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PROFESSOR: Economics--
oligopoly.
Which is basically trying
to move towards the most
realistic modeling of
markets that we can.
We've talked about two extreme
versions of modeling markets.
One is perfect competition,
which is the extreme case of
perfect entry and exit.
Free entry and exit.
Perfect consumer information.
An idealized market.
We know that doesn't really
exist in practice anywhere.
The second extreme was monopoly,
which we do see in
practice in some places.
In particular, when there's
natural monopolies.
We do see that.
But that's still doesn't
describe most markets.
Most markets are better
described as oligopolies.
These are markets where there's
more than one market
player, yet where each firm is
large enough to actually
affect the price.
So an oligopoly market is where
there'll be a small
number of firms in the market
with substantial barriers to
entry from additional firms.
An oligopoly market where
there's a small number of firms
with enough barriers to
entry that additional
firms don't enter.
So the classic example
of an oligopoly
industry is the auto industry.
Here's a market with a small
number of dominant players.
There's been some entry and exit
over time, obviously, but
it moves pretty slowly.
By and large it's a market
where there's
very limited entry.
And the question is, how do
firms behave in this market?
Obviously it's not like perfect
competition where they
can lazily take a price out of
the market and just produce
based on that price.
But it's also not the same as
monopoly where they can just
get to set the price and
not worry about what
other people do.
They're in this in-between
situation where they have
price setting power.
They have some market power but
in a context where they
have to worry about
competitors.
And so in this context there are
two different ways firms
can behave. It's important
to lay out to start.
There's two different ways for
firms to behave. They can
behave cooperatively or
non-cooperatively.
If they behave cooperatively
we say
that they form a cartel.
So our cartel is what happens
when oligopolistic firms, when
firms in an oligopolistic market
behave cooperatively to
determine the outcome.
We call that a cartel.
The classic example, of course,
here being OPEC.
The Organization of Petroleum
Exporting Countries, which is
a cartel that drives
the price of oil.
Those countries cooperate in how
much oil they produce to
move the price up or
down according to
what the group desires.
And what cartels do is
essentially turn oligopolies
into monopolies.
So what cartelization does, what
a cooperative equilibrium
does is essentially say, let's
all get together and behave as
if we're one big monopoly
by cooperating.
And therefore, if you cooperate
you can get all the
wonderful things monopolies get:
huge market power, huge
markets et cetera.
But as we'll talk about next
time, it turns out to be
pretty hard to get a cooperative
oligopoly.
There's lots of reasons why
it might fall apart.
And that's why in most
oligopolistic markets firms
behave non cooperatively.
In most oligopolistic markets
firms are behaving
non-cooperatively.
They're competing with each
other, not cooperating.
And that's what we're going to
spend today analyzing is the
case of non-cooperative
oligopolies.
Yeah?
AUDIENCE: [INAUDIBLE]?
PROFESSOR: Depends
on the context.
In the US, and I'll talk about
this, in the US there's
anti-trust legislation which
can make it illegal in many
contexts to cooperate.
Obviously OPEC is not subject
to some world legislation.
But even in the US there can be
implicit cartelization and
implicit cooperation, and
we'll talk about that.
It's a good question.
So technically you're right.
Technically it is illegal in
the US in most contexts to
form a cooperative,
to form a cartel.
Whether in practice those laws
can be enforced is an
interesting, legitimate
question.
So today we want to focus on
the case of non-cooperative
oligopolies.
And to do so we're going
to turn to a new tool.
And one of the fundamental tools
of economics in the last
30 years which is game theory.
So today we're going to talk
about game theory.
Game theory is a tool of
economics that was not really
used early in economics but
has come to dominate
theoretical economics over
the past 30 or 40 years.
And basically the way that game
theory works is to think,
literally, of oligopolistic
firms as engaging in a game.
So when you play, don't want to
say play Monopoly, that's
confusing terms. When
you play Sorry!
or whatever with someone, or
play some online game with
someone, you're competing
to win.
You're behaving
non-cooperatively.
You're competing to win.
So basically what the insights
of game theory are that all
the tools we used strategically
to make
decisions in playing games can
actually be used in modeling
how firms compete
non-cooperatively in
oligopolistic market.
The key insight is that each
firm will develop a strategy.
Just as when you're playing
chess you have some strategy
going in, firms develop
a strategy.
And that based on that strategy
they will determine
their behavior.
And what is going to determine
that behavior is going to be
how firms' strategies combine to
determine a market outcome.
When firms come in with
different strategies, or when
a bunch of firms with strategies
come in to compete
with each other, what determines
the market outcome.
And what that's going to depend
on is something we call
an equilibrium concept.
Which is how do we measure--
essentially the equilibrium
concept is in game theory
terms, think about how
do we determine
when the game's over?
How do we determine when
we've decided on the
outcome of the market.
What's the equilibrium
concept?
So when you're reading the rules
of a new game the first
thing you look for is how
do you decide who wins.
That's kind of like what the
equilibrium concept is.
It's what determines whether
the game has ended.
What determines whether you've
reached equilibrium.
Where you've reached a point
where the market is stable and
therefore the game has ended.
Not ended in the sense the firm
shut down, but ended in
the sense that you know what
everybody's doing.
So it's not quite like
winning or losing.
It's more just like what
determines when you're at the
point where that market
is at equilibrium.
Now the most famous concept is
due to John Nash, who many of
you heard of from the movie and
book A Beautiful Mind, and
that's called the Nash
Equilibrium.
A Nash equilibrium is the point
at which no firm wants
to change its strategy
given what the
other firms are doing.
I'm going to say that again.
A Nash equilibrium is the point
where no firm wants to
change its strategy given what
the other firms are doing.
It's a little bit bizarre,
but we'll work it out.
In other words, more formally,
the idea is that holding
constant, given the strategies
all your competitors use
there's nothing that I can do
to raise my profits further.
Given the strategies all my
competitors are playing,
there's no strategy I can choose
that will make me more
profitable than the
one I'm choosing.
And likewise for every player
in the market that will turn
out to be true.
So have players sitting
around a game board,
going around the circle.
Each player says, given what I
know each of the rest you are
doing, I'm doing the
best thing I can.
And they go around the circle
and everybody says, OK, I'm at
that point.
You've reached a stable
Nash equilibrium.
This was named, of course,
for John Nash.
You all know the story
of John Nash.
He was a famous, actually
mathematician.
We use his tools in economics,
but he was a mathematician.
Developed these incredible
theories, and then developed
schizophrenia, went crazy.
But not before he developed
some of the most important
concepts in both mathematics
and economics.
The most important is the
Nash equilibrium.
Now the best illustration we use
of the Nash equilibrium is
an example that we refer to
as the prisoner's dilemma.
And many of you will be familiar
with this from more
popular reading you've
done in economics.
But let me just go through it
because it's important to
understand it.
The prisoner's dilemma.
The prisoner's dilemma the title
comes from the old way
they used to make
police movies.
Where the idea is you catch
two guys at a crime.
You can't put them away unless
one of them fesses up.
So what you do is you put them
each a separate room.
And you say to the one,
your buddy's cracked.
He's going to he's going to
sell you down the river.
You better, I'm using all my
'50s analogies, he's going to
put you away for good.
But if you admit that he's
guilty and he did the crime,
we'll let you off with
a light sentence.
Then they go to the other room
and say the same thing to the
other guy hoping they'll both
rat on each other and they'll
both get a sentence.
So basically the idea is, let's
say that you walk into
each room and you say to each
person, look, we have enough
evidence right here, and you
show them, to send you each to
prison for a year.
We would have enough evidence
to send you each to
prison for a year.
But we aren't sure about
this other thing.
If you'll admit that your friend
did this other thing,
then he'll go for five years
and you'll go free.
And then we go to the friend
and say the same thing.
If you'll admit that your friend
did the other thing
he'll go five years and
you'll go free.
But if they both admit then they
both go for two years.
So if they both admit, they
both go for two years.
Now the way to write this
down, what we do here to
explain this, is we write down
what we call a payoff matrix.
So write down a payoff matrix.
So the idea is we have
prisoner A here
and prisoner B here.
And they each have an option.
They could remain silent
or they can talk.
Silent or talk.
Now if they both remain silent,
if they both say I
would never rat out my friend,
I'm happy to go to jail for a
year rather than rat out my
friend, then they each get one
year in jail.
a equals 1, b equals 1.
However if prisoner A rats out
his buddy and prisoner B
chooses not to rat out his
buddy, then A gets--
so I'm sorry, if prisoner
A talks and
prisoner B remains silent.
Prisoner A talks, prisoner B
remains silent, then A gets
zero but B get five
years in prison.
On the other hand, if prisoner
B rats out his friend, but a
prisoner A is true and doesn't
say anything, then prisoner A
is going to get stuck with five
years and prisoner B is
going to get nothing.
And if they both rat each
other out then they
both get two years.
So people understand
the payoff.
Are there questions about
the set-up here?
This is complicated so
got to make sure you
understand the set-up.
Now, could someone tell me, if
A and B could truthfully
cooperate, what would be the
optimal cooperative strategy?
Yeah.
AUDIENCE: You both
go for a year.
PROFESSOR: Right, you'd
both be silent.
So the optimal cooperative
strategy is clear, which is to
both be silent.
So if the cop said, you know
what, we'll let you guys get
together and discuss what
you want to do first--
which the cops would never be
stupid enough to do-- but if
they did and the guys can trust
each other, then that's
the optimal cooperative
strategy.
What we call optimal in the
language of game theory, we
call that the dominant
strategy.
A dominant strategy is the best
thing to do no matter
what the other guy does is
the dominant strategy.
So the dominant cooperative
equilibrium strategy is to
both stay quiet.
But what's the dominant,
non-cooperative strategy?
What is the dominant
non-cooperative strategy?
So the ways with dominant
strategy, we run through.
Take prisoner A, ask
the following.
The dominant strategy is, is
there a strategy that makes
him better off regardless
of what B does.
Is there a strategy that makes
A better off regardless of
what B does.
Let's go through.
If A remains silent, if B
remains silent he gets a year.
If B talks he gets five years.
Now compare that to prisoner
A strategy of talking.
Well if he talks he's better off
than if he doesn't talk,
if B's remaining silent.
If he talks he's better
off than if he
doesn't talk if B talks.
That is regardless of what B
does, he's better off talking.
Regardless of what B chooses to
do, his dominant strategy
is to talk.
Because if B is silent, he's
better off if he talks.
If B talks he's better
off if he talks.
So matter what B chooses to do,
A is better off talking.
What about B?
Well B, by the same logic,
is always better
off talking as well.
No matter what A chooses
to do, B is
better off if he talks.
So where do we end up?
What ends up as the
Nash equilibrium?
The Nash equilibrium is that
both prisoners talk.
The dominant strategy for both
prisoners is to talk.
And they both end up worse off
than they could have if they
could have cooperated.
So the dominant non-cooperative
strategy is to
both talk, even though if they
could get together they'd be
better both not talking.
And this is basically how
game theory works.
Game theory math gets
incredibly hard.
And if you're interested,
14.12 is one of our most
popular undergraduate courses,
game theory.
It's a great course where you
take this and go run with it
for a whole semester.
It gets very complicated
mathematically.
But the basic idea in game
theory is pretty
straightforward, which is just
ask, are there dominant
strategies that can be played
by each player.
If each player has a dominant
strategy and those dominant
strategies lead to a Nash
equilibrium then you're done.
Here we're in a Nash
equilibrium.
Why are we in a Nash
Equilibrium?
Because given that A has talked,
B's strategy, which is
talking is the optimal
thing to do.
Given that B has talked, A's
strategy which is talking is
the optimal thing to do.
So given what the other person's
doing, each person is
doing the right thing.
So you're in Nash equilibrium.
Given that B has chosen
to talk, A is talking.
That's the profit maximizing
thing to do.
Given that A is talking,
B is talking.
That's the profit maximizing
thing to do.
So given the strategy the other
player's chosen that's
an equilibrium.
Yeah.
AUDIENCE: If they both talk and
got 10 years would that be
the Nash equilibrium.
PROFESSOR: No if they both
talk, the 10 years only
happens if one talks and
the other one doesn't.
AUDIENCE: No, I mean
like, [INAUDIBLE].
PROFESSOR: Oh, if they
both got 10 years?
So let's ask that.
Let's change this.
Now let's just rework it.
So now what's A's choice?
Well A if he talks
and B's silent,
then he's better talking.
But if he talks and B talks,
he's worse talking.
So then what he does depends
on what B does.
What B does is going to
depend on what A does.
And we can't obviously see the
Nash equilibrium here.
Because there's no dominant
strategy.
What you do depends on what
the other person does.
So there's no dominant
strategy.
Dominant strategies only occur
if there's something that you
should do no matter what
the other person does.
So in this case were these are
both 2, there is a dominant
strategy, It's to talk.
If those are both 10 there's no
longer a dominant strategy
so we can't quickly get
the Nash equilibrium.
It's a good question.
Now this is not just a cute
example that you can use for
prisoners, but actually
explains firm
behavior in many contexts.
So the best example I like to
think of of this is to think
about advertising.
So imagine if Coke and Pepsi,
and imagine a world where
Pepsi was as popular as Coke.
That should never happen.
Coke's way better.
But imagine that
was that world.
So imagine a world where if
there's no advertising then
basically Pepsi and Coke would
split the market 50-50.
Imagine that set up.
So if Pepsi and Coke could agree
not to advertise they'd
split the market 50-50.
However, it's going to turn out
that while that may be the
dominant cooperative outcome,
that's not the dominant
non-cooperative outcome because
each firm is better
off advertising if the other
one doesn't, or regardless.
So for example, imagine the
following payoffs matrix.
I'm just making this up.
But here you have Pepsi and
here you have Coke.
And imagine the payoff matrix.
And the payoff matrix is if they
don't advertise, so Pepsi
can choose not to advertise,
or it can advertise.
So if they both don't advertise
Pepsi gets 8 and
Coke gets 8.
I don't know what 8 is.
8 is billion dollars.
I'm just making up numbers
here, doesn't matter.
So $8 billion each.
If they both do advertise then
they still end up splitting
the market.
Because basically they're just
as good as each other.
So they both spend all the money
advertising and just
back up where they would have
started, except they've wasted
all this money in advertising.
So if they both advertise they
each earn $3 billion instead
of $8 billion.
That is, they each
split the market.
They end up back where they
would have started but they
pissed away a bunch of money
advertising along the way.
However if Coke advertised
and Pepsi doesn't.
Then almost everybody sees Coke,
Coke, Coke everywhere
and is like, Pepsi?
Never heard of that.
Coke makes $13 billion and
Pepsi loses $2 billion.
And likewise if Coke doesn't
advertise but Pepsi does,
people are like, I've
never heard of Coke.
I'm going to drink Pepsi.
So Pepsi makes $13 billion and
Coke makes minus $2 billion.
Once again I just made numbers
here so it would work, but
these aren't real
world examples.
So once again we can see there
is a dominant cooperative
strategy, which is
they both should
agree let's not advertise.
But if they can cooperate, then
in fact what's the Nash
equilibrium?
Let's work it through.
And there's no shortcuts here.
You've just got to work
this through.
Let's look for Pepsi.
Well Pepsi says if Coke doesn't
advertise I'm better
off advertising.
If Coke does advertise, I'm
better off advertising.
So my dominant strategy
is to advertise.
Coke says, well gee, if Pepsi
doesn't advertise I'm better
off advertising.
I make $13 billion instead
of $8 billion.
If Pepsi does advertise I make
$3 billion instead of negative
$2 billion.
So I'm better off
advertising too.
So my dominant strategy
is to advertise.
So for both firms the dominant
non-cooperative
strategy is to advertise.
So they both advertise and you
end up in this equilibrium.
It's an example of how a
non-cooperative equilibrium
can lead to what we call
a race to the bottom.
You can think of it as
a race to the bottom.
In other words, if they could
cooperate they could just be
better off.
But because they can't trust the
other, there's this race
to the bottom where they
both end up worse off.
This is pretty striking.
I thought they brought this out
well in A Beautiful Mind,
both the movie and the book,
which is that all we've
learned about economics
so far is that
competition is good, right?
Competition is beneficial.
Well here's a case, where in
fact, at least in the firm's
perspective, competition
is bad.
If they could just get together
and cooperate they
could make more money.
Now, in fact, this example
is not so far-fetched.
I don't know when it
started but it
was during your lifetimes.
When you were young, hard
liquors, scotch, bourbon,
whisky, et cetera, did not
advertise on television.
You never saw a Johnny Walker
ad or anything on television
until, I don't know when
it changed maybe five
or six years ago.
Maybe 10 years ago,
I don't know.
But certainly in
your lifetimes.
That was not by government
regulation.
Many people thought there
was a government
regulation, they couldn't.
That was not.
That was a cooperative
equilibrium where the makers
of hard liquors got together and
agreed not to advertise on
TV. And they said it was in
the "public interest" yada
yada yada, but that wasn't.
It was just they recognized the
benefits of cooperating
and not wasting money
advertising on TV and
competing with each other.
Well that broke down some
number of years ago.
And now you see whiskey ads
and scotch ads and other
things on television.
And they've moved to this
non-cooperative equilibrium
where they're all losing money
by having this advertising.
So that's in advertising.
For me, once again, this is a
hard thing, what intuition
works for you.
For me the intuition works best
maybe from my scars from
my dating life is thinking
about personal decisions.
So imagine that there's some
girl named Allison.
And Allison has a potential
problem with her boyfriend.
They've had a fight and now
she's deciding whether or not
to make up or break up.
Now we can think of this just
like Coke and Pepsi.
Allison is going to be thinking,
well gee, if he
wants to make up with me and I
want to make up with him then
we're both better off.
But if I want to make up with
him and he doesn't want to
make up with me, that makes me
look like a total idiot.
Whereas if I break up with him
preemptively, yes it would be
sad if he wanted to stay with
me, but at least if he wanted
to break up with me
I look better.
So she preemptively breaks
up with him.
John, her boyfriend, thinking
the same thing, behaves in
exactly the same way.
So it could be that even though
they both would be
better off if they just said,
look the honest truth is,
we're both wrong, let's make
up and we'll both be happy.
Because they're so afraid of
being the one being dumped,
they end up breaking up.
Now we all know of examples
like this from life, where
people stupidly if they could
have just cooperated had a
better outcome because they're
so afraid of being left with
the short end of the stick,
because they don't cooperate
you end up with the worst
outcome for both.
That's an example of
a non-cooperative
equilibrium in real life.
Now in real life there is one
aspect of oligopolistic
non-cooperative equilibria
that allow them to be
enforced, however.
That allow you to overcome
the prisoner's dilemma.
There's one thing that allows
you to overcome the prisoner's
dilemma and that's
repeated games.
Repeated games can
help you overcome
the prisoner's dilemma.
Now let's take the Coke and
Pepsi example and let's
imagine that they're making
the advertising
decision every period.
Every period they
have to make an
independent advertising decision.
They can advertise or not
advertise every period.
And imagine Coke says to Pepsi,
I've got the following
deal for you.
I commit to not advertise as
long as you don't, but the
minute you advertise I'm going
to advertise forever.
So as long as you don't
advertise I won't.
But if you ever run an ad, the
bet's off and I'm never going
to cooperate with you.
I'm going to advertise
forever.
Let's think about Pepsi's choice
in period one if Coke
presents them with this deal.
Let's think about Pepsi's choice
if Coke presents them
with this deal.
Well one thing is they could
say, ha ha, great Coke, good
job trusting me.
I'm going to screw you in
advertising period one.
So Pepsi could say, great,
Coke's laid down arms in
period one.
I'm going to go and advertise.
I'll make $13 billion in period
one because Coke's
wimped out.
And then I'll make $3 billion
forever after, because forever
after we're both going
to advertise.
But at least I' beat them
up that first period.
However, if Pepsi says, wait
a second, if Coke's really
right, honest, then I can get
an equilibrium where we make
$8 billion forever.
And certainly $8 billion forever
a better deal than $13
billion one year and
$3 billion forever.
So in fact if Coke's willing
to live up to that promise
then that is a good deal.
And actually we can turn this
non-cooperative equilibrium
into a cooperative equilibrium
through the enforcement of a
repeated game.
Through the fact that this game
gets played over and over
and over again you can enforce
a cooperative equilibrium.
We can come back to
relationships again.
If you're in a committed
relationship and you know that
if I say it's your fault over
and over again, eventually
person's going to leave. Then
people say gee, I'm willing to
take some of the blame and not
always say it's your fault and
we have a fight.
Because I know that if I always
say it's your fault
ultimately that will break the
relationship up and that makes
me worse off then admitting it
was my fault some of the time.
It's the same logic.
Yeah.
AUDIENCE: Is the point of the
game to make more than the
other guy or to make as
much as possible?
PROFESSOR: Make as
much as possible.
That's a good point.
I presume that the point is to
make as much as possible.
I'm ruling out cut off your
nose to spite your face
equilibria.
So in other words, I'm assuming
the goals is to
maximize profits not relevant
mark position.
That's a good point.
I should have made that
assumption clear.
It's the assumption we're always
making whatever we
confirm behavior is assuming
it's profit maximization.
So repeated games can enforce
a cooperative equilibria,
essentially.
Even in a non-cooperative
set up.
But it turns out this
only works if the
game goes on forever.
This only works if the game
is going to go on forever.
So, for example, imagine that
Pepsi knows that in 10 years
the US government is going to
ban the advertisement of
sugared sodas.
The US government is going to
finally say, look, people are
too obese, no more advertising
sugary sodas.
Pepsi knows this.
In 10 years that's
going to happen.
Well Pepsi's thinking,
gee, that means in
year 10 I should advertise.
In that last year I should
advertise because Coke can't
punish me the next year because
no one can advertise
the next year.
So I know starting after 10
years we're both in this
equilibrium because
the government's
going to enforce it.
So in ninth year, right
beforehand, right before that
government ban I should
advertise and Coke can't get
me the next period because
they don't have the
tool to punish me.
Well Coke, of course,
knows Pepsi is going
to behave that way.
So Coke says, wait a second,
if Pepsi's going to behave
that way then I better advertise
in the ninth period
too or I'm going to get hit
with a minus $2 billion.
So I'm going to advertise
in the ninth period too.
Well Pepsi says, look, if Coke's
going to advertise in
the ninth period for sure, I may
as well advertise in the
eight period because Coke's
going to advertise in the
ninth period for sure.
And by the same logic you can
work it back that they'll both
advertise right away and
you'll end up with a
non-cooperative equilibrium.
That is a repeated game that
does not enforce the
cooperative equilibrium.
Because by working that logic
backwards if it ends in some
realistic time frame, then you
better off just breaking it
now rather waiting for
that period where
you're the one who loses.
Yeah.
AUDIENCE: [INAUDIBLE]
what if Pepsi [INAUDIBLE]?
PROFESSOR: Exactly.
If they don't then you could
imagine that if Pepsi knows
this and Coke doesn't, then
Pepsi's optimal strategy will
be to cooperate to the next to
last period then go ahead and
screw Coke and then
Coke will lose.
But presuming symmetric
information, repeated games
cannot enforce these equilibria
if they end.
So this is just an incredibly
quick introduction to the fun
that is game theory.
We're going to go on now and do
more rigorous versions of
these models.
But this is just to get you
excited about the tools you
can do with game theory
with fun examples.
Game theory is about taking
these fun examples and
thinking a lot harder
about a lot.
What if there's asymmetric
information?
What if the game ends long
enough in the future that
you're willing to be patient?
How far off in the future does
the game have to end to still
enforce the cooperate
equilibrium?
What if there are
three players?
What if players move in
different orders?
What if one player goes first,
the second player responds to
that, is it different than if
they go simultaneously?
These are all really interesting
issues that are
very relevant to the real world
firm behavior that you
learn about game theory.
So this is just to whet your
appetite for that.
Having done that we're going to
now turn, leave aside these
more interesting dynamic issues
and focus on a specific
example of a non-cooperative
oligopoly.
Because, once again, this is
all fun intuitively, but we
want you to be able to work
through a problem.
And the way to work that through
is we're going to have
to move to a specific,
simplified example.
And the example we're
going to focus on is
called the Cournot model.
The Cournot model of
non-cooperative oligopoly.
The way we're going to do this
here, is we're going to return
to the example we had with
the prisoner's dilemma.
But instead of just facing two
choices, talk or not talk,
we're going to talk about firms
facing a whole continuum
of choices.
Firms choosing how much they
produce in a non-cooperative
equilibria situation.
So, for example, let's
take the example
they use in the book.
Let's imagine there's two
airlines that fly between New
York and Chicago, American
and United.
And let's imagine for simplicity
those are the only
two airlines.
Because of the hub and spoke
system we talked about last
time, let's say all the gates in
Chicago that are available
to come from New York are
taken by two airlines--
United and American.
Those are your only two options
flying New York to Chicago.
And the question we want to ask
is, get in that world, how
do United and American decide
how many flights to run and
what price to charge?
If they're monopolies
we'd know.
If it was a perfect competition
we'd know, but how
do they decide this
all oligopolistic.
The way we figure this out is
by looking for the Nash
equilibrium in this case, which
we also call Cournot
equilibrium.
Which is basically the quantity
is chosen by each
firm such that holding
all other
firms' quantities constant.
So each firm chooses quantity
such that holding all other
firm's quantities constant they
are maximizing profits.
So I choose a quantity such
that holding all the other
firm's quantities constant
I'm choosing a
profit-maximizing quantity.
And if each firm can choose a
quantity that makes the market
function where this is met,
then you're in Cournot
equilibrium.
You're in Cournot equilibrium
when each firm has
decided, I'm happy.
It's the same as the
Nash concept.
I'm happy with what I'm
producing given what everybody
else is producing.
If everybody feels that way
then you're in a Nash
equilibrium or a Cournot
equilibrium.
So to see this, this is not
immediately intuitive.
Let me just talk you through
the steps of how
you'd solve for this.
How do you actually solve for
a Cournot equilibrium?
So basically what are the
steps to solving?
Step one for solving a Cournot
equilibrium is to create each
firm's residual demand.
So compute residual demand.
We talked about residual
demand curves earlier.
Which is, that's the demand for
my firm given the quantity
absorbed by other firms
in the market.
In this case it's quantities
absorbed by the one other firm
in the market, but in
general you do this
with multiple players.
So first you calculate
residual demand.
Then having computed your
residual demand you develop a
marginal revenue function.
You calculate your marginal
revenue which will be a
function of other firm's
quantities.
So your residual demand will
lead you to calculate a
marginal revenue function.
It's a function of other
firms' quantities.
You then do the same, do one and
two for all firms. So for
each firm you end up with a
marginal revenue function and
a function of all the
firm's quantities.
Step four is you have
n equations and n
unknowns and you solve.
So you develop a series of
equation where each firm's
marginal revenue function is a
function of each other firms
quantities.
You get one equation like
that for each firm.
That leaves you n equations
and n unknowns you solve.
If you can solve it then
you reach equilibrium.
If you don't have a solution
then there is no stable Nash
equilibrium.
But if you can solve that there
is a Cournot equilibrium
and you solve for it.
So what we're going to do here
is I'm going to illustrate
this to you graphically today
and we'll work through some
more of the math of
it next time.
So we'll start by doing
this graphically.
So let's start by considering
the case of American Airlines.
Let's start with figure 16-1.
Start by considering the case
of American Airlines.
And let's say that the demand
curve in this market in our
example we're going to do,
let's say that the demand
curve is of the form p
equals 339 minus q.
So there's 339,000 flights that
are demanded each month.
Each month there are 339,000
flights demanded
in the whole market.
So 339,000 people want to
go from New York to
Chicago every month.
And let's also assume the
marginal cost is $147.
I don't know where Perloff came
up with these numbers,
but let's just go with them.
The specific numbers
don't matter.
Now what would American Airlines
do if it was a
monopolist?
If American Airlines was a
monopolist, it would set
marginal revenues which are 339
minus 2q by the same math
we did before.
You just multiply it through
by q and then differentiate
and you get 339 minus 2q
equal to the marginal
cost which is 147.
So if it was a monopolist it
would choose a quantity of 96
and it would choose
a price of $243.
A prices of $243 which
we would just get
out the demand curve.
If the quantity is 96,
the price is $243.
And that's what we see here.
The marginal revenue curve
intersects the marginal cost
curve at a quantity of 96,000.
You then go up to the demand
curve to read off the price.
Remember for a monopolist you've
got to still respect
the demand curve.
You get the demand curve
to read off the
price, that's $243.
That's what American would do if
they were monopolist. So if
they were the only folks flying
New York to Chicago,
they fly 96,000 people a month
at a price of $243,000.
However, now let's say American
recognizes that
United is in the market.
And let's say American
recognizes that United is
going to deliver some amount
of flights q sub u.
They know American is going
to do some amount of
flights q sub u.
They don't quite know yet what
it is, but they know there's
going to be some amount
of flights q sub u.
So the residual demand for
American is q sub a equals
total demand minus q sub u.
That's their residual demand.
So, for example, let's say that
American just guesses
that United will fly
64,000 passengers.
Let's say Americans says, look,
I just know, I've got
some corporate spy who's told me
that United will fly 64,000
passengers.
So what you want to do is then
you just re-solve the problem
but using residual demand.
So then you say, well if United
is going to fly 64,000
passengers then my residual
demand is that price equals
339 minus the quantity I sell,
q sub a, minus q sub u, which
I think is 64,000,
which is 64.
So my new residual demand is
p equals 275 minus q sub a.
That's my new residual demand.
Because I thought United is
going to sell 64,000.
So instead of my demand
being 339 minus q, now
275 minus q sub a.
That's what's left.
So if I use this as my new
demand function and re-solve,
if this is my demand function,
my marginal revenues are then
275 minus 2 qa.
My marginal cost is the
same which is 147.
So instead of my equation being
339 minus 2q equals 147.
Now it's 275 minus
2qa equals 147.
If I do that I'm going to get
a qa star of 64,000 flights.
I'm going to say, well look, if
I was a monopolist I would
have deliver 96,000 flights.
But given that United is
delivering 64,000, that's it's
going to be optimal for me
to also deliver 64,000.
At 64,000 flights what's
my price going to be?
Well my price is 275 minus qa.
So my price is going
be to be $211.
If I think United is delivering
64,000 flights then
I'm going to deliver 64,000
flights at a price of $211.
So that's basically how American
would function.
Now what's strange about this
is American doesn't know how
many flights United is
going to deliver.
There isn't such a thing.
In fact, it's not like there's
not some rule which says we're
going to go 64,000.
United is trying to figure
this out too.
So, in fact, simultaneously to
American making this decision,
United is making the
same decision.
And they're going through
the exact same math.
They're saying, well gee, given
how much American flies,
how much should we fly?
They're going through
the same math.
And in fact if we assume that
both firms have to face the
same marginal cost and the same
demand curve, then in
fact they're solving a
symmetric problem.
They are also creating a
residual demand function, but
instead of being qa equals d
minus qu, now United is making
qu equals d minus qa.
They're making a parallel
residual demand function and
they are solving as well.
And both firms, therefore, are
ending up with choices of
quantities that depend on the
other firm's quantity.
And in particular what they're
developing is what we call a
best response curve.
So figure 16-2, I skipped
over figure 16-2.
This just illustrates what
happens when American thinks
United is committing 64,000.
Let's go through that
in one second.
Get through it mathematically.
This is an example where
American knows United is doing
64,000 flights.
So they say, well look, my
residual demand is essentially
this new line d super r.
And that's what I choose
on that new line.
So that creates a new marginal
revenue curve, mr super r.
That new marginal revenue curve
intersects marginal cost
at 64,000 and that's why I
fly only 64,000 flights
at a price of $211.
So you see here is one example
of how given an amount United
is flying, how American chooses
how much to fly.
Questions about that graphic
that ties the math I did here?
What figure 16-3 does is say,
look, we can actually do this
for a whole host of possible
production levels
by the other firm.
And we can develop what we call
best response curves.
Best response curves are, given
what the other firm
does, what should I do.
So, for example, American's best
response curve is given
that-- so on the x-axis we have
how many thousands of
flights American's passengers
are flying per quarter.
On the y-axis how many thousands
of flights United
passengers are flying
per quarter.
So, for example, if American
decides to fly zero flights
then United should fly
96 flights, right?
Then United is a monopolist.
So that's the point on the
y-axis, to 96,0 point
on the curve.
With a 0 on the x-axis,
96 on the y-axis.
If American decides to fly 0.
United should fly 96.
That's the monopoly case
we just solved.
If American decides to fly
64, United should fly 64.
That's the case we just
solved as well.
Likewise, American's best
response curve is
this steeper line.
But it's the same thing.
If United flies 0, American
should fly 96 then at 0 on the
y-axis, 96 on the x-axis.
So if United flies 0 American
should fly 96.
If United flies 64, American
should fly 64.
So you can actually, literally
trace out these curves asking
at every single point, given
what the other guy's doing,
what should I do.
So we solved for two points
on this curve.
We solved for the other guy
producing zero point, which is
you produce 96.
We solved for the other guy
producing 64 point which is
you produce 64.
That same math can be used
to solve for every
point on this curve.
Yeah?
AUDIENCE: [INAUDIBLE]
192 point.
PROFESSOR: The 192
point is it's the
question is the following.
At what point would American
produce zero.
How much when United have to
produce for American to
produce zero.
Well they'd only produce
zero if United
was producing 192,000.
Only at that point would they
actually say, forget it, we're
just going to produce zero.
That's what the 192
point means.
Only if they knew United was
producing all that much would
they just drop out
of the market.
So that's the 192
intersection.
A backwards way to
read the curves.
But the bottom line, is
essentially we can write these
best response curves.
They're basically the quantity
I'm going to produce given the
quantity the other
firm produces.
And the key thing is
that these are
symmetric in this example.
Since the costs are the same
and they both face the same
market demand then these
curves are symmetric.
What that means is that these
curves are having figured out
one you can automatically
draw the other.
A trick for solving these
problems is that if you have a
symmetric Cournot equilibrium
you don't need to calculate
the math to find each firm's
best response curve.
Once you calculate one you know
the other firm's just a
complement of it.
So having calculated American's
best response curve
we could have automatically
drawn the United best response
curve as a complement of that.
The other key point is by
drawing this diagram we can
see the Cournot equilibrium.
Remember Cournot equilibrium.
Cournot equilibrium is where
I'm happy with my quantity
given what the other
firm's doing.
Given what the other firm's
doing I can't
make any more money.
Once again, I don't care about
market share, I just care
about money.
So given what the other
firm's doing I can't
make any more money.
Well that happens
at 64,000 each.
Because when American is
producing 64,000, United is
happy to produce 64,000.
That's their profit
maximizing choice.
If United is producing
64,000 American's
happy to produce 64,000.
That's their profit
maximizing choice.
So that point of each producing
64,000 we are in a
Nash or Cournot equilibrium.
Both firms are happy given what
the other firm is doing.
Both firms are profit maximizing
given what the
other firm is doing.
Now basically, for example,
another way to look at this is
that you're only in equilibrium
if you're on both
firms' reaction curves.
So, for example, American
might say, look the
equilibrium I like is
where I do 96,000
flights and you none.
So the equilibrium I like is on
the x-axis the point 96, 0,
where I do 96,000 flights
and you United do none.
United says, however, no that's
not optimal for me.
Because if you're doing
that, then you're
charging a price of $243.
So there's money to
be made for me.
I can come in and start stealing
some of your flights.
So that's not an equilibrium
from my perspective.
Might be an equilibrium
from your perspective.
You're delighted you're a
monopolist. But not from my
perspective.
At that price I'll
come in and start
stealing some your business.
And I'm going to start stealing
some of your business.
As I steal your business you are
going to have to move up
your best response curve because
your residual demand
is shrinking.
And you'll only reach
equilibrium when you're both
happy with the outcome.
If only one firm is happy with
the outcome the other firm can
always change its behavior,
raise its price up or down or
its quantity up or down to
change the market share and
change the outcome.
So equilibrium will only be when
you're at both firms best
response curves.
You'll only be at both firm's
best response curves where
they intersect.
Let's stop there I'm going
to come back next time.
Jessica we should have the
same handout next time.
Let's make sure this figure
is in the handout
next time as well.
And we'll come back and talk
about this last figure and
we'll do the math behind
it as well.
