Original subtitles

okay so I want to set up on a a new

topic today uh and to get us started I

thought we'd play a game so the game is

going to be called cash and a hat and

we'll see what this game is like in a

minute so the idea is this there's going

to be two players I'm going to pick on

two of you hope I hope I can find people

who brought some money to class all

right so player one will have a choice

player one can put nothing $1 or $3 into

a hat the Hat will then be given to

player

two and player two can look at what's in

the Hat and either she can match what's

in the Hat I.E add the same amount in so

one if it's one or three if it's three

or she can simply take the

cash all right the payoffs this game

will be as follows uh player one if they

put nothing in they're not going to get

anything if they put one in and it's

matched then they double their money so

they get two back

if they uh put three in and it's matched

then they double their money so they get

six back they'll net three uh however if

they put one in and player two takes it

they've just lost their dollar and if

they put $3 doar in and player two takes

it they've lost

$3 right everyone ever understand that

pretty simple from player two's point of

view uh if player two matches then they

get them their investment back

[Music]

who here wants to be player one who

brought some money to class today I'm

quite willing to pick on somebody all

right good good good so player one is uh

what's your name again Justin Justin so

hold on to that hat for a second all

right and uh who wants to be player two

all right so this gentleman here whose

name is Nate Nate all right so we have

Justin and Nate all right so Justin you

have to decide how much money you're

going to put in the Hat did you bring

some money too Nate but make sure you

have otherwise borrow some from your

neighbors all right I'm going to put in

a bck all right all right so the M money

has been put in the Hat and delivered to

uh Nate so I'm going to put in the buck

too so that I get all right so if we

empty out the Hat here's our beautiful

pink hat I really had the Hat passed

across the room rather than have me do

it but uh we have $2 in the Hat so I'm

going to pay each I'm going to pay uh

what am I going to pay I'm going to pay

player

one uh $2 I'm going to give back the

original dollar and give them two in a

second and and I'm going to play player

two a $150 you just hold the Hat we'll

do that $250 $250 uh yes well you you

got your money back trying to cheat you

here is that it all right so player I'll

get you the rest in a second hang on a

second right for now we double the money

all right all right all right so this a

one reason to take this class is if you

play well you get

money all right now let's just try again

all right so we had one round of this

let's have another round who wants to

play player one now all right so uh

KD is player one all right K you bring

some money yeah sure all right and who

wants to be player two some further away

let's have um uh Steven isn't it is that

right so Steven's going to be player

soon do you bring some cash I think so

all right all right otherwise borrow it

from your neighbors I can have IUS here

so here's the Hat I've only got coin

only got coins ah ah all right all right

put okay great so so pass the Hat pass

the Hat down we'll see if it makes it

there test the honesty of the class here

it's working its way down I'm have to

there we go here we go all the way down

to Steven okay check how much he's in

there's a dollar here there's dollar you

you can decide whether to match or not

okay I'll match it all right so Steph's

going to match as

well all right once again we have this

time rather annoyingly a dollar and some

coins in here which I will empty on the

stage to prove it everybody all right

and I will I

will all right there are coins in here

right so I'll match this in a second and

give it back to you guys right so

everyone understand the game right

everyone understand how this game worked

so we're going to spend a while

discussing this and I we'd go on playing

except I eventually lose so much money

I'm going to run out of lunch

money the tea would object all right so

what I want to do is I want to analyze

this game I want to think about what

this game's about what's really going on

here all right so first this is just a

little game involved putting some money

in a hat but I want to suggest to you

that this is a a toy version of a much

more important game this is a toy

version of a game involving A lender and

a borrower so you could think of our

player ones here that was Katie on the

second round and uh is it is it Justin

on the first round Jus on the first

round as imagine them working in an

investment bank or perhaps in a venture

capitalist firm right and what they're

doing is they're giving a loan to

somebody some budding entrepreneur who's

come up with a new project so Steven in

round two and who was my budding

entrepreneur in round one what was your

name Nate in round one have come up with

some budding project they've left Yale

perhaps after their junior year they

just know they've left early because

they've got some great idea for

something which is going to make the

millions so either it's a new mouse trap

or a new version of Facebook or

something and they go to the that's half

isn't it so something better than the

new version of Facebook right and they

go to the this venture capitalist firm

uh maybe it's some firm in New York or

maybe it's the Y Investment Trust

whatever and they explain this great

idea to them and they ask for some money

to invest in this firm to buy machinery

and to pay early wages and so on right

and the lender the lender the guy who

works for the venture capitalist firm

has to decide how much money to invest

in this project right after having after

this money has been invested in the

project the person who borrowed it faces

choices they could go forward with their

Project work hard spend the money on the

things they're supposed to spend or they

could just disappear to Mexico all right

all right go back to Yale for that

matter all right and there's actually

something in between they could do Which

is less dramatic than disappearing to

Mexico they could just not work

particularly hard sh perhaps join join

in someone else's projects and just let

the money run down without the lender

really knowing about it all right so

this is a very real problem that some of

you if some of the budding entrepreneurs

in the room are going to face when you

leave Yale and more of you who are going

to end up working for Investment Bank

perhaps unfortunately are going to face

as well all right okay so we're going to

spend the whole of today analyzing this

but before we even start let's notice

that there's something different about

this game other than its sheer

triviality there's something different

about this game than games we've played

all the way up to the midterm so far

what's different about this game what's

different yeah can I um can I get a mic

in in here sorry uh yes what's different

moves aren't simultaneous the moves are

not not simultaneous this is a

sequential move game put the rules up

here and bring this

down so for the first time we're looking

at a

sequential move

game and we're going to spend most of

the rest of the term looking at

sequential Move games or at least

looking at games that involve sequential

elements now what's really what makes

this a sequential move game let's be

careful about this what makes it a

sequential move game is not simply that

player one moved first and player two

moved second although that's true what

really made this a sequential move game

is that player two knew what player one

had done before he got to make his move

it isn't the timing per se that matters

it's going to turn out it's the fact

that player two could observe player

One's Choice before having to make his

or her choice that matters and notice

just while we're on the subject more

than that player one knew this was going

to be the

case all right so let's just get that

down so in this

game player

two

knows player

One's

Choice

before she chooses she being player two

four let's say before two

chooses all right and

second player

one

knows that

this will be the

case and the way we dramatize this just

now is player one put the money in the

Hat the Hat was transported across the

classroom with people very honestly not

stealing the money to player two player

two could look in the Hat could see how

much money was in there before Steven or

Nate had to make their choice is that

right all right so how do we go about

analyzing games that have this

sequential structure so it turns out

that a useful way to analyze them and a

way I want to get us used to today

already is to draw a tree so in the

first half of the class we drew a lot of

matrices now we're going to draw trees

and for those who haven't seen trees

before it's not a big deal it's an

object that looks like a tree that's why

it's called a tree all right so let's

have a look so in this particular game

here is player one making her choice and

in fact she has three possible choices

she can put nothing one or three into

the Hat all right player two then

chooses although really player two only

has choices to make if there's some

money in the Hat and and player two has

two choices in this particular game in

either case either player two is going

to

add a dollar or $3 into the hat or

they're going to disappear off to Mexico

taking our investors lunch money with

them all right and let's put down the

payoffs and let's put down as payoffs

the net gains they make all right so if

nothing goes

in no one makes any money so zero Z will

be the payoff if one is matched by one

then the investor the lender doubles her

money so she makes a net profit of

one if if uh if the money is taken out

by player two then she loses

one right down here if she if if two

matches her investment of three she gets

a she doubles her money again so she

makes a net profit of three and if the

money is taken out she loses three

everyone all right with that let's do

player two's

payoffs in the case in which he in which

he matches one he makes a net profit of

150 in the case in which he just steals

the one he makes a net profit of

one and down here in the case where he

matches three he makes a net profit of

two he gets five back but he' invested

three to start with and here if he just

takes the money

out he makes a profit of

three all right right so this game is

Just Illustrated on the board and for

some of you this is the first time

you've seen a tree but I'm going to

claim it isn't such a it isn't such a

complicated object and we could spend a

lot of time analyzing this in terms of

connected graphs and so on but it isn't

really worth it it's just a tree all

right okay so let's just make sure we

understand that the payoffs here

represent player one's payoff and player

two pay two's payoff

respectfully all right so how do we

analyze what to do in these games it's a

good idea always to write up the tree

like it's a good idea to write up the

Matrix but how to analyze what we should

do well before we do that let me just

grab the mic and find out from our from

our

players what they should do all right

all right so where are where was my

first investor all right so uh Justin

why why did you put $1 in there well if

I put $1 in he has an incentive to put

$1 in too if I put in $3 he's just going

to take the money and run all right okay

so so what what's Justin doing Justin is

looking forward if you like he's putting

himself in Player Two Shoes this was who

was our invest Our receiver Nate's Nate

Nate's shoes and anticipating what

Nate's going to do and as Justin said if

he puts in three Nate's gonna have an

incentive to Take the Money and Run in

fact what would Nate have done Nate if

three had been in the Hat what would you

have done um I like Justin but I I would

have taken the money all right all right

even though you know Justin you've taken

the money and and disappeared somewhere

we don't quite know right right is the

same true for for the pair so so okay

you also put one in is that your

explanation as well same reasoning same

reasoning okay so everyone figured out

what was going on and once again we

think probably let's try Stephen if

there had been $3 in the Hat what would

you have done uh I would have taken it

taken it all right so so we're basically

getting what the what what's predicted

here uh out of the

game all right and let's just see that

more formally that idea so the idea here

is that the players who move early on in

the game should do something we've

always talked about before they should

put themselves in the shoes of the other

players but here that takes the form of

anticipation right they're anticipating

what players down the tree are going to

do right so the key idea here is

anticipation all right what they're

going to do is they're going to look

forward down the tree a manine

themselves in the shoes of the later

players look at the incentives facing

those later players

imagine that they do the best they can

those L players do the best they can and

then walk backwards through the tree so

the key idea here is to look

forward look forward to the end of the

tree and work

back look forward and work

back all right and that's exactly

exactly the process that Katie and

Justin describe themselves as

doing all right

right now in this tree let's have a go

at this so let's imagine ourselves in

Steven or Nate's shoes having found as

they did in fact having found $1 in the

Hat they then are making a choice

between adding a dollar which Nets them

a dollar 50 or taking the dollar which

Nets them Nets them one 150 is bigger

than one so we think they're going to go

this way right everyone happy with that

conversely if they found themselves with

three in the Hat uh then if they add $3

if they match they're going to get

$2 they're going to net $2 and if they

take the money out they're going to get

away with $3 all right three seems

bigger than two so we think they're

going to go this

way again we're assuming that these are

their real

payoffs okay so from player one's point

of view since player one can knows that

player two will observe the choice

before making her own choice and since

player one can can put him put him or

herself in player two's shoes and

anticipate this Choice player one is

essentially choosing between what if she

puts in zero she gets zero if she puts

in one she knows two will match and

she'll double her money and get one and

if she puts in three then she knows

player two will take the money and run

in which case our lender will have lost

$3 so she's choosing between 0 1 and

minus three and it's going to

one which is exactly what happened in

the game right everyone happy with how

we did that right so this idea of

starting at the last player the player

who moves last solving out what they're

going to do and then working our way

back through the tree has a name the

name for this is backward

induction and I apologize for the

business school students in the room

who've had this hammered into them too

many times already so I apologize for

them in

advance all right backward induction now

it turns out there's precisely one

controversial thing about backward

induction which is whether you should

say backward induction or backwards

induction so I'm going to leave the S

off and call it backward induction but

uh it's up to you which you think the

correct English

is all

right

okay so since we've got got this game

here let's talk about it a bit this idea

of the lender and the borrower it's not

an unimportant situation we we've you

know we've simplified it down to a very

simple Choice here but it's a very basic

Choice out there in the real world all

right and it's important choice after

all what keeps the economy running is

the ability of lenders to lend money to

businesses that then uh uh invest them

profitably and are able to make returns

so this un this underlies a whole bunch

of what of stuff going on in the economy

all right so let's talk about this and

the first thing I want to talk about is

I want to point out that there's there's

a there's a problem here there's a

there's a bad thing here much like there

was a bad thing in the very first class

of the of the semester in the very first

class of the semester the bad thing was

a prisoners dilemma right but here it's

a little different and let's but let's

focus on it a while so the bad thing is

we ended up here not a

disaster right the lender doubled her

money the borrower was able to go ahead

with the project on a small scale and

make some money the bad thing however is

that we would have liked to end

up

here all right had we' been able to have

a large project funded with $3 and had

the borrower uh uh repaid those dollars

so matched in effort or whatever it

happens to be then we'd ended up at an

outcome that is better not just for the

lender it's obviously better for the

lender but it's also better for the

borrower everyone see that right so the

outcome we'd like to have reached gets

us gets the lender three whereas he's

only getting one where we ended up and

it gets the borrower two where he's only

getting 150 where we actually ended

up all right why is it that we were

unable so both of our pairs both Justin

and Nate and Katie and Steven why were

we unable to get to here why were we

unable to get to here

it take us what got us what what

prevents us from getting to this to this

good

outcome let's go back to to to Katie a

second and see if we can yeah you go

ahead well I'll come it's all

right all right so so Katie was saying

why she invested one I picked on J

before so so you know here's this good

outcome it's better for you it's better

for Steven who's your who's your Bor

why aren't we getting to this 32 outcome

because if I play three um him matching

my money is dominated all right strictly

dominated all right so the problem here

the problem here is Katie would like to

invest three if she knew in fact Steven

was going to match but she knows

Steven's not going to match right Steven

in fact is going to run off with the

cash all right it's going to end up

being spent at Starbucks or something

all right and from Steven's Point of

view he would actually like to be able

to borrow the $3 he would like to be

able to end up at this 32 outcome as

well the problem is he knows and Kat he

knows that ktie knows and Katy knows

that he knows that in fact he's going to

run off with the cash is that right is

that right all right so we're in a bit

of a problem here we'd like to get this

good outcome but incentives are

preventing us from getting there what do

we call this kind of situation what do

we call this kind of

problem

anybody noakers all right this is called

moral

hazard this is called

moral hazard how many of you have heard

the term moral hazard before all right

number people heard it so here we are

moral hazard here is the problem that

the agent in this case the Bor the

borrower has in has incentives will have

incentives to do things that are not in

the interests of the

principle all right we're not careful

and as as for example by giving too big

a loan the incentives of the borrower

will be such that they will actually not

be aligned with the incentives of the

lender and that will prove to be bad for

the

lender but notice the existence of this

moral hazard problem isn't only bad for

the Lend it ends up being bad for the

borrower as

well right let me give you another

example in Insurance there's a classic

probably the classic moral hazard

problem if an insurance company insures

me against having my car stolen there's

a moral hazard problem in that I might

if I if the car is fully insured I might

now have the incentive not to bother to

lock my car or to leave it anywhere on

the street in New Haven all right right

because I'm not bearing the cost

all right so we need to be able to the

insurance company needs to worry about

that in in writing an insurance contract

for me and in practice what the

insurance company does is it forces me

to take a deductible it doesn't allow me

full insurance it makes sure that some

of the cost of having a car stolen is

going to fall on me that's bad for me by

the way because it means I can't get

full

insurance all right and notice that what

happened here is rather similar in this

case both both the lender and the

borrower would rather have a big project

a big loan and have the uh have the

agent pay back that loan they'd prefer

this 3u outcome but they can't get there

and therefore rather than having a

fullscale project Casey or Justin only

offered the borrowers a small scale

project all right so the idea here in

this example was in this

example what happened was we kept

the size of the project or the size of

the

loan you could think of this as the

project if they're borrowing

something

small to

reduce the

temptation to

cheat okay to reduce that Temptation not

to not to repay the

loan all right so these problems are all

over the you know all over Society but

they're particularly prevalent in

situations involving uh lenders and

borrowers all right so good question is

how might we solve this problem a lot of

you are about to go out and try and

borrow money to set up your project to

run your new version of Facebook

whatever and a a lot more of you as we

said before are going to end up loaning

money perhaps someone else's money

probably at least for a while and we

want to know how you might solve this

moral hazard problem we've seen one way

to solve it one way is simp to keep the

size of the project small what else

could we do let me come down and try and

have a bit of

discussion what else could we do Steven

what else could we do you with a

borrower what else can you do like uh

impose laws we could impose laws okay so

we could impose laws much like we talked

about in prisoners LMA we could regulate

this Market there's going to be a little

bit of a problem we're going to run into

in regul the

law in in using the law here what's the

problem we're going to run into here

well I we do have laws that that

regulate borrowers and lenders what's

the what's the law that regulates

borrowers and

lenders bankruptcy law right so right we

have we have law that that regulates to

some extent what lenders and borrowers

can do uh one of the things we do in

that law is we limit the degree to which

we're allowed to punish the borrowers

right so bankruptcy law pretty much says

we're going to put some limit on how

much much Casey can inflict pain on

Steven for running off with the lunch

money right Steven can simply say I

can't repay I'm bankrupt and you know

he's more or less allowed to get a fresh

start so the L the Lord would be good

here but there's limits to what we can

do right we could go back to the de

kenian world of throwing Steven in jail

for not not repaying the loan but it's

tough there are downsides to that it

turns out all right so what else what

else could we do yeah uh I'm going to

have to dive in there a little bit so

shout into the mic uh the Venture C can

impose uh restrictions on what the

person can do with the money all right

all right so so he could try and say uh

there's only certain things you can do

with the money and for example to make

that credible what you might have to do

is to say show me what you're going to

do with the money show me the receipts

right one you could say is I will I will

only give you uh the money if you show

me exactly how you're going to spend

this right that's a good that's a good

solution notice that one you could you

could regard that as changing the order

of way right it's a little bit like

saying let's have the borrower have to

move first let's have the borrower have

to commit what their actions are going

to be how they're going to spend the

money before and show you show the the

the contracts before the before the

lender lends them the money right and

that's a good solution but again there

are limitations to this solution what

are the limitations to that solution in

the real

world let's go back to all of you are

thinking about making millions with your

new Facebook what are the limitations to

to uh having some contracts with the

with the with the bank you know with

Chase saying exactly how you're going to

not only saying exactly how you're going

to spend the money but actually

detailing it already with contracts

ahead of time what are the problems for

that someone else's thinking of going

into business here let me pick on

somebody a second so what's your name

sir Kelly Kelly so what you know imagine

you have some project you're you're

going to borrow some money from Chase or

Mr swensson to set up this fund why

might you worry about having everything

written out and contractually had a

sign um I mean then it restricts your

freedom on what your ideas are I guess

right so one problem is just sheer lack

of flexibility all right if if in fact

the entrepreneur is not going to leave

any is not going to be flexible in how

they uh actually run the project there's

not much point of being an entrepreneur

in the first place right there's a limit

I mean to how much control you want to

give to the lender the lender doesn't

really want to run the project for you

right there's also simply a problem of

timing you simply it's simply not going

to be possible to specify all the

expenditures of a project up front

you're going to need some money to do

some things ahead of time all right

right so it's a good idea changing the

order of players a good idea but there's

going to be limitations to this what

else could you do as the

lender what else could you

do thinking of loaning some money in

here loaning some money to one of your

classmates for some project let's try

again something like loan money over

time in stages and observe progress good

good so one possibility sorry one

possibility is to break the loan up and

give

it let it come in small installments if

you do well on the first installment

I'll give you a bigger installment next

time all right and notice that's a

little bit like something we talked

about the very first week it's a little

bit like taking this one shot game and

turning it into a repeated game right

it's it's turning a oneshot interaction

into a repeated interaction we'll come

back and talk about repeated

interactions later on in the course

again notice that there might be some

limitations to this I mean I think it's

a good idea and in general you should be

trying to do this but it could just be

that to set up for Nate to set up his

new Facebook and for Steven to set up

his new mous trrap Factory they just

need a chunk of money at the beginning

there may be some limit to how little

money you can give them at the beginning

since they have to hire workers and set

up the factory and make some Big Splash

and advertising and so on and so forth

all right so again it's a good idea but

there may be limitations here what else

could you do let's have a look at the at

the numbers on the board right now the

numbers on the board say that if

Steven's mous trp project was were you

the Facebook or Steven's the fact if

Steven's mous trap project goes well and

it ends up being a big project with lots

of money available there are five units

of money available in profit right three

plus two right the way we' the way we've

designed things so far our lender I gave

you these payoffs in the game the lender

is going to double her money she's going

to get three six packs from to net three

and Steven's going to get two so the

division of that five is three and

two but we don't have to divide the

money like that if you're a lender you

may want to think about how you divide

up The Spoils of a successful

project all right so how else could you

divide up those $5 that three plus two

in a way that might be better for

everybody Nate give the investor $31

Cent if they uh do that other choice and

then take a little bit of a hit but that

way uh you'll still have something

that's preo optimal to the other the

other choice that we came to before all

right I'm guessing people didn't hear

that but that was right so just say it

that's exactly right so what you could

do here is you could redesign the

payoffs of this project in the event

that it's successful all right what you

could do is take these five units of

profit and instead of having three2 it's

right in a different color we could give

the the borrower the entrepreneur

3.1 leaving uh 1

9 to uh the lender all right so we could

change the payoffs of this

contract to be 1.9 3.1 in the event of a

big project why does that help because

now our borrower Nate or Steven were

they to end up with a hat with $3 in it

they now will find it in their interest

to match the the $3 and get 3.1 rather

than three

all right right so what's this an

example of this isn't this this idea of

changing the contract to give the

borrower incentives to repay incentives

not to sh incentives not to disappear

with the cash is an example of what's

called incentive

design all right so the idea here here

is in a lot of

businesses incentives are not given by

God they're designed by the people who

write the

contract all right and if you're in if

you're the either the borrow or the

lender you should be thinking about

writing a contract that's going to

achieve the end that you want now notice

in this particular example exactly as

Nate said the lender is going to take a

bit of a hit here they're not going to

get a 100% return but they're ending up

doing better than they would have done

by giving a small Lo

right they've ended up getting

1.9 rather than

one getting 1.9 rather than one so in

this particular example it won't always

be the case but in this example they're

taking a smaller

share a smaller share of a larger

pi and sometimes a smaller share of a

larger Pi is bigger than a larger share

of a smaller Pi not always but sometimes

right the reason the pi is larger is

we're able now in intent and compatible

way we're able to go ahead and have a

large project so in this example the

smaller share of the larger Pi actually

ended up being bigger than the larger

share of the smaller Pi so a a smaller

share of a larger Pi can

be

bigger

than a large

share of a small P not always of

course all right this is just an

example all right now let's just be a

little bit careful here all right so in

this particular example even though this

this 1.9 this return that our lender is

able to make by accepting a smaller

share of a larger pie even though it's a

bigger absolute return it's smaller in

another sense in what sense is it

smaller let's be careful here so to say

look it's 1.9 1.9 is bigger than one

that's got to be a good thing but since

some of you actually are going to go out

into investment Banks you might be posed

this question let me just not let me

just make sure we don't BL make a

blunder that's going to spoil your

interview so what what what might you be

worried about as an investment banker

about this deal about this about this

this

contract somebody else anybody else

let's I'll come down again it's

right what might you be worried about

who here's be honest who here is in has

been interviewing with either investment

Banks or Venture Capital firms or

private Equity firms raise your hands oh

come on it's could be more than

that all right all right there was a

hand was where was the hand at the back

there was a hand way back

here

no yeah can I

so what what what might be wrong with

this project from your point of VI

actually take can I can I get in the mic

on that

side this gentleman here what might be

wrong with with the project from your

point of view if you could actually just

find three small projects then you could

still get 100% returns just by dividing

it up good good you're gonna get you're

gonna make lots of money for Morgan

Stanley whatever it is good good your

name is Bri Brian right so there's a

good aat a good ad to hire Brian Morgan

Stanley all right all right so what what

Brian said was it's true that you're

making a bigger absolute return

here this is a bigger absolute return

but this return up here is a 100% return

on your Capital the rate of return on

capital is higher making a 100% return

on an investment of one than making a

1.9 return on investment of three the

rate of return is better in in in the

smaller case so which is the right

answer should we worry about the rate of

return

the 100% rate of return or should we

worry about the absolute

return if you're in the business of

investment banking who thinks you should

worry about the absolute return who

thinks you should worry about the rate

of

return who thinks it

depends what does it depend on what does

it depend

on keep keep me from falling off this

thing what does it depend on someone who

said it depends what does it depend on

depends is only a good compromis vote if

you you know what it depends on yeah the

here since an investment banking firm

only has a limited amount of money to

invest you want to see if you can get a

higher rate of return investing

elsewhere all right so so there's two

there's I think you're on the right

lines there's two things to worry about

one is what is your supply of of funds

to invest and the other is what's the

other Supply you're worried about as as

an investment bank or a venture

capitalist firm or a private Equity

investor what's the other Supply coming

your way

yeah the number of projects coming

across your door if like the demand for

your C the demand for your cash the

supply of projects all right all right

so the what we have to worry about here

is what is the true opportunity cost of

that

money right if there are very few

projects out there all right then you

basically just want want to go down the

list of projects picking off absolute

return however go the other extreme if

there's an infinite supply of projects

all coming in all of which will offer

100% return then as our our Banker at

the back told us you should just go for

three small projects rather than one

large one right but the question is

question of which is better three it

isn't as simple as saying yes we should

always go for three small projects there

may not be three small projects out

there that offer 100% return all right

so what's going to matter here is what's

the true opportunity cost of the capital

and that's going to depend on what

projects are available to you all right

this was just an example of incentive

design it's one example of incentive

design let's talk about other examples

of incentive design been a lot on the

news lately who who else tends to have

incentive contracts other than

borrowers who else out there tends to

have incentive

contracts it's a big Topic in you know

in the news these days so who has

incentive Contra incentives written into

their contracts yeah way over here let

me let me run over at the risk of

blurring the camera all right so who who

else has incentives in their contracts

managers managers all right so CEOs have

huge incentive Clauses in their

contracts all right sometimes in the

form of options right why do they have

those incentive causes in their contract

well there's two interpretations of this

one interpretation is it's just a bad

thing and they're just trying to screw

the world but there's a more there's a

more um moderate view of this the more

moderate view of this is that those

incentive Clauses in their contracts are

attempts to align the interest of the

managers with the interest of the

shareholders just as this contract is

attempting to align the interest of the

lender and the interest of the borrower

all right so by managers I took you to

mean CEO but what other kind of managers

recently in the Press very recently this

weekend have have been talking about

incentive

contracts uh some way over there I'm

going to caught on the wrong side as

usual but um yeah can I squeeze through

I'll try and squeeze through can I

squeeze through sorry all right sorry

here we go where was it where was where

was my answer to that question here we

go managers of baseball teams all right

so so so managers of sports teams also

have incentive contracts these days

right incentives to to achieve certain

levels all right here it's not quite

clear to me exactly what's going on

right we call those incentive contracts

but you might want to worry a little bit

I mean do we really think that the

manager has an incentive to lose

otherwise right so part of what's going

on with incentive contracts isn't

actually incentive contracts part of it

is about sharing the risk right

particularly the kind of contracts have

been written about over the weekend with

Joe tor's contract for the Yankees which

he turned down is partly perhaps to give

him incentiv to try and win but perhaps

is more to do with sharing the risk

among the general manager and the

manager of the team if they don't make

it to the playoffs but all right

there're still incentive contracts now

we see incentive contracts elsewhere and

we've seen them since the Middle Ages

right so in the Middle Ages incentive

contracts took a particular form and the

form was called two things peace

rates let's put it up here peace

rates and in agriculture it took the

form of

sharecropping what are peace

rates somebody what are peace rates what

what are peace rates anybody anyone know

anyone who's on peace rates what is is

sharecropping somebody must been from a

farming

State yeah there's somebody out

here that guy in Orange out here

yeah um sharecropping is where the uh

landowner takes a portion of the um of

the farmer's crop at the end of the at

the end of the farming season all right

so sharecropping is a is a contract

whereby part of the output of the farm

goes to the landowner and part is kept

by the farmer all right going back to

the Middle Ages

part of the output would stay with the

peasant and part of it would go to the

Lord of The Manor right peace rates are

a similar idea rather than playing

paying wages to workers just bundles of

cash the amount of which they're paid

depends on output so P rates would say

if you produce uh 17 yards of cloth then

you'll get paid the the the revenue

that's derived from three of them say

right both of these forms of Contracting

are there partly to create

incentives they create incentives

because they they create the incentive

of the farmer to increase

yields and they increas incentives to

the part of the worker to increase

output all right so peace rates are a

big part of the

story all right incentive design is a

pretty big topic and we don't really

have time to go into it much in this

course but it's worth mentioning that in

fact uh the Nobel Prize that was won

last week by those three economist we

talked about was partly about incentive

design all right so it's regarded as an

important enough topic for the design

the design of incentives across society

as a whole to have been worthy of

winning the Nobel Prize and my guess is

there's another Nobel Prize that's going

to come out in this same area in the

next five or 10 years all right just to

make it clear uh you can have problems

you can bad you can write incentives

badly it's classic story that you've all

all heard of I'm sure that in often in

uh in the provision of public goods that

say Bridges or highways or tunnels the

incentives for the construction

companies tend to be rather badly

written they they're meant to have

incentive Clauses but they never seem to

quite get them right it's easy to get

these incentives wrong and just to prove

this doesn't just happen to management

let me just tell a story against myself

so uh a year ago a year and a bit ago I

was uh picking fruit with my then

three-year-old daughter and I wanted to

make sure that we got some fruit home to

eat for dinner and she didn't just eat

all the fruit as we picked it these were

raspberries uh so I decided to have a

rule that sounds efficient I said any

any item of fruit that gets picked

that's in good condition we'll take it

home for dinner but if it's squashed

then we'll when we'll eat it then and

there when we're picking the fruit all

right so my three-year-old proceeded to

go along the the uh bushes of

raspberries picking the raspberry

turning around to me and saying squashed

and putting it in her mouth all right

all right squashed squashed squ right

which shows that a three-year-old knows

more than a professor about moral hazard

at some all right all right so one thing

we can do is worry about incentive

design in the design of the contract

there's another thing we can do here

what's the other thing we can do here

we're missing out something very basic

what is what is it that that our

borrower step and Nate can do or put it

more generally for all of you if you go

out and start a company and you borrow

some money to start your company when

you leave Yale what are you going to

have to

do what's the borrower what's the lender

what's the Bank going to insist on what

are they going to insist

on

anybody they're going to insist on

collateral they're going to insist on

collateral what is

collateral I'm I'm somewhat Charmed to

see how few of you going to end up

borrowing money but uh uh for those of

you who haven't got Trust you're going

to end up borrowing money

so what is collateral let's yeah yes

what's collateral you give someone the

hold you you let the bank hold on to

something right you let the bank hold on

to something in the event in the event

that you default on the loan all right

you're going to let the bank hold on to

something in the event that you default

on the loan now for most people here

what are they going to post as scat

let's assume that we we're back to our

original contract here we can't we can't

do this we're back to our original

case

what are most of you going to end up

using us collateral if you borrow

money yeah everyone say a house I'm

guessing that for most of you I'm not

going to look around the room because I

don't know how many trust fun trust fun

babies I've got in the room but for most

of you it's going to be what it's going

to be your parents'

house all right all right so why why is

it that your parents house being posted

as collateral is going to prevents you

from disappearing to Mexico with the

loan well let's have a look how it

changes the payoffs now now if you take

the money and run you disappear to to

Mexico but you end up with $1 minus a

house here and

$3 minus a house there of course we're

relying here on you liking your parents

enough not to mind about the fact

that'll be sleeping in the rain but as

long as that's the case long as that's

the case with all I think with high

probability you're now going to decide

to return the loan at least if you can

is that right now notice that the way in

which this collateral worked there's a

subtlety to how this collateral works

you might think that the way in which

collateral works is that now the lender

feels safer because even if you end up

defaulting on the loan at least they get

this

house all right and that's true there's

some truth in that but that's really not

the key here right frankly most Bank

lenders don't want your parents house

right I me your parents might have very

nice houses but you this isn't a good

housing market right now and they don't

particularly want to see your parents on

the the street the way in which this

works is not not so much that it gives

an extra positive return to the lender

the way in which it works is it gives an

extra negative return to the

borrower all right so just do this

backward induction again with the house

in place right so with this house in

place as before you'll return the loan

up here but now provided you like your

parents enough you would also return the

loan here because you refer $2 to your

to $3 minus your parents house in which

case you'll get a loan of

three all

right right so the way in which the

collateral worked was by hurting you

enough in the OR in this case hurting

your parents enough in the event of

default in such a way as to change your

behavior but notice it helps

you so here's a subtlety coming in here

by issuing collateral we actually

lowered the payoff of the borrower at

certain end points of the tree we

lowered the payoff of the borrower at

certain end points of the tree but as a

consequence we were able to end up at an

outcome that was better for the

borrower sometimes having lower payoffs

can actually make you better

off and the reason it makes you better

off is it changes the behavior of other

players in the game in such a way as it

may as May benefit you in this example

by by inducing the lender to give you a

bigger

loan all right so the way the collateral

works is it

lowers it lowers your

payoffs if you do not

repay but it leads to you being better

off and the reason it makes you better

off is it

changes it

changes the

choices of

others changes the choices of others in

a

way in a way that helps

you all right we're going to see lots of

examples of that in the next couple of

days all right now collateral is an

example we talk about intive design

collateral is also an example of

something larger the larger thing is the

idea of

commitment collateral is a commitment

strategy it's a commitment strategy it

commits you to to repaying the loan

all

right I want to give another example of

a commitment strategy right because I

think this idea of commitment is an

important one and we have just about

time to do it so I wanted to go

completely away from the context of our

lender borrower game a second and look

somewhere else entirely right so we get

rid of this for

now I want to take us back to uh

1066

what happened in

1066 what happened in 1066 I know I know

this is America and no one gets an

education anymore but still what

happened in

1066 the Norman Conquest took place in

1066 right so the Norman Army invades

from Normandy led by William the

Conqueror and lands on the Sussex

beaches at Hastings all right and what I

want to imagine is a game involving the

Norman Army or William the Conqueror in

particular and the Saxon Army all right

so here's the little game so we're now

in the we're we're in the area of

medieval military

strategy all right and here is the game

uh we'll start with the Saxons here the

Normans have already invaded so I guess

I guess the Normans have already mov

moved uh but here's the uh here's the

the Saxon Army making a decision they're

deciding between uh fighting and the

important medieval military military

tactic known as running

away and of course the Normans are going

to know whether the Saxons are actually

going to charge down the beach and

attack them and they are going to have

to decide whether to fight or run

away all right and let's put the payoffs

in now leave some space below here leave

some space down here on your notes all

right let's put the payoffs in so I'm

going to put the Norman payoffs first

and the Saxon payoff second okay Norman

payoffs first Saxon payoff second right

so the payoffs are going to be like like

like this if both if both sides fight a

lot of people end up dead and we'll call

that z z if the Saxons fight and the

Normans run away the Saxons get two and

the Normans get one because at least

they're alive if the Saxons run away and

the Normans fight then uh the Normans

get two and the Saxons get one it flip

things around and if both Lots run away

then ultimately it's good for the

Saxons all right so this is the

game all right let's be careful I've put

the Saxon payoff second the Saxon payoff

second if we analyze this game by

backward induction we can see that the

Normans are in trouble why are the

Normans in trouble because if they are

attacked by the Saxons then fighting

yields zero and running away yields one

so they're going to run away

and conversely if the Saxons run away

then in fact the Normans will stay and

fight because it's easy to stay and

fight against people who running away

even I can do that all right so that's

so they're going to go for two rather

than one but now the Saxons face this

choice they know that if they attack the

Normans the Normans will run away and

the Saxons will get two but if the

Saxons run away then the Normans will

stay and fight and the Saxons will only

get one so the Saxons are going to end

up

fighting all right everyone everyone see

how we did the backround induction so

this is not a good situation if you

happen to be the Norman Commander if

you're the guy who led these troops

across the Channel all right so what did

William the Conqueror

do he burnt his ships right so let's now

make this game a bit more like the real

historical situation here's a move that

William the Conqueror the king of the of

the Normans can do he can either not

burn his

ships or he can burn

them if he burns them then the game is

rather different once again the Saxons

can decide whether to fight or run away

but now the

Normans really don't have any choice

they have to stay and fight because

swimming back to France wearing armor is

difficult all right so the payoffs

become Z Z and 21 as

before all right so we know now that the

Normans are going to stay and fight

that's all that's available to them i'

I've put it that they don't even have

the option of of running away if you

want you could put running away yield to

them you know minus infinity or whatever

it is to get drowned all right so

now if the

Saxons if the Normans have burnt the

boats the Saxons know that if they fight

the Saxons will get zero if they run

away they'll get minor one so now

they'll run

away and then from from William the

conqueror's point of view what's he

choosing between he knows that if he

doesn't burn his boats the Saxons will

fight and his troops will run away but

if he does burn his boats the Saxons

will run away and his troops will fight

so he wants to burn his

boats right everyone okay with the

example all right now this is probably

the classic example

of a commitment

strategy right William the Conqueror in

this example or or Cortez in perhaps the

more famous example burn the boats to

get rid of some strategies to get rid of

some choices altogether and you might

think how can get ridding how can

getting rid of choices make me better

off and the reason in a game in a

sequential game but in the game

generally the reason getting rid of

choices can make me better off is it

changes the behavior of people on the

other side of the game in such a way as

benefits me in this particular example

it makes the other side less likely to

fight all right so once again this is a

commitment it's a commitment and the way

it works is this example of a commitment

is actually to have fewer to have fewer

options

have fewer options and it

changes it

changes the

behavior of others if it didn't change

the behavior of others it wouldn't be

worth

doing all

right so let's just talk about this a

little bit more there's another famous

example of a military commitment

strategy uh that occurs in the movie

Doctor Strange Love how many of you have

seen seen the movie Doctor Strange Love

how many have not seen the movie Doctor

Strange Love right good homework

exercise for the weekend rent the movie

Doctor Strange Love great it's a very

good movie all right Stanley kurick I

think all right so in the do in Doctor

Strange Love there's a famous commitment

strategy what is the famous commitment

strategy in do Strange Love Somebody

it's going to it's going to M uh Al can

we a mic down here that there's one on

the way the guy in white there you go

there you go there you go great they um

lose radio contact with the base which

means that they're going to end up

dropping the bomb all right that's true

I was thinking more more deliberate what

was what's the more deliberate the guy

in red there somebody in red here here

we go try the Soviets construct a

doomsday device so if they're attack

they automatically launch their all of

their nuclear weapons good good so the

worry that the Soviets have is they

think the Americans might attack them

and they worry that the Americans might

attack them thinking that they won't

retaliate because it won't they won't

really have any in to retaliate once

their cities are destroyed so they

construct a device they call the

doomsday device that will automatically

launch nuclear missiles back on the

Americans if the Russians are attacked

all right it's a commitment it's a

commitment device to make it credible

that they will actually respond were

they were they to be attacked by the

crazy Americans all right so there's a

mistake however that the Russians make

what is the mistake that the Russians

make what's the mistake the Russians

make tell while over here the guy in the

Yale sweatshirt

here they don't tell anyone about the

machine right they don't tell the

Americans that they've built the

doomsday device all right so this is

really an important idea hidden in

what's really a great movie commitment

strategies are a good idea they can make

things credible but the only reason that

having fewer strategies is good for you

is because it changes the behavior on

the other side in this case it be

changes the behavior of the Saxons it

doesn't work if the other side doesn't

know about it it's crucial that the

other side

knows so the other

players

must must

know all right just to hammer this home

notice that the expression in the

English language is burning your boats

it's not going over to your boats and

quietly drilling a little hole in them

right it's burning your boats you want

the other side to see this big bonfire

on the beach and to know that the boats

are no longer available right just as in

Doctor Strange Love it's crucial and

it's a terrible mistake for the Russians

not to tell the Americans that they've

built this

machine all right all right so knowledge

here is crucial knowledge of the other

side now I should just complete the

history of this this didn't work in the

case of the Battle of Hastings the

Saxons attacked anyway and it just

turned you there was a big blood blood

bath and the Normans really only won

this battle because somebody got a lcky

lucky shot and hit the hit hit King

Harold in the eye so actually this is a

good story but didn't they as as a

military tactic not not actually a true

story I do that I'm adding that in

because otherwise I'm going to get

hundreds of letters from people who

watch who watch the

video all right now we've had a bunch of

lessons today but I'm not done I want to

play one more game before I do though I

want to make sure we understand we're

going to play another game so everybody

stay put I want to make sure that

there's a bunch of lessons on the board

and I want you to understand what's

important and what's more important

everything's important but some things

are more important all right so the idea

of commitment is an important idea and

the

idea of incentive design is an important

idea but there's one idea here that is

more important than anything else and

that idea is backward

induction

all right we little Sun around it okay

how important is backward induction

backward induction is the most important

thing I'm going to teach you in the

second half of the of the semester it's

probably the most important thing I'm

going to teach you in the whole semester

and it may be the most important thing

you're going to learn at Yale all right

how it's the answer to all questions if

I ask you a question and as happens from

time to time you've been sleeping in

class and you wake up startled because

I've now asked you a question question

and that camera is on you right and you

don't know what the question is then the

answer is backward

induction all right I'm stressing this

because six weeks from now whatever it

is in December there's going to be a

final exam and I guarantee now that

there will be a question on the final

exam that involves backward induction

and I guarantee that at least one person

in the room will forget to solve it by

backward

induction all right so are you going to

use backward induction on the final exam

yes yes you're all going to remember it

okay okay good now we'll play one more

game just for fun all

right oh before we play one more game

I'll do one other thing sorry one other

thing before we play one more game I

apologize um the one other thing I want

to do here is uh uh I put up a tree here

but I forgot to tell you anything about

the tree this was a

tree and I would be I would be remissed

if I didn't tell you a few things about

trees so there's a certain amount of

jargon that goes along with trees and I

want you to go a to read the text Book

and know what that jargon is so these

spots these dots in the tree these

things are called

nodes all right they're called nodes and

in fact the end points of the tree where

the payoffs are these are also called

nodes but they're called end

nodes all right and these branches in

the tree the branches here they are the

branches are called edges

all right so a tree consists of nodes

edges and these missing end missing dots

of the end nodes the end nodes are

associated with payoffs we need to write

that that's obvious right they're asso

with payoffs and every other node

belongs to somebody whose choice who

whose turn it is to make a decision at

that

node all right so the these other nodes

the ones that are on end nodes are

called decision

nodes

and it's perfectly possible for example

in our in our Norman Conquest game for

somebody to have several nodes somebody

could move once and then later on in the

game there may also be noes that are

never reached in a game one last piece

of jargon a route through a tree from

the beginning to an end is called a

path a path a way of getting through the

tree from the beginning to the end so

we'll have a pop quiz on that jargon

later and now let's play the last game I

want

play we've got 10 minutes

right okay everyone understand the

jargon I want to play a game now all

right so the game we're going to play is

a game we're going to call the Hungry

lion game all right it's a hungry lion

game and what I'm going to do is I'm

going to pick on a a row of the class

actually I'm going to pick on this row

of the class all right and this row of

the class everyone can see this row

there you lean over the balcony this row

of the class we're going to imagine that

everybody in this row is a

lion all right they're all do they all

look like lions not much but no pretend

they're Lions right suspension of

disbelief all right they're all lions

and they're all

hungry except except for one person

who's this guy at the end whose name is

Alex Alex so Alex is a

sheep Alex has the had The Misfortune of

wandering into this pack of pride pride

of lions and is liable to get eaten

because they're hungry all right however

one thing stands between Alex Alex the

sheep and being eaten the one thing that

stands between him and being eaten is

that in Lion Society the only lion who

is allowed to eat the Sheep is the head

lion the big lion whose name is Ryan

Ryan right Ryan is the head lion here

right only Ryan can eat Alex the Sheep

No Other lion can eat Alex the Sheep all

right now there's a catch if Ryan eats

Alex if Ryan the lion eats Alex the

Sheep the catch is that if Ryan the lion

eats Alex the Sheep then Ryan the lion

will fall into a postp paranal stuper

fall asleep at which point the second

largest lion whose name is Chris Chris

can eat

Ryan now notice Chris can never eat the

Sheep he can only ever eat the lion the

the big lion and only then if the lion

is eaten the sheep and falls asleep this

is very strict right lion Society is

very hierarchical like England all right

right if however Ryan the lion eats Alex

the sheep and is then eaten fall asleep

and his then eaten by chryst theion then

and only then he will fall into a stuper

when at which point he can be eaten by

Isabella Isabella who's the third

largest lion and so on ever understand

the game all right no questions no

talking among yourselves write down what

you would do if you were our key

decision maker who who is Ryan Ryan the

LI but before we write it down can I get

Alex to stand up a second stand up all

right camera on him right this is this

is the

menu all right all right thank you all

right all right okay so you have to

write down in your notepad whether you

Ryan the lion in

Ryan's um shoes or paes whatever whether

you would eat Alex the

Sheep everyone written something down

all right now let's let's ask Ryan the

lion what he's going to do so Ryan are

you going to eat Alex the Sheep No he

says no he's not going to eat what why

not well because then I'd be shout out

shout out then I'd be eaten as well then

he'd be eaten well let's see if he would

have been eaten so had he eaten Alex the

Sheep then he would have fallen asleep

and then he'd have been in danger of

being eaten by CHR by Chris Chris would

you have eaten Ryan no ah so he wouldn't

have eaten him in fact in fact looks

like Ryan would have got a free lunch

right there are no free lunch economics

something's wrong all right all right

and why is Chris worried about it Chris

is worried about it because Chris

because Chris is worried about Isabella

Isabella eating him and what am I doing

wrong what's wrong with this analysis by

the way before we say what's wrong how

many of you how many of you in Ryan's

shoes would have eaten the sheep and how

many of you would not have eaten the

Sheep okay what am I doing

wrong I'm in totally the wrong part of

the room I shouldn't be here at all

right I shouldn't be at all in this part

of the the classroom I can't get round

wait a

second excuse

me all right I should

be which row was my were my Lions

where's my lion row okay I should be way

over here with the baby lion whose name

is e EG yeah so EG is a little baby lion

very cute but EG if he gets a chance to

eat is going to eat why is he going to

eat cuz there's no one to eat him all

right so if a gets the chance to eat the

second last the second babiest lion

whose name is John John then EG will eat

all right so if John gets a chance to

eat Ben Ben is John gonna eat Ben John

are you gonna eat Ben no no John's not

going to eat Ben because John knows

he'll get eaten by EG so Ben if you get

a chance to eat vid vid are you going to

eat are you going to eat vid wait a

second wait a second so we we just

argued that that if you eat then the

second largest lion whose name was John

John is not going to eat you yes okay so

we have we know the littlest Lion's

going to eat so the second littlest lion

is not going to eat so the third

littlest lion can eat safely so the

fourth littlest lion should not eat

right so the fifth lion should eat we've

got eat not eat eat not eat eat eat not

eat eat not eat eat not eat eat not eat

eat not eat eat not eat eat not eat eat

not eat eat is that right is that right

so in fact you should have eaten him but

the more important point is how should

we have analyzed this

game IND what should we have used

backward induction how many of you use

backward induction be honest how many of

you so what's the point here the point

the point is

this five minutes ago I said the most

important thing you'll ever learn at

Yale is backward induction then I

distracted you with some fairly

irrelevant

nonsense and 5 minutes later nobody used

backward induction so the main lesson

from today the we're going to pick up

and Wednesday is to use something what

are we going to

use all right we'll see you on

Wednesday