just a little bit of
housekeeping and a refresher while i get
everything set up so firstly with the um
homework um i converted the scores to be out
of four i've updated the bright space and
i've like made the the other thing worth
nothing but it will still be there on
your mcgraw hill don't worry though I've
done what I needed to to get it and be
correct on Brightspace. So while I'm going
through everything let's just play
a quick game. Everyone chooses a
number between one to a hundred and the
winner is the one who chooses a number that
is closest to two -thirds of the average
choice in the class. So while you're all
doing that and thinking about that just a
reminder of What we did last week is we
started talking about this idea of strategic
interactions and game theory. And this idea
of Nash Equilibria, which once again,
remember, is defined as a situation where
no one on their own can be made better
off by changing their strategy, given everyone
else's strategies. That's all
Nash Equilibria is at the end of the day. And we looked at one
-shot games, and we looked at what happens
in one-shot games when there's no pure
Nash Equilibria. but you can still find
a Nash Equilibria in terms of mixed
strategies. So mixing your strategies with
different probabilities. We then went on to
talk about repeated games. And can
anyone remind me, in a 10-round Prisoner's
Dilemma, where both players know
how many rounds there are, what is
a Nash Equilibria? Yeah? It's just
about always, or betrayer. Yeah,
always defect. Yeah. So in the 10th round, This is essentially a
one-shot game, it ends after this, both players
know that, so they should both treat it
as the one-shot game and both defect, which
means, if we go back to the ninth round, because
decisions have been locked in for the
tenth round, the ninth round is now essentially
the last round where people can make a free
choice, so they treat that as a one-shot
game, they both defect, and we keep rolling
back until the first period, and we find that
the national equilibrio is to defect in every
period. On the other hand, we looked at
both infinite games and games that have a
probability of continuing or ending, which means
there's not a certain end point. And we found
that in those games, there are many
strategies, in fact, an infinite amount of
strategies that are plausible in our equilibria,
including always cooperate, always defect, and a
couple of interesting strategies we talked
about, tit for tat, that you start by
cooperating, then just do whatever your opponent
did in the previous round. and grim trigger
strategies where you say you'll cooperate
but as soon as someone defects on you you defect
on them forever and we showed using these
grim trigger strategies that you can actually
sustain cooperation depending on the
interest rate in infinite games and on the
continuation rate in these games where there's some
chance the game ends and some chance the
game continues and i ivan do you want to give
the quick lowdown on what you told me after
class on friday i found it's really interesting
yeah yeah I work overseas in the summer
for my family's liqueur business and one of
the things I do there is I work on the market
so all the stores that we sell to you
have to restock what do you sell by the way
like different types of liqueur and spirits and
once you restock the products you have to put
them on the shelf and like put the box in
the back they don't really have many people
who do it for you there and when you're like
when you're restocking like your product next
to competitors a lot of different brands
kind of like to like mess with your stuff
almost like the defective like you were saying
like the defective part instead of cooperating
where like you kind of just you put your
stuff there and leave it and then you don't
touch theirs then once you know someone messes
with your product or like people start
messing with each other products it just goes
like a catastrophe and it makes everyone's uh
job ten times better and you have good
relationships with some brands that you cooperate
with but if someone defects on you and the
other brands you'll defect back on them
essentially well i'm gonna try not to try not
to okay you probably should though grim trigger
strategies are important okay great so has
everyone filled this out fantastic so this
is another very famous game and i and i'll
show you why i decided to add this in last
minute last night it's called a keynesian
beauty contest and the question i have for you
is in this game where there's what 30 of us
in the room right now so 30 players is there a
Nash equilibria in this game where everyone
plays a strategy where no one can be made better
off by unilaterally deviating even everyone
else's strategy. Crack at it? I mean
either there isn't one or it's everyone picks
one. It either isn't one or everyone picks
one. What's your intuition for the latter? Why
everyone picks one? My intuition is
just it's the lowest number you can
possibly pick. Okay. So yeah okay and
no no reason to the rhyme just like the
intuition there yeah exactly yeah so there
is a Nash equilibrium in this game and
you're right and the logic is perfect
there it's one why is this the case we're
going to use backwards induction the
rollback equilibrium here and this is one
reason why I wanted to bring this game in
is that we're going to talk a bit more
about backwards induction today and I
think this is another way to think about
it so in this game assuming everyone
is rational which is the assumption we make
if everyone picked the highest possible
number of 100 that would mean the
winning guess which is two-thirds of
the average would be two-thirds times 100
which is 66.6 so 67 what that means is no
rational player should pick a number above
67 since 67 will always do better than
any of these numbers compared to those numbers
this is a dominant strategy so if
anyone's rational if everyone's rational no
one will pick a number above 67 that's the
first step and what this means is now rational
people aren't picking between 1 and 100
they're picking between 1 and 67 then if
everyone picked this new highest possible
number based on cutting down the range due
to rationality if everyone chose 67 then
the average would be two thirds of 67 and
that would be 46.7 once again what this means
is no player should rationally pick a
number higher than 47 as 47 dominates 48 49
50 so on and so forth and then step three
to end we just keep repeating and iterating
this process diminishing the range until we
get down to one, which is the Nash
Equilibria of this game. However, how do
people actually behave? Hands up
if you chose one. Did anyone choose
one? So no one played the Nash Equilibria.
People played different things. Michael,
what did you pick? Why 67? You just just
thought like a kind of a random
guess? Yeah. Perfect. Random guesses
totally like fine or good? Did anyone choose
33 by any chance? Did anyone choose 33?
Why did you choose 33? Did anyone choose like
between 20 and 25? Okay, let's go
up here. Why did you choose
between 20 and 25? Okay, in case
everyone was thinking like that. Yeah. Anyone do like
15 around there? Did anyone
pick around 15? Yeah? Why did you pick
15? Oh, I chose 11, but it was kind of
like that rollback thought like, oh, I pick
67. I'm thinking about picking that. If
everyone else does that, I'm going to be wrong,
so I should kind of keep rolling that
down. Fantastic. Anyone else want to share
their strategy before I move on? Any other
interesting insights? So when we run
these in the lab, this is a very
well-known game. We find that the average guess is usually
around 21, meaning the winning
guess, which is two-thirds
of 21, is 14. And this is due to
people being different types of what we call
K-level thinking, the order of thinking,
and Atava, I think you asked me this after
class last week, this is another reason why I
want to include this, shows about how you
think about how others are going to play, and
that is a lot here. so the zero level is
people who are kind of unsure how the game
works there's a lot of moving parts going on
and just doesn't random guess usually let's
say around 50 and then we have our level
one thinkers and they think is exactly as
Atava thinks in the sense that hey you know
everyone's guessing like kind of randomly then
the average will be 50 and that means two
-thirds of that will be 33 and that will be
the winning guess so that's how people who
think that most people zero level thinkers
but you can go a stage beyond that and be
second level and think that hey if everyone
else is first level thinkers then they're
going to pick 33 because they think everyone
else is going to choose 50 but if everyone's
doing that then i should choose two-thirds
of 33 which is around 22 because then i
will win because two -thirds of 33 is around
22 and then it's logan yeah then as logan said
um he picked around what was it 11 yeah
so around 11 to 15 would be the third level,
so on and so forth. So your challenge
was not to select the answer our rational
decision-maker, our homo economicus would give,
but to select a number that reflected your
best guess of what other people would do in
this class. And no one here actually selected
what the national equilibrium is. So this
is data from a typical experiment and this
is kind of what we find. All the modal
points are these different level of k thinking
so our first level of thinkers pick 33 second
level 22 our winners around here and a lot
of people still play the national equilibrium
some people find out about it in classes
like this go off to the lab and be like
oh i know what the national equilibrium is
and they don't win they select what the national
equilibrium is but they don't win and this
is a nice difference in terms of how
people you know should rationally act according
to theory but there are deviations when
you go a bit beyond the basics of theory as
well so a couple of professors who work a
lot on k-level thinking in games and how these
high order beliefs should affect your
strategies and finally the other reason why i
brought this in um this game besides it being
cool and looking at backwards induction
is that it's the first game we've looked at
here that involves multiple players so
we've only looked at two player games so far up
until then which was everyone in this class
and could be you know an infinite amount of
people really and the other multiple player
game I want to look at is the public goods
game so this goes back to our idea of public
goods as a market failure and we can now
look at it in the game theoretic framework
so recall that in our public goods problem
the thing that people should do is free ride
and we showed graphically that it's always
better to say you don't value a public good,
then you value the public good. So hopefully
you remember that. So the public goods
game works as follows. There are, let's say,
five players, and each person starts with
an endowment of $10. Every player can
choose whether to contribute some,
none, or all of their endowment
to the public pot. Every dollar a
person doesn't contribute they
keep for themselves is just worth a
dollar to them. Every dollar they
contribute to the public pot will get multiplied
by a factor of two and get equally divided
amongst all people so if you give one
dollar it'll turn into two dollars and they
can divide it by five and then everyone
receives 40 cents of those two dollars two
dollars divided by five so a public goods game
when you think about it is an essentially
a multiplayer prisoner's dilemma where
you have two types of strategies you can
cooperate by putting money into the public
pot or you can defect by not putting anything
into the public pot and like the prisoner's
dilemma in the national equilibria
everyone defects and nobody transfers anything
to the pot however once again similar
to the prisoner's dilemma if everyone
cooperated everyone would be much better off
so once again we have kind of this tension
between the incentives and what's actually
best for society. So here's an
example. We have our five players,
A, B, C, D, E. They each start
with $10, and in this scenario,
they all contribute $10 to
the public pot. So the pot is worth $50, and it gets multiplied
by K, which is 2 in our case, and
it becomes $100, and that multiplied
pot gets divided by 5 and evenly
distributed to all players. So
100 divided by 5 is 20, and all players
receive $20. So they're all $10
better off than what they started with. If none
of them gave anything into the public pot,
they'd all have $10. So they're all twice
as much better off. However, what happens
when one person defects on the
group's plan? So in this case, they've
all agreed to, let's say, put $5 each
into the public pot. Let's say PlayE also
actually puts in $5. So if they all put in $5, the pot will be $25. multiplied by k will
be 50 so multiply by two will make it 50
divided by five they each get ten dollars from
the public pot so they all kept five dollars
themselves put five in the public pot so
five plus ten what they get back is 15
every player gets 50 but as you see here play
is defected on the plan here play is
contributed nothing so the public pot is 20
multiplied by k is 40 divided by 5 is 8. So
that means all players get 8 back from the
public mob. So all the players who put in
5 get what they have remaining 5 plus 8 which
is 13 and player E who put in nothing gets
10 plus 8 which is 18. 18 is better than 15 so
they have an incentive to not follow through
the plan or not to cooperate and this
holds the logic holds for every single
player so you always do better by not putting
in versus putting in. When you think about
it every dollar you put in you only get 40
cents back yourself. It gets multiplied
by 2 divided by 5. So you're always better
off by keeping the dollar for yourself
but then that leads to an outcome where
everyone gets $10 when you can do much better
as you can see here. So this is an
essentially a multiplier prisoner's dilemma and
this is another way to look at public goods
as a market failure in general that no
one will actually contribute anything
into the public poll. Any questions on that? Great, so let's move on to
sequential games. We've spoken about
simultaneous games where everyone acts at the
same time. Sequential games on the other hand,
as the name suggests, involves playing
making decisions in order with knowledge
of previous actions. These games are
typically represented in what we call extensive
form which uses a game tree remember our
simultaneous games we use normal form which
is the game table so normal form extensive
form and we can analyze and find the
Nash equilibria in these sequential games using
backwards induction so this is what a
game tree looks like and the way it works
is here we have two players player one and
player two and they each have different
nodes and at each node is when an action occurs
so this game starts with player one up
here at this node and they can choose either
up or down those are their two actions at
this node and then player two can act
depending on what player one does if they chose
up player two can choose left or right they
choose down player two can choose left or
right as well and then you have the payoffs
in each situation the first payoff in the
bracket so here this corresponds to the first
mover in the game so player one and the
second number of the bracket corresponds to
the second um person moving the game which
is player two and so the representation of
this game in extensive form summarizes the
players the information available to them to
each stage we're going to assume perfect
information for now, the strategies and
actions available to them, the sequences, so
the order of moves is really important, and
the resulting payoffs. So as we talked
about before, what backwards induction
is, is a solution technique for
solving dynamic games of complete and
perfect information. So information is
complete when players pay off functions
of common knowledge, everyone knows what
everyone else can get, and information is perfect
when each player knows the full history
of the game at the time she or he moves.
We're probably not going to get into it
in this course but there are a number of
classes of games where you don't have this
perfect information. Where you don't actually
know what decision the previous player
took and it actually matters what they took
for your payoffs but you're under some
shroud of uncertainty. So as we talked about
with the 10 round prisoners dilemma or just
now with the Keynesian beauty contest, the
process proceeds by first looking at the
last possible action determine what the last
player will do in each since you in in each
situation using this information one can
then determine what the second to last player
will do this process continues until one
determines all possible actions so let's go
back to our game here sorry what was your
name again kevin kevin Great. Kevin, so you're
player two here. Yeah? Yeah. So let's say
player one chooses up. What are you going
to choose, Kevin? Left or right?
You're player two. Left. You're going to
choose left? Why left? Not sure. Not
sure? So what do you care about
as player two? What do you want
to maximise? Oh, am I going to be on
the right side? Yeah. So player two's
payoff is on the right here. You want to maximise
your payoff. So what are you going to choose?
right okay brilliant so you're going to
choose right so that means this option is
never going to be chosen we can essentially
cut it off completely and kevin if player one
chooses down what are you going to choose
left or right yeah left one is greater than
zero once again that means this option right
is never going to be chosen it's essentially
locked off completely so this is how backwards
induction starts so as you can see we've
cut off both these options and what
this means is now we go up to the node before
it we've done this node this one only has
two moves essentially the second mover
and the first mover but now what player
1 needs to decide is to choose up or down
and they know that if they choose up player
2 will choose right they'll never choose
left and if they choose down player 2
will choose left they'll never choose right
so they shouldn't ever consider the
possibility of getting 3 here because they know this option is
not possible All they compare is
up right to down left. And Kevin, I'm going
back to you here. You're now player
one. Are you going to choose up or down
based on all this? Up. So you're now in
the... I should ask someone else because
you're in player two's mindset. But I want
you to be in player one's. You're now
player one. What do you do as player
one? The first payoff is the one you care
about as player one. What do you do to
maximize your path? Another option. Yeah, so if you choose
up, you know player two is going to choose
right. you're going to end up with one but
if you choose down you know player two is going
to choose left you're going to put two two
is better than one so you're going to
choose down and that's because you know what
player two is going to do in each situation
that's how backwards induction works you can
cut off all these branches until you're only
left with one in this case this is the only
branch left and this is going to be our sub
game perfect Nash equilibrium of this game
which we found using rollback arm equilibria
or backwards induction. So a little bit of
a technical term here is this idea
of sub games. So a sub game is
a part of a game that can be
played as a game itself. It begins
at a single node and contains every
successor node. So does anyone
want to guess how many sub games there
are in this guy? I'll come back to
you in a second. Does anyone else want to
take a crack at it? Okay. Three. Okay. Three is the
correct answer here. Why do you think
it's three? You have three
total nodes. One for the first player
and then two for the second player.
Exactly that. So let's look at
this node here. So if player one chooses
up, then we're at this node here and
this is a sub game it's not the most interesting
game players who just makes a decision
between left and right but it's still at a single
node and encompasses the remainder of the
game so this is a sub game and as a result
we can look at the other side here and
this is also a sub game and finally sorry
remind me your name as Zach said the entire
game itself is a sub game and this is the
one people forget a lot of people will look at
this and say two but the answer is three
because the entire game starting here going
there is also a sub game so an exam question
i could easily ask is you know how many
sub games are here zero one two three and i
have 50 percent of people will get this
wrong and say two so be aware that it's three
the whole game is a sub game so a Nash
Equilibria is sub game perfect if every player
plays a Nash equilibrium in every sub game
so this seems pretty technical I'm going to
give you a couple of examples in a second but
in terms of the logic a sub game perfect
equilibria are always Nash equilibria so it's
a sufficient condition to be in Nash
equilibria but not all Nash equilibria sub
game perfect and we'll get into the reasons
for that in a second so in this case here the
unique sub game perfect Nash equilibria which
encompasses all the games is player one
plays down player two plays left and it
takes into account what happens off the
equilibrium path player one plays up and player two
plays right. So those are the two pathways
that it could take and that results in
player two, player one choosing down and player
two choosing left. So yeah we have this
here. So let's talk about mutually assured
destruction and we'll get more into this idea
of sub game perfect national equilibria
and credibility so since world war ii the
usa and russia have um had a large arsenal
of nuclear weapons um this was especially
true during the the cold war why didn't we
see a nuclear attack any um political science
history majors want to talk about why like
isn't it weird that like with all these
stockpiles or nukes all these proxy wars everyone
hating each other there was no nuclear
attacks. Kevin? I think it was the concept that
if one person fires everyone fires so no
one loses. Exactly. So you can use
the nukes as a deterrent
essentially saying if you fire on us
we'll fire back. So that's what mutually assured destruction is. So it's essentially
this military doctrine very famous that
when there are two superpowers that
have large arsenals of destructive
capabilities, they can actually maintain
cooperation and peace by threatening to
annihilate the human race in the event
of an enemy attack. Is this threat actually
credible though? So here's a simple
game to talk about credibility. So you
have two players here, 1 and 2. Player
1 can choose down, the game ends,
they both get 2, 2. And player 1
can choose up, player 2 can choose
left, and the playoffs are 5 and 1. or 2, and
they both get 0, 0. So, let's say, player 2 says
to player 1, before player 1
makes a decision, that if you choose up, I'm going to choose R. If this is the case, then down right is
a Nash Equilibria. It's a Nash Equilibria
based on this. However, is
this a credible threat from player 2? Is it credible
for player 2 to say to player
1, if you choose up, I promise
I'll choose right? As player 1, would
you believe this? Kevin? I don't think
so. Why not? Because it's more
rational for player 2 to choose L because they
get 1 over 0. Exactly. So remember, in
game theory, in this framework
we're looking at, everyone just wants
to maximize their payoffs. and
just tangentially your payoffs could
end up being like utilities and they could
encompass all sorts of things but it's
that number there that matters and because
player 2 gets more if they choose left
they get 1 then right that means the
threat of R is not credible and player
1 should know that if they choose up player
2 will choose left so this actually isn't
a credible threat so why did mutually
assured destruction work if it might not seem
credible in this way one you can kind of
take gripe with the payoffs themselves but
it's more about what constitutes a credible
threat or not so players firms or world
leaders even can take strategic moves and these
moves are actions that change the actual game
being played typically from a single stage
to a two-stage game they come in two different
forms unconditional which are commitments
to an action and conditional which are
threats and promises. For commitments
to be effective they must be both
observable by everyone and irreversible.
Once you commit to it there's
no backing down. Unconditionally strategic moves, these commitments, what they essentially
do is they cut off options from a game tree
so you have no other choice except a certain
action so for example using our mutually
assured destruction example if the country
creates a technology where they detect nukes
from the other country it automatically fires
back there's no way to override it they're
locked in if this happens and now we can
talk about what happens if there's error and
in fact there's a famous story with
Stanislav Petrov I don't know if anyone's heard
that name, but we're all sitting here today
because of him. He was a Russian, a high
figure in the Russian, the USSR army, and they
detected nukes from the US, and they were
told to fire everything back, and he said, no,
let's just wait and make sure. It wasn't
actually nukes, it was like ducks flying in
a bee or something like that, that got
misread, so we could have had a catastrophe,
and this is definitely a risk with these
types of automatically fireback systems but
what this does is by committing to r in advance
for this autonomous choice mechanism you're
cutting off l l is gone from the game tree
so when player one's making a decision
they're like if i choose up player two is
committed to choosing r i get zero i might as
well choose down so you can use these commitments
to trim your choices essentially to make
the other player act in a different way so
this is the idea of a strategic move the
other thing you can do is conditional and
these involve threats and promises so a
threat involves specify negative consequences
to the other player if they do not play as
you wish if you don't clean your room you
won't get dessert for example if you
hand your homework in light you're not going
to get graded on it. Threats and promises
only achieve their objective if they
are credible. That is, they only
work if the other player believes they'll
be carried out as stated. Otherwise,
it's cheap talk. So a simple example
of a credible threat that we talked about is
grim trigger strategies in the repeated
prisoners' dilemma. This is a threat. You're
saying, I will cooperate with you, but if you
defect on me once, I'll defect forever. And
as we show mathematically, this is a credible
threat. so things like repeated games
where there's reputation on the line like if
you tell a student that if you had in
your homework plate i'm going to give you a 50
penalty or i'm not going to grade it but then
you do end up grading it then you can't say
that to anyone else anymore you've lost
all credibility there so credible threats
are really important finally another thing
you can do is make the other player believe
that you are crazy or irrational and you might
take an option that hurts both of you so
there's a famous game called um chicken has
anyone seen the movie footloose by any chance
okay i'm old um 1980s film with kevin
bacon where they band dancing in a town and
there's a whole thing anyway one of the the
scenes he gets challenged to some competition
by like the the school like hot shot and
what they do is they drive two tractors
towards each other this is known as the game of
chicken they have two actions each they can
keep going straight or they can swerve and
if you swerve you're essentially a coward
which is bad so if they both swerve they're
both considered cowards they both kind of lose
they both go straight they crash into each
other that's the worst outcome they
both end up in hospital but if one goes straight
to the other swerves the person who swerves
is considered an even bigger coward the
person who you know drive straight is the
the macho person and they win the game so you
see what we just talked about can anyone give
me an idea of how you can change this
guy through all the conditional unconditional
strategies if you want to win this guy what
can you do yeah yeah to make it quicker yeah
they need to believe that you actually want
to hit them so you keep accelerating
exactly if you rock up to the tractor looking like
someone from Mad Max Fury Road you know you
can probably give off this vibe of you're
absolutely crazy and if they believe you want
to do something even if it hurts you a lot
then that you know changes what actions
are possible they think you're going straight
no matter what it's better for them to swerve
than it is for them to go straight they're
better off even though they still have negative
utilities better than what it would be
if they would strike so that's a good example of
a conditional strategy an unconditional
strategic move would be something like just
before you're about to start or as you start
accelerating rip the steering wheel off and
throw it away it has to be observable to
them so yet with some caveats you can't swerve
you can only go straight that essentially
removes an action from your game tree so once
again they can only choose between swerving
and going straight given that you're going
straight given that they should swerve instead
of going straight and you win so here are
two like kind of things talking about these
unconditional commitments so this is from a
movie called Dr. Strangelove or how I
learned to stop worrying and love the bomb famous
film from the 60s by Stanley Kubrick this is
Peter Sellers playing Dr. Strangelove and the
movie is about nuclear war as we talked
about between the USSR and the USA and the USA
essentially develops this doomsday device
that will go off if the USSR attacks him and
destroy the world and the US like military is
telling Dr. Strangelove that it's you know
this great deterrent device and it will
save all of us and then he asked him have you
told the Russians and he's like no we haven't
and then he famously says the whole point
of the doomsday machine is lost if you keep
it a secret the whole point of a deterrent is
it needs to be observable and credible this
might be credible but it's not observable
the USSR has no idea about it so in their
minds the game hasn't changed so if you are
using commitments make sure they're observable
and secondly Sun Tzu art of all I kind of
like this because it has the opposite sort of
logic build your opponent a golden bridge to
retreat across so if for example player two
in this game cuts off option l and they only
have option r what you can try and do is
play one is build them a new option like some
negotiations or something like that by giving
them an out they're not going to go all in
on what's making them in the world worse off
so just like it's in your own of best
interest to cut off your own strategies to make
a commitment feasible and the reason why
it's in the art of war it's the idea is if
they burn you know the bridge and there's no
retreat they're gonna like fight until death even
if they lose you'll have casualties as well
so by building them a golden bridge you
can still win but make sure you don't have
any casualties yourself so the last thing on
credible threats some of you may have seen
this video before. It's called Golden
Balls. It was a game show in the UK for
a while, but they'd play a bunch of games
for 40 minutes to make money, and then the
two players at the end would do split or
steal, essentially. And they both split,
they'd both get half the money, they
both stole, they both got nothing, and if
one split and one stole, the person who
stole got everything. And this is a very
famous interaction in the game. They
usually talk about it and split or steal
whatever yeah actually a really good point
what's your name sorry Cole so yeah thank
you for raising this and I think it's actually
important to discuss so in this framework
no because players will always choose
what's better for them but the thing is in
our current model we're not taking into account
things like spite inequality and things
like that So when you change the way
you think about what people care about, and
we have models such as inequality aversion
models, intention -based models. For any of
you considering taking behavioural economics,
this is what we go into, that if people
played this game, a lot of people
would probably choose 0-0 over
5-1 because they don't like
the inequality. So this is actually
behaviour we see a lot. But that would actually
change what the payoffs are into utilities
based on people's utility functions.
So the numbers still matter. So the answer
is no. but great point okay back to
golden balls so this is a famous example of
one of the discussions happens when
you get a genius to play split or
steal 100% I'm going to pick
the steel ball I'm going to choose
the steel ball I want you to do split
and I promise you that I will split
the money with you you're going to take
steel I'm going to take split so you
take the money And I will split it with
you. I'll show you. I promise you
I'll do that. If you do steal, we
both walk away with nothing. I'm telling
you 100% we're going to do it. I appreciate
that. The only way you can guarantee
to walk away with 6,800 is to guarantee
that you both put the split ball in.
And I do now have to push you for a decision.
It's a tough one. We've lost it. We've
lost everything. We've lost it. We're walking
away with nothing because you're an idiot. Split or steal? Yes, congratulations,
you have both split and each
received 6,800 pounds. Okay, so if you go
on and see the full video, I did the brain
rot like one minute short here, just for
time's sake, but it's like a five minute
video, I think, and it has like 15 million
views. People love this clip. Does
anyone want to try and tell me what the guy's
strategy was? What was he trying to do
by saying I'm going to steal even though he
ended up splitting? The only viable way
for him to be with anyone is to go with
split and take him on his board. Because if
he goes with steal, it's 100% zero. Yeah.
So the other person guaranteed that he's
going to go to split. So the game was
now in his hand. So he could go
back on his board and go to split,
and everyone wins. Exactly. And sorry,
what was your name? Julian. Julian, were you
going to say the same thing? Yeah, I was
going to say a similar thing, just that he's
making sure that the other person okay great
um and he says I'll give you I'll give you
half the money after so everyone loves
this it's like a great strategy like cutting
off this guy's options and making sure that
he doesn't steal however is this promise
credible to share the money no it's not
like there's no reason that he should believe
him so essentially what this guy's deciding
between is I can split and if this guy
steals then i'll get nothing and he gets
all this money and if i steal and he steals we
both get nothing and as cole mentioned
before some people might like dislike this might
feel spiteful so the national equilibria
if this was a game for him to like split or
steal given the other guy's stealing it's
actually indifferent between what he should
do he gets zero every time but once you
throw in things like spite envy inequality
aversion etc i wouldn't have been surprised
if someone actually stolen that situation
because i was pissed off so everyone loves
this strategy but i think thinking about
credible promises and these other factors as
well i think matters a lot daniel is that
like the love thing technically uh so like
he was like pretending to like deceive the
other guy by like saying that he was going to
like like say steal it's a good question
so like we call this cheap talk so if
there's no credibility behind a statement
you shouldn't take it into account at
all so whatever he's saying doesn't really
matter he could say like anything really
but there's no credible way to determine
what he's saying there's a lot of models
some will look at these sibling models
where people will do something and you try
and update your beliefs based on what they
do or they say but content like this you
shouldn't change your beliefs at all based on
it okay great so let's finish up today with
another game so can I get um two volunteers
please anyone want to volunteer yeah Zach
yeah Cole come on up Zach can you stand
here Cole can you stand here I'll dump this
out on the table so it looks nicer um okay
so we're going to play this game we have our
two players here and you each can take an
action either pass or take so cole you're
going to be player one zach you're going
to be player two and the way this game works
is cole you're going to start here and you
can take and get one piece of candy get
zach get zero and the game ends or you can
pass it to zach and then zach makes the same
decision to take or to pass and this game
will end either when someone chooses to
take or when zach the last player chooses to
pass here do you guys understand the rules
do you want to you can talk about it for a
few seconds what you want to do i mean
i'll pass all the way through down down yeah
you guys stand okay so cole you're up first
you're gonna pass or yeah okay so we're now
here zach i'll pass Cole? I'll also
pass. Nice. Pass. I'll pass as well. I'll take. You'll take. Okay. So Zach, you get six.
Cole, you get four. You can choose
whatever ones you want. I'll be kind
in that respect. Zach, while you're
doing that, you agreed to pass all
the way through, correct? And then
you chose to take. Why did you choose to
take? I wanted more. Okay, exactly. He wanted
more. Cole, did you think there was a
chance he would take at the end? Um, yeah, I
thought there was a chance, but I mean, I
don't know, low stakes. Yeah, this is why,
this is why stake size matters a lot. If
we were playing for a million dollars, I
would have taken the one before. You
would have taken the one before, so you
would have taken here? Yeah, I totally would.
Okay, Zach, what would have you done
if we were playing for a high stakes? I
probably would have taken sooner than
that. Okay, fantastic. And we've
essentially worked out what the Nash
Equilibria is here. So think
about this game. So, oh, you guys can
sit down. Take your candy and sit down. so
let's start at the last node here so this is
zach zach chose to take here because six
is greater than five so cole here his two
options are to pass but he knows zach is
going to take so this option is never available
so if he passes zach will take and cole
will end up with four or sorry yeah or cole
can take himself and end up with five five
is greater than four so cole will actually
take here so for Zack that means if he passes
he knows Cole will take and he'll end up
with three or if he takes here he'll end
up with four so Zack will take and this
keeps going back all the way to the first node
where it's better for Cole to just take here
get one Zack at zero because he knows if
he passes Zack is going to take and Cole
ends up with zero so this centipede game
has a unique sub game perfect Nash equilibria
so we can count the sub games here so one
two three four five six there are six sub
games not seven I need to change that so the
unique sub game perfect equilibria for the
center big game is both players take it
every possible node essentially and the six
no player two takes fifth no player one takes
so on and so forth and to finish off today
i want to talk about this famous paper called
checkmate exploring backward induction
among chess players does anyone here a chess
player or has dabbled in chess at all by
any chance yeah okay christian why do you
think they care about chess players to study
backwards induction fair enough does
anyone want to take a crack at
this one yeah exactly that so I don't
know if anyone's um maybe during the
pandemic when we're all watching videos online
and stuff if you've ever watched like a
classical chess game either the world championship
or the candidates when they have
commentary and they sit there for 20 minutes
and they think about every possible not just
next move but like 15 20 moves down the track
in multiple different ways they're essentially
doing backwards induction in their own
way and in fact like game theorists like
to try chess players because technically
chess is a solved game it's you know got
these final payoffs essentially 1 0 0 1 or
half half and you can go all the way back it's
10 to the power 120 sequences which is
only more than the like grains of sand on the
beach or something like that so they haven't
solved it even though computers are really
close but technically it's a solid game so
the idea here is players that your people
that know how to use backwards induction should
be better at it than your average layperson
so what they did was they ran a centipede
game and another game as well with chess
players and famously in this paper um when
they were running this experiment john list
um told me that he had to get his ra to run
to the bank to take out money urgently because
the chess players weren't playing the
national equilibrium of taking the first time
they were passing it so they were earning
more money like um zach and and cole got like
what is it like nine of my my my little
candies here instead of one so they didn't have
enough in their budget they have to go out
and take money to pay the chess players so
even those that are experts in backwards
induction weren't playing the Nash Equilibria
so it's important to keep in mind what the
strategy says what the Nash Equilibria
says for these rational players as we saw today
in the Keynesian Beauty contest as we discussed
about you know other things such as
social preferences and you know anti-social
preferences like spite