Game Theory - Thinking Strategically

I'm alaya.
Hey, Betsy, you've joined us wearing boxing gloves. What's going on?
I'm just back from my workout where I was sparring
with a punching bag.
That honestly sounds a little dull to me.
Well, the good thing about working out with a punching
bag is I can focus on my technique without having
to think about what the bag's gonna do next.
Well, look at because Nas has just entered the ring.
Are you out for a match? Betsy?
How does this change things for you? Betsy?
Yeah, this sounds a little bit more fun, but I'm
gonna have to work a little bit harder.
Sounds like you're gonna have a lot more to think about.
Now, That's right.
Instead of just thinking about my technique, Now I gotta
start thinking about what Nas is gonna do? Is she
going to use a jab or a hook?
St back?
Step forward, lean left, lean right. I'm gonna have to
really be on my guard to think about what her
next movie is.
Well, what do you think she's gonna do next?
Well, it's gonna depend on what she thinks I'm gonna do.
Of course, my best response depends on what she does,
and so it depends on what I think she thinks
I'm going to do, And I'm pretty sure that will
depend on what she thinks that I think that she
thinks that I'm going to do.
It sounds like turtles all the way down. Now for
those of you who are listening, you're probably thinking, what
does all this boxing have to do with economics? Well,
a lot of life is like a boxing ring.
We don't mean everyone is out to punch each other,
but that a lot of life involves strategic interactions, which
is the word we use to describe situations where your
best decision depends on what others are going to do,
and their best choice depends on what you do.
And strategic interactions are all around us, whether you're dealing
with a business partner or a business rival, a geopolitical superpower,
or in your personal life.
The study of strategic interactions is called game theory, and
game theory is our topic for this week's episode of
Think Like in Aymist with me Betsy Stevenson and I'm
Justin Wolfers.
This is the podcast where we'll teach you the tools
from economics to transform your life and help you make
the best decisions. From the boxing ring to the boardroom,
or even just catching up with a friend. Journalist and
former economics student Nestra and Tuberculi far joins.
Us people often hear the term game theory and they
think it's about chess or some other sort of cerebral game.
You know knows.
I'm going to confess that's what I thought when I
signed up for the glass in college. And it turns
out it is kind of about games, but only if
you think all of life is a game.
We're talking about something far more broadly applicable here. Game
theory is relevant whenever your best choice depends what someone
else is going to do, and their best choice depends
on what you're going to do.
Most of life involves not just thinking about what you
want to do, but what the people around you are
going to do and how that affects what you should do.
So, if we go back to the boxing example, Betsy
hitting a boxing bag is not a strategic interaction because
the bag is just there and it's not going to
do anything. However, Betsy's sparring with me is a strategic
interaction because what Betsy does is going to depend on
what she thinks that I'm going to do.
So This is the interdependence principle applied to decisions, and
this sort of independence is everywhere.
Let's move from the boxing ring to the business arena.
As a business owner, you're going to have to think
about what your rivals are going to do a lot.
Take the example of trying to decide whether you should
cut your prices. Whether you're going to get more customers
is going to depend a lot on whether you expect
your rivals to react by also cutting their prices.
We also deal with strategic interactions in geopolitics. In fact,
a lot of game theory was developed during the Cold
War as the US tried to figure out how to
respond to Soviet aggression and the Soviets tried to figure
out how the US would counter. It's game theory, but
it wasn't a game.
Strategic interactions also happen just every day in our personal life.
You know, should you go to that party on the weekend, Well,
the answer is likely to depend on who you think
is going. So what you want to do will depend
on what they're going to do, and their choice might
depend on whether you're going.
But don't get overwhelmed. We can think through this systematically
using four steps to help us make good strategic decisions.
First, we need to consider all the possible outcomes from
a scenario, and that means considering all the choices you
may make and the choices the other party could make.
For each possible outcome, think about the payoffs, which is
to say, what you stand again and what they stand
to gain.
Strategic interactions can get tricky if you start thinking about
what they'll do, because that'll depend on what they think
you think they'll do, And pretty soon you're thinking about
what they think, you think, they think, you think they think,
and it feels like a whole way of mirrors.
The second step gives us a simple way out of this.
The second step tells to think about each of their
possible choices separately, or, as we like to say, think
about each of the what ifs separately.
On to the third step. For each of these what
if scenarios, your goal should be to play your best response,
which is to say, make the choice that yields the
best outcome or the highest payoff in that scenario.
And the fourth and final step is to put yourself
in someone else's shoes. Your best choice will depend on
what you and the other person may do. So you'll
need to consider things from their side too.
It's best to get as groups with all this through
an example, So let's do just that. We're going to
look at a game called the Prisoner's Dilemma using our
fourth step approach.
It's called the Prisoner's Dilemma because the original story used
to illustrate it involves two criminals who will call Bonnie
and Clyde. But before we dig in, realize this isn't
just a story about prisoners. It's a metaphor for the
many different ways in which it can be hard to
get people to cooperate what's in their best interest.
So for this example, Betsy, you're going to be Bonnie
and Justin you're going to play Clyde. You've both just
robbed a bank and fled from the scene. Now I'm
the police officer in charge, and I've arrested both of you.
My problem is that if I can't persuade one of
you to confess to robbing the bank, then I can
only charge you for fleeing from the scene, which has
a sentence of only one year.
Clyde and I discussed this before our bank heist, and
we both decided that we'll deny everything so that you
can only get us on that minor charge of fleeing
the scene.
Well, the thing is, I'm not going to put you
in the same jail cell, and I'm going to interview
you about the crime separately.
Hmm, this could be a problem. Indeed.
First off, it's you, Bonnie. If you help me out
and rat Clyde out and confess, then I'm gonna let
you go free, but I'll use that confession to get
a harsh three year sentence for Clyde. Me warn you, though,
that if you persist with denying, and if Clyde rats
you out, well then I'll throw the book it's you instead,
and you'll get the harsh three year sentence and I'll
let Clyde go free as thanks for the information.
So if we both deny, that's our original plan, we're
going to get a year in jail each, right.
That's right, and one more warning. If you both confess,
then neither of you really did me much of a favorite,
so you'll each get two years.
So we've now done step one, which is to think
about all of the possibilities in their associated consequences. What
I need to do now is move to step two,
and think about.
Each of the what ifs separately.
Bonnie, Whilst you deliberate, I'm gonna hop over to Clyde,
who's in a separate interview room. I'm going to offer
him a similar deal, so he'll have the chance to
rat you out and to go free.
Hi, Clyde Heynes, Welcome to my jail cell.
So you fled from the bancheist. You can deny the
crime or you can confess. Now. If you and Bonnie
both deny the robbery, you'll spend a year in jail each.
If you both confess, you'll both spend two years in jail.
Well, that's easy. I'm just going to deny.
Hang on, Clyde, I'm not done. If you confess and
Bonnie persists with her denials, then as a measure of
my gratitude, you'll go free and will throw the book
at her, so she gets three years. I'm going to
warn you, though, if you deny and Bonnie confesses, she
gets the free pass, and I'll throw the book at
you instead and you'll get three years.
Well I was going to deny it. Let me think
like an economist and move on to step two, which
is to think about each of the what ifs separately here.
The first possibility is that Bonnie denies.
Yeah, that was the original plan. Now, if she denies
and I follow through on my promise to deny it,
then we'll each just get one year of jail.
Is that what you want to do? Remember if you
rat her out, you'll go free.
You're right, And no, I really want to avoid jail time.
So if Bonnie denies, I'm better off confessing.
And the other possibility is that Bonnie confesses.
If she confesses and I deny, then it's like she
readed me out and I'll get three years.
Right, And remember I told you that if you both confess,
you'll get two years each.
So again, I think I'm better off confessing.
It seems like you're better off confessing.
Whatever Bonnie does, that's right, So look for kit that
earlier plan we hatched. I'm going to confess to rubbing
the bank.
Okay, I'm going to leave this room and head back
to Bonnie. Hey, Bonnie, have you made up your mind?
I know that Clyde and I told each other we'd deny,
but I just can't stop thinking about what will happen
if Clyde pulls out.
Of our plan.
Okay, tell me more.
Well, if he confesses and I stick to the plan
and deny, then you're gonna give me three years. But
if he confesses and I also confess, that I'm only
going to get two years.
So if he confesses, you also to confess.
Yeah, if he confesses, I really want to confess.
But here's the thing.
If he denies, I'm also better off confessing because by
ratting him out, you're gonna let me go free.
So you have this fabulous plan where you are each
gonna deny the crime, but now it sounds like you
wants to confess.
The problem is, I just don't trust him. Who's to
say that I'm sitting here denying and thinking of what's
best for both of us and he just thinks about
himself and instead confesses and gets to go free. Denying
is too risky. Clyde is not trustworthy enough. I'm gonna confess,
are you sure?
Yes?
So Bonnie and Clyde both confess and both go to
jail for two years.
Okay, I'm then being Bonnie. I'm Betsy again. What we've
just seen is something called a Nash equilibrium. That means,
if I'm making the best decision I can based on
what I think Clyde is doing, then I have no
incentive to make a different decision.
And if Clyde is deciding on what's best for him
given what he thinks Bonnie will do it, then same same.
So in a Nash equilibrium, we're each doing the best
we can given what the other is doing, and so
neither of us wants to change what we're doing, and
that makes it an equilibrium.
We need to be clear and Nash equilibrium, that's our
forecast for what will happen. We're not saying that it
should happen or that it's the best outcome, but we're
saying that when Bonnie and Clyde each pursue their individual
self interest, we may actually get to this outcome, which
is worse for both of them.
Don't forget, and the equilibrium is a forecast of what's
going to happen and not necessarily what's best for society.
Now here's a really big thing. Bonnie and Clyde could
have cooperated with each other and stuck to their original plan.
They could have both denied the crime and gotten one
year each in jail. But when you separated them, nets
they didn't trust each other. They didn't trust that they'd
take the sweet deal you were offering if they can fist.
So by not cooperating, Bonnie and Clyde ended up with
a worse outcome.
It's a worse outcome for each of them. It's a
worse outcome for Bonnie and it's a worse outcome for Clyde.
Right, they've both been better off cooperating, but in the
end they didn't and now they're both worse off.
Yeah, it's crazy, right.
You know.
I recall when I was an economic student and we
learned about Adam Smith and the invisible hand and how
if you let the market do its thing, then everyone benefits.
Or rather, if you allow people to pursue their self interest,
you'll end up with the best outcomes for everyone, which
is a really idealistic notion. But this example seems to
fly in the face of all of that.
Yeah, because by thinking about themselves, Barnie and Clyde ended
up making decisions which aren't in their interests.
They don't end up doing what would be mutually better.
This is one of the most important insights in social science.
Even when it's in our joint interest to cooperate, sometimes
we fail.
Adam Smith was thinking about perfect competition. When you have
lots and lots of businesses in a market, one person's
choice doesn't affect the other person that much. But when
you're dealing with situations outside of that, well, your best
choice will depend on the best choices of others. So
you need to think hard about all this.
Remember game theories about strategic interactions, those cases where your
best choice depends what other people choose. That doesn't really
apply to perfect competition.
We ended up with Bonnie and Clyde thinking that the
other may dub them in, so the best choice was
to save themselves and to confess. So the Nash equilibrium
is both confessing and getting two years in jail each.
The prisoner's dilemma comes up in all sorts of scenarios,
not just ones involving jail time. Think about politics.
Yeah, so I think there's too much money in politics,
and if I run for Congress, I want to commit
to not taking corporate donations.
I'm going to run against you. I'm also disgusted by
the influence of money in politics. So given that we
both agree on this, noble aim, Betty, it should be
pretty easy for us to agree not to take corporate donations.
I'm guessing it's going to be harder than that, though,
because of the prisoner's dilemma. Betsy, tell me what you're thinking.
Well, if Justin takes a lot of corporate contributions and
I refuse them, then I'm not going to achieve anything
because I won't get elected. So I feel that if
Justin accepts donations, I'm going to have to accept donations
as well.
And if Betsy decides to take corporate contributions, then I'm
going to have to accept them as well, for the
same reason. The alternative is letting Betty by herself an election.
So there's a Nash equilibrium hit in which Betsy accepts
corporate contributions because she fears that Justin will, and Justin
accepts corporate contributions because he feels that Betsy will. Either
of you want money in politics, but you both accept money. Now,
remind me of why.
If Justin's taking their money, my best response is to
take their money.
And given the Betty's going to accept corporate money, my
best response is to take corporate money.
There's a better world out there, but I don't know
if I trust Justin enough to help us get there.
And like Betty, I want to get rid of money
in politics, but honestly, I don't trust her to take
the first step, and.
So you're both sort of trapped in this outcome that
neither of you want. That really is a dilemma.
Yep, it's the prisoner's dilemma.
We've just looked at strategic interactions where there can be
a difficulty with cooperation, so both parties end up with
a worse outcome than if they had cooperated. There are
also strategic interactions which may become tricky due to issues
with coordination. This is less about each party not trusting
the other and it's more about problems with coordinating with
each other.
Right about coordinating can come up in everyday life. I
mean when I first started dating Justin, we'd talk on
the phone. If the phone call dropped out, you think,
should I call him back or should I let him
call me back?
Why is this a strategic interaction?
Well, I want to organize a date with him, and
I can call him back and continue planning where we're going,
what time we're meeting, or I can wait for him
to call. I mean, if he's interested surely he'll call back.
And I'm pretty much thinking the same thing. I mean,
I want to go on a date with Betty, so
I'm happy to call to sort it out. But maybe
I should wait for her to call back, because if
I pick up the phone as she's calling, then we'll
never connect.
It's such a delicate balance, tell me about it. So
what if you're both being really call pa DM and
assertive and both of you call back, Well.
Then we can both end up getting each other's voicemail.
Or you can both wait for the other person to.
Call, and then we might not end up speaking at all.
The problem here is we both want to have the
conversation so we can organize that next day. So there
are two outcomes that would work well for both of us.
Either Betty waits an I call back, or I wait
and Betty calls back. The problem is that we might
never get to either of these If I think Betty's
gonna call, all wait. But if I'm wrong and she's waiting,
we'll never connect.
This sounds kind of trivial, but really, the way to
think about this is the phone is just a metaphor
for the difficulties of coordinating when your best choice depends
on what someone else does.
In our macroeconomics season, we talked about expectations and how
what people expect can end up happening. Well, that's got
a lot to do with coordination games.
For example, you'll often see newspaper reporters the media start
talking about a recession, which will lead people to feeling
a little bit nervous about spending. And then businesses worried
that people aren't going to spend, so they cut their
production and they freeze hiring and so on, and all
those worried murmurs about it recession, they can actually end
up causing a recession.
This is really interesting. Let's break this down a bit, Betsy,
shall we say you're the representative for all businesses in
the economy, and justin you represent all workers who then
go out and spend their wages.
So basically, Betty's the aggregate supply side of the economy
and I'm aggregate demand.
Yes, now, what's going on here?
Well, businesses usually have two options. We can produce a
lot of goods and services and therefore us will hire
a lot of workers, or we can cut back on
production and hiring.
We workers have choices as well, we can go out
there and spend our wages, or we can cut back
on spending if we're worried about losing our jobs.
Now, let's see what happens by breaking this situation up
into a series of what ifs. What if Betsy's businesses
produce and hire a lot justin, how will your workers respond?
Well, we feel like we have job security, so we're
gonna spend a lot of money.
Okay, And Betsy, what's your best response to workers spending
a lot?
It makes sense for us to keep producing a lot,
which means that we have to hire a lot of workers.
Okay, So this is an equilibrium. If Justin's workers are
spending a lot of money, Betsy's best response is to
produce a lot of things for them to buy. They're
each making the best response based on what the other
is doing. And this is what we call a Nash equilibrium.
And this good equilibrium is basically good economic times.
Now let's look at the other what if scenario. What
if Betsy's businesses are cutting back, hirings down, and Betsy's
factories aren't producing as much Justin, how will your workers respond.
We're worried about losing our jobs, So we're going to spend.
Less and Betsy, how will you respond to Justin's workers
spending less money?
Well, if people aren't buying as much, then we need
to produce less, which means that we don't need as
many workers, so we'll probably have to cut our workforce.
So now we're at another Nash equilibrium. You're each playing
your best response to what the other person is doing.
The sad thing here is that this is a Nash equilibrium,
which yields a recession.
And our overall point is that when both parties can't
coordinate with each other, we can end up with more
than one equilibrium. And sometimes one is a really good outcome,
like a boom, and the other is a really bad outcome,
like a recession.
And the problem is we can get stuck in the
bad equilibrium even though we all prefer the good equilibrium.
And this is why expectations are so important. If I
can convince Justin's workers to believe we're in a good equilibrium,
they'll buy a lot, and that's enough to convince me
to produce a lot. But if they don't believe me,
they'll worry about their jobs and cut back on their spending.
And that's the problem that FDR was talking about when
he warned it the only thing to fear is fear itself.
So today's tour of game theory seems pretty grim. The
prisoner's dilemma tells us that it can be hard to
get people to cooperate even when it's in their best interest,
and coordination games tell us that it can be hard
to get us to coordinate on the better of many options.
So nas, let me conclude with a bit of good
news instead. All the examples that we've been talking about
what economists call one shot games, in which you and
your rival get to meet once and you both make
decisions at the same time. But in the real world,
we interact with our friends, our colleagues, and our business
or political partners many many times we form relationships, and
we interact repeatedly.
In this matter is because there's a more advanced part
of game theory that analyzes these repeated interactions and it
comes up with a sunnier conclusion than even though it
can be hard to cooperate or coordinate on good outcomes,
when you work with someone over time, you can often
figure it out.
And do you have some homework for our listeners to
think about, with their newfound insight into game theory.
The big one. As you go about through your week,
I want you to start to recognize all the places
where game theory applies to your life. That's any strategic interaction.
So whatever your next choice is, ask yourself whether your
best choice depends on what someone else chooses. If so,
you might be able to apply the tools from today's show.
And realize that not everything in life is either a
prisoner's dilemma or a coordination game. But if you practice,
you'll start to recognize that these ideas apply in many
aspects of your life.
Betsy, justin thank you, I'm going to start thinking about
all the what ifs in all my interactions this week.
And if you do that, then maybe my best choice
is to think about the what ifs too.
It is turtles all the way down.
Yes,