffs are minus one

and minus three, and here they're minus

three and minus one. And what's the idea

here? These aren't the only other

possible payoffs. This is just an idea.

Suppose I get an A and my pair gets a C,

then sure, I get that initial payoff of

three, but unfortunately, I can't sleep

at night I'm feeling so guilty. Right? I

have some I have some kind of moral

conscience, and after I subtracted off

my guilt feelings, I end up at minus

one.

So, think of this as guilt.

Some notion of morality.

All right?

Conversely, if I choose 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. All right?

So, that moral indignation takes us down

to minus three.

All right? So, again, I'm not I'm not

claiming these are the only other

possible payoffs, but just another

possibility to look at.

Okay. So, suppose these were the payoffs

in the game.

All right? 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.

All right? And 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.

Not all writing. The guy in the England

shirt isn't writing. You got to be

writing if you're 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?

You're not allowed to abstain. Let's try

it again. Alpha alpha in this case. No

abstentions here.

Beta in this case?

So, we're roughly splitting the room.

Roughly splitting the room. Uh someone

who chose alpha. Can you raise the

alphas again?

Uh let me get this guy here. Ali, can we

get this guy here? So, what why did you

choose alpha?

Uh you would minimize your losses. You'd

get zero or negative one instead of

negative three or one.

All right. So, so this gentleman is

saying

strategy, so Right. So, this this this

gentleman is saying a good reason for

choosing alpha in this game is it's it's

less risky. Right? The worst-case

scenario is less bad. That's what he's

saying. All right? What about somebody

who chose beta? A lot of you chose beta.

Let's have a Let's have a show of hands

on the betas again.

Let me see the betas again. So,

raise your hands. Raise your hands.

Can we get Yeah, can we get the woman

here?

Can we ask her why she chose beta?

Um because if you choose alpha, the

best-case scenario is you get zero.

Good. Okay. So, that's a that's a good

counterargument. 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 one

here.

All right? 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 zero, beta

minus three, so alpha would be better.

But if my pair chooses beta, then alpha

yields minus one, beta yields one. In

this case, beta would be better. Right?

So, alpha in this case is better against

alpha, and beta is better against beta,

but neither dominate each other.

All right? So, here's a game where it's

We just changed the payoffs. We have the

same basic structure, the same outcomes,

but we imagined 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. Right? In fact, this kind of

game has a name, and we'll revisit it

later on this semester. This kind of

game is called

a coordination problem.

And we'll talk about coordination

problems later on.

But the main lesson I want to get out of

this for today is a simple lesson. It's

the lesson that payoffs matter.

Right? We changed the payoffs. We

changed what people cared about, and we

get a very different game with a very

different outcome.

All right? So, there's a the basic

lesson is

that payoffs matter. But let me say it a

different way. Without giving away my

age too much, well, I guess I will

actually. When I was a kid growing up in

England, there was this guy there's a

there was a pop star and slightly

post-punk pop star called Joe Jackson,

who none of you will have heard of

because you're all about 10 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."

Right? You can't get you can't get what

you want unless you know you know what

you want. And as a statement of logic,

that's false.

Right? It could be that what you want

just drops into your lap without you

knowing about it. All right? 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.

All right?

So, payoffs matter.

Well, 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've heard of

Joe Jackson?

Oh, it makes me feel old. Oh, man. Okay.

It goes down every year.

All right. So, so far, we've looked at

this game as played by people who are

evil gets.

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 get,

but you know that the person you're

playing against is an indignant angel.

Right? So, again, imagine that you know

you're an evil get, 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 you do in that case?

Who thinks you should choose alpha in

that case? Let's have pan the room

again. We can. Keep your hands up so so

that you can see you.

All right.

Who thinks he should choose alpha Who

thinks he should choose beta in that

case?

Who's abstaining here?

You're not allowed to abstain in this

class. It's a complete no-no, okay? So,

we'll allow some abstention on the first

day, but not beyond today. Let's have a

look. Let's analyze

this combined game.

All right. So, what does this game look

like?

It's

an evil get

versus

an indignant

angel.

All right. And it 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.

Okay. My payoffs are going to be what?

Uh my payoffs are going to be the evil

get payoffs. So, they come from the

matrix up there. So, if someone can help

me with reading it off there, that's a

zero

a three

a minus one and a one.

All right. My opponent's or my partner's

payoffs come from the indignant angel

matrix. So, they come from here. There

is zero

a minus three a minus one and a one.

Everyone see how I constructed that? So,

I'll just remind you again. The first

payoff is the row player's payoff, in

this case the evil get.

And the second payoff is the column

player's payoff, in this case the

indignant angel.

All right. Well, 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 get. Those

are your payoffs. You're playing against

an indignant angel. What would you do?

Right? So, once again, no abstention

this time. Who would choose alpha? Let's

have a show of hands again.

Keep your hands up a second.

And who would choose beta?

Very few betas, but mostly alphas. Alpha

I think is the right answer here, but

why?

Why?

Why is alpha the right answer here? So,

yeah, can can can we get this guy here?

Yeah. It's the dominant strategy.

Good. Good. Actually, nothing has

changed from the game we started with.

The fact 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 zero,

beta I get minus one, so alpha would be

better. If my opponent chooses beta, and

I choose alpha, I get three, beta I get

one. 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?

What was the first lesson of the class?

Shout it out, please.

Right. Right. So, you should all have

been choosing in this game

You all should have chosen You You all

should have chosen alpha, right? So, the

one person who didn't will let him off

for today, okay? Okay. So, alpha

dominates beta here.

All right. Let's flip things around.

All right. 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

get.

All right. You're an indignant angel.

So, you have the payoffs that are still

there, and you're playing against the

evil get, which is the payoffs we

covered up, but we'll reproduce them.

Let's produce that matrix. By the way,

this is going to sound like a a

wrestling match. I don't mean it to.

Let's try here. Alpha, beta alpha beta

pair

me.

All right. So, my payoffs this time are

the indignant angel payoffs. So, mine

are zero

minus one

minus three

and one.

And my opponent's payoffs are What would

have been my payoffs before? They They

come from the other matrix. Let us show

you it.

They come from this matrix. So, they're

going to be zero, minus one, three, one.

Zero, minus one

three, one. Okay. I took the I took the

second payoff

from that matrix and made it

the second payoff

in this matrix. Okay. Everyone see how I

did that? Once again, the row player is

the first payoff, and the column player

is the other payoff.

All right. What should you do in this

case?

You're the indignant angel. You're

playing against this evil get. What

should you do? Write down in your

notepad what you should do. Show it to

your neighbor so you can't cheat.

Well, you can cheat, but you'll be

shamed shamed in front of your neighbor.

And uh

raise your hands. Let Let Let Jude see

it. Raise your hands and keep them up uh

if you chose alpha now.

And how about if you chose beta now?

So, one or two betas, mostly alphas.

Well, let's see it Let's Let's reason

this through a second. Does alpha Does

my alpha dominate my beta?

No, in fact, alpha doesn't dominate beta

for me. Doesn't dominate beta. If my If

If my pair chooses alpha, then alpha

gets me zero, beta minus three, so alpha

does better. But if my pair chooses

beta, then alpha gets me minus one, beta

gets me one. In this case, beta is

better better. So, once again, as we saw

before, alpha is better against alpha,

beta is get 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?

Uh somebody. Can we Can we Can we Can we

get the guy with the with the beard

here?

Yeah. Wait Wait for the mic. Here you

go. Great.

We've acknowledged that alpha is a

dominant strategy for my opponent, so we

must choose based upon

or knowing that my opponent's going to

choose alpha. Good. Good. All right. So,

and your name is

Henry.

Henry. So, Henry's 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, she gets zero,

beta she gets minus one, alpha is

better. If I choose beta, if she chooses

alpha, she gets three, beta one. Again

Again, alpha is better. For my opponent,

alpha dominates beta.

So, my 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.

All right. So, here

this time, my alpha

does not

dominate

beta.

But my pair's

My pair's choice of alpha

dominates her choice of her possible

choice of beta.

So, she will choose

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 zero rather

than beta and get minus three.

So, I

should choose alpha

also.

All right.

Okay. So, now we've seen four different

combinations. We've seen a case where an

evil get was playing an evil get, where

an indignant angel was playing an

indignant angel, and we've seen both the

flips of those, the evil get versus the

indignant angel, and the indignant angel

against the evil get. Why are we doing

this? Cuz there's an important lesson

here.

What's the lesson here?

The lesson is

comes from this game, that a great way

to analyze game, 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.

All right. So, the big lesson of this

game is

I forgot what number we're up to. I

guess this is lesson four, I think.

Lesson four 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 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 quote 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.

And 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.

Right? I might not know whether I'm

playing someone who's an evil get or an

indignant angel. So, I'm going to have

to figure out what the odds are of that

in doing this exercise. And that gets

That's 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 alphas and

betas, or essentially the same game, has

been played many many many times in

experiments. All right. So, out there in

the real world, and 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 uh almost a third choose beta.

Now, what do we think's going on? Why

are so as a as a as a third of the

people who seem to be choosing a

dominated strategy, or or is it?

What's going on there? Why Why do you

think Why do you think 30% of people are

choosing are choosing beta?

Anybody?

Yeah, can we catch this guy here?

Um

they they might be motivated by the fact

that every every person who chooses beta

raises the the average Right. So, they

could be moral people. They could be So,

one possibility is this 30% of people in

the real world who choose beta are just

nice people.

All right. What else could it be?

Yeah.

I know this might be changing the game a

little bit, but if you ever expected to

play the same game with the partner,

All right. So, they could be they could

be thinking they're going to play again.

Long-run payoffs are greater if you

choose beta every time.

So, they could be that they think 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? Let's let's let's

What's the simplest explanation? What's

the other obvious explanation?

They just don't know it. They could just

be stupid, right? It could be, right?

Right? Are we allowed to say that in

class? Right? Right? Right? 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 on in economics, really

means undergraduates at the University

of Arizona.

All these I mean, I'm not making it up.

It just does. They all are.

And and I don't know anything about Any

of you from Arizona? I don't know. I

don't know. I don't know whether the

average undergraduate at the University

of Arizona just has a sunny personality,

or whether they spent too long in the

sun. I just don't know what it is,

right?

Right?

We can't really distinguish from this.

Right? How about at Yale? What are

What's our numbers here? How about in

this class?

Do you Do you want to mic your your

colleague here? Yeah. 238 versus 36.

So, 2

38 at Yale. This is Yale.

versus 36. So, even even at my level of

arithmetic, that's a lot less than 30%,

right? That's more like less than 15%.

No, it's about 15%, I guess. All right?

All right. So, 236 as in 238 chose

alpha, and 36 chose beta.

Now, there's a there's one more lesson

in this class, and this is going to be

it. This is going to be 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 7th,

whatever it is, the end of the end of

the end of term. All right. So, look

around each other. You better get to

know each other a bit.

All right. And what do we learn today

about you guys?

The lesson here

Lesson five is Yale students

are evil.

All right. Be aware of that when you're

playing games.

All right. I want to play one more game

today in the remaining minutes. It

doesn't matter if we finish a little

early, but I want to try and get this

game at least started. So, do you all

have game number two in front of you?

I just want to Just while you're reading

that over, can I also make sure you've

all got your legal forms and you're

you're going to sign Don't walk away

with your legal forms. You need to get

those collected in. So, we're going to

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. All right? If you don't have

a legal form, if you've lost it or

something, it's online.

All right. It's online. All right. Let's

have a look at that second game. I'll

read it out for you.

Game two, 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 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 2/3

times the average in the class.

Again, the winner

is the person whose number is closest to

2/3

times the average number in the class.

And the winner will win $5

minus the difference in pennies between

her choice and that 2/3 of the average.

All right. 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.

All right. So, 25 + 5 + 60 is 90.

People should feel free to correct my

arithmetic cuz it's often wrong.

90, right? And 90 uh 2/3 of 90

So, 2/3 of 90

2/3 of

uh Whoops. Whoops. Uh what do I need?

Start again.

Start again. I need to divide it by

three to get the average, right? So, the

average The average is 30.

Okay. Somebody So, so shout it out. All

right. So, the total is 90. The average

is 30. Am I right so far?

All right. So, 2/3 of the average

2/3 of the average is 20.

I'm looking desperately at the TAs. Is

that right?

Okay. All right. So, the average is 30,

and 2/3 of the average is 20. All right.

So, who's the winner here? Which Which

number would have would have won here?

25 would have won.

25 would have been the closest. And what

would they have won? They'd have won

five bucks

minus

five cents for a total of 4.95.

All right. Now, to make this

interesting, let's play this for real.

So, this of course relies on me having

brought some money, and we have to do

this without dislodging the microphone.

All right.

I'm going to see if I have Sorry about

that. I'm going to see if I have enough

money to do this class for real. When we

play this game in the in the old days,

during the dot-com boom with the MBA

students, you had to put 50 bucks 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 a Okay, this is

Lincoln, apparently. Lincoln,

apparently. Who knew? Lincoln, okay? All

right. So, this is a $5 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, right?

I'm not No no magic tricks here. And uh

This is going to be the prize for this

for this game.

And we better give this to someone we

trust.

All right. So, prize

for 159.

Who do you guys trust?

The camera guy. Okay, Jude. We know

Jude's going to be there next week.

All right. I'm giving it to Jude. You

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 Jude has to therefore show

up next week with the prize, okay? All

right. 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?

What do you

All right. We'll never mind. We'll We'll

give it to you. We know Jude's going to

be here. All right. Has everyone put a

number down? Any questions You have

questions? Yes. Just shout them out.

It's okay. So, given that we only have

one $5 bill, does there have to be one

unique winner? And if so, how is that

determined if we have multiple people

who are close?

Well, we'll We'll That's a good

question. If there's multiple winners,

we'll divide it, but we'll make sure

everyone has a positive winning, okay?

All right. Good question.

Good.

Given the number of people in the room,

there may be multiple winners. I accept

that accept that possibility. Has

everyone put down a number now?

All right. So, hand your numbers to the

end of the row, but don't go yet.

Hand your numbers to the end of the row.

Before you go, I want five things from

you.

All right. I want to know the five

lessons from this class.

All right. Tell it Tell me what you

learned. What were the five lessons?

Without looking at your notes, what were

the five lessons? Anybody? What's

Shout out one of the lessons. Yes,

madam. Don't play a strictly dominated

strategy. Don't play a strictly

dominated strategy. Anything else?

Anything else? Yes, sir. Yale students

are evil. Yale students are evil. Two

lessons down, three to go.

The The guy over here. Yep.

Rational choice can lead Rational

choices can lead to bad outcomes. We put

it more graphically before, but that's

fine. Two more outcome Two more

Put yourself in other people's shoes,

and I'm missing one. I can't remember

what I'm missing now.

All right. You can't get what you want.

You 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

learned today, hand in your numbers and

the legal forms, and I'll see you on

Monday.