So, a little bit of
housekeeping, the next exam's on Monday,
so next week, and the topics that that
we'll cover is the chapter 9 we did on
market structures, chapter 10, game
theory, or I should say topic
10, game theory, and then in terms of
what we're doing now, up until what we end
up on today, we'll be on the exam or assessable.
So we don't have our homework on the
oligopoly stuff, but hopefully the stuff we
cover in the lecture, as well as the practice
questions I give as well, are sufficient
for understanding. So just keep
that in mind when studying, and if you
have any questions, please feel free
to reach out. So going back, what
we discussed on Monday and Wednesday is this
idea of oligopoly and the key difference
between that and the other market
structures is that your decisions affect
the profits of other firms in the oligopoly
market structure, and these other firms'
decisions directly affect your profits as
well. And that's not the case in the other
types of markets. So we covered the
SWEASY oligopoly model, And if you remember, the
key feature of Sweezy is there's multiple
firms in this oligopoly market, and if you
lower your prices, other firms will match
it. But if you raise your prices, other
firms won't match it. So we have demand curve
two, when other firms don't match your
prices, and demand curve one, when other firms
match your prices. So the demand curve
that you face is going to be demand curve
two, when it's above the pricier B. so here
and then it's going to switch to demand
curve one because when you lower your price
below B other firms going to match it so
that gives you the marginal revenue curve
A to C to E to F and the key implication
of the Sweezy model is as you can see any
time your marginal cost lowers from zero
anywhere up until One, what this means is
your marginal cost decreases usually
means that you produce more, but
in the Swayze model there's this area
here where you don't end up actually
producing any more even though your marginal
cost decreases. And that's because
if you produce more, then prices would
lower and you'd actually be worse
off. So it's a little curiosity that is
only present in the Swayze oligopoly
model, nowhere else. but today we're going
to talk about probably the most important of
the oligopoly models if i only could teach
you one of them it would be corno if
you take industrial organization or anything
else or any other further econ classes
corno will come up again and the way i'm going
to cover corno to aid understanding is i'm
going to start off by going through the
um the mathematical derivations of the corno
national equilibria because i actually
think that's better in terms of helping to
understand what is going on now for the exam
i'm not going to assess you on the calculus
but i really do think that the ideas in the
mathematical derivations of corno help
understanding more than the graphs because the
graphs are a little bit of a dog's breakfast
as we say in australia just an absolute
mess as you will see so what's our corno
situation once again there are only a few
firms in the market that serve many customers
the goods produced can either be differentiated
or homogenous. And importantly,
each firm believes rivals will hold their
output constant if it changes its own
output. And like before, barriers to
entry exist, this is going to maintain
being an oligopoly. So the key thing about
Cournot is that each firm will have a way
to respond to other firms output so if
you think a firm will produce x then you will
produce y no matter what x is so each
firm makes an output decision under the belief
that its rival will hold output constant
when the other or when they change their own
output level and the implication here is that
each firm's marginal revenue is not just
impacted by their own production but by
the production of other firms as well. So this
relationship between firms and their profit
maximizing output level is called the
best response or the reaction function.
Now you've seen these reaction or best response
functions before. If we go back to our
game theory topic we looked at mixed strategy
and hash equilibria and we drew those
interestingly shaped reaction functions
but the same premise occurs here. What will
each firm do given the production of the
other firm? So let's look at the reaction
function of firm 1. So what this is
telling us is how much firm 1 should
produce given how much firm 2
produces. So we pick any point at
Q2 on our y-axis. So let's say firm 2 is
producing this much. What we want to do is
move horizontally until we hit our own reaction
function of firm 1 and that's where you
should produce so if firm two produces zero
units then you should produce here at q1m
and it's called q1m because this is what your
monopoly out would be as firm two so this
is the duopoly case there's only two firms
here the other first producing nothing you're
essentially monopolist so that's where you
should produce you can see at q2 then you'll
end up producing where it hits at E, so on
and so forth. And it's the same thing for
firm 2. This is their reaction function in
blue here, and what they do is they see how much
firm 1 produces, and then what they do is
they move vertically until they hit the
reaction function, that's how much they produce.
So at this point here, if firm 1 is producing
here, then they should produce at this point
here so this much if firm one is producing
zero we move vertically up until q2m that's
the monopoly output for firm two and as
you can see where both of these reaction
functions cross at point e this is going to be our
Cournot Nash equilibria so where they intersect
similar to our best response functions
in mixed strategy Nash equilibria that's
going to be the equilibrium point and to show
you why it's the equilibrium point we can
look at how each firm would react if we're
not at equilibria if they could react so
imagine firm one is producing at their monopoly
output q1m given that output what should
firm two do they should produce by moving
up to their reaction function here and produce
a point i so at this point here q um one
is here q2 is zero but now Firm 2 has an
incentive to produce at A. But if Firm 2 is
producing at A, that means there's this
much of Q2, and that means Firm 1 has
an incentive to produce where the Q2
intersects with their reaction function,
which is point B. And then, once again, Firm 2 is going to
have an incentive to change their output
because Firm 1 is producing here, and if we
move all the way up, we get to point C.
So as you can see, we keep zigzagging in
the same way until we reach the point of
intersection then neither firm has an incentive
to change their output so this is the
equilibrium for that reason given the
other play strategy no player unilaterally
has an incentive to deviate everywhere
else they do So this is the Nash Equilibria,
graphically at least. Ah, so the key feature
of the Corneau model, where the one thing
that you have control over is how much
you're producing, is that the total
quantity in the market is made up of the firm's
individual production. So in this simple case,
we're going to look at a duopoly of two
firms, but if there were three firms the
quantity of the mark would be q1 plus q2 plus
q3 so as you can see the inverse demand
function here is price equals a minus b quantity
but quantity is made up of the quantity
firm one produces and the quantity firm two
produces this is integral to the corno model
and the cost functions as we give here are
just going to be c1 times q1 and c2 times q2
they're both just linear cost functions for
simplicity so the total revenue function is
just going to be the price times the quantity
that firm one produces because we care about
the total revenue of firm one but what
we need to do is incorporate the price
function here over here so as you can see this
is our expanded price function multiplied by
the quantity of firm one and it means that
total revenue function equals a times q1 minus
b q1 squared minus b q1 q2 so we now have
the total revenue of firm one we also have
the cost functions of both firms so
how do we find the profit maximizing
output for firm one what do we need to do and
my hint is everyone in this class should
know the answer. Set what equal? The marginal
revenue equal to the marginal cost. Yeah,
set the marginal revenue equal to
the marginal cost. We have our total
revenue function, we have our total
cost function, nothing changes in the
environment. You want to set your marginal
revenue equal to your marginal cost.
So, we can do this. So, if I go like, so you
can't see the screen, please let me know,
because I'll keep on going and no one will
be able to see. So, we have our total
revenue function and we have a total cost
function so we can just find our marginal cost
for firm one which equals the changing
cost given the changing quantity of one and
this just equals c1 fairly straightforward
then our marginal revenue equals the
change in revenue given the change in your
output quantity of 1, and that equals A
minus 2BQ1 minus BQ2. So we now have our
marginal revenue and our marginal cost,
and as mentioned, all we need to do
is set them equal to each other. So
marginal cost of 1, because marginal
revenue of 1, and we get C1 equals A minus
2 BQ1 minus BQ2. So what we want to
do now is, because what we care about
as Ferm 1 is deciding on what our own
output should be, we want to isolate Q1 in
terms of everything else. So what we can
do is C1, take the A across minus A,
take the BQ2 across, And that equals
minus 2BQ1. Then what we want to
do is divide everything through by minus 2B.
And that's how we isolate Q1. So what
we end up with is Q1 equals A minus C1 over
2B minus Q2 over 2. and this is what we call
our reaction function and this is a reaction
function because as you can see the
output of Q1 that is the optimal amount of
output not just depends on your own parameters
and your own cost but it also directly
relates to the amount of Q2 being produced
as well so what this is saying is if the
other firm produces more then you should produce
less and if they produce less then you
should produce more. And because everything
is symmetrical here we can just write
Q2 as A minus C2 divided by 2B minus Q1
divided by 2. Because everything is symmetric
we can do that. So that's a simple
case and as I said the implication is their
quantity output decision directly depends how
much the other firm decides to produce, and
Nash equilibrium occurs when these reaction
functions intersect with each other, so when
they equal each other. And we can figure
that out. It's a bit hard to do with all
these parameters here, but if we give them
numbers, and we simplify it a little
bit, we can do that. Alright, so let's do that now, so let's go on
the back of this. So each firm faces
a demand curve of p equals 10
minus q, where the quantity is just the
production of Firm 1 plus the
production of Firm 2. Just for simplicity,
assume cost is zero, how much will
each firm produce? So total revenue of
Firm 1 equals price times quantity of
1, which equals 10 minus Q1 minus Q2
multiplied by the quantity q1 so total revenue
just equals 10 q1 minus q1 squared minus
q1 q2 the marginal cost equals zero
because the total cost equals zero and
our marginal revenue equals the change
in revenue given the change in
output of firm one and that just
equals 10 minus 2Q1 minus Q2 so to find
the profit maximizing output once again
we want to set marginal revenue
equals marginal cost so we just get 10 minus
2Q1 minus Q2 equals 0 once again we want
to take everything over and isolate
Q1 so we get minus 2Q1 equals Q2 minus
10 so we get Q1 equals 5 minus Q2 on 2 and that's our reaction
function for firm 1 and due to this being
symmetrical we can do the exact same thing for
our reaction function of firm 2 equals 5
minus Q1 divided by 2 so now we have both
reaction functions, and the other important
piece of information is we know that the Nash
equilibria is when these firms' reaction
functions intersect. So what we can do
is we can substitute Q2 into the Q1 equation. So Q1 let me do it like this. So Q1 equals 5 minus,
and then we put in q2 so 5 minus q1
divided by 2 all this divided by 2 that
equals 5 minus 2.5 so 5 divided by 2
is 2.5 minus so this is plus q1 on 4 we
want to gather our like terms to take
this across and we get 3 Q1 on 4 equals
5 minus 2.5 is 2.5. Q1 equals 4
times 2.5 is 10. Then divide by 3. So Q1's optimal output
is going to be 10 divided by 3. And
because it's all being symmetrical, it should
be the same for Q2, but we can double
check that by plugging back in Q1 into the
Q2 reaction function. So Q2 equals 5 minus
Q1 on 2, which equals 5 minus 10 divided
by 3 divided by 2, 5 minus 10 divided by
6, and then if we take this it's 30 minus 10
divided by 6 equals 10 divided by 3 so
the optimal output of both firms is to produce
10 over 3 units and importantly what that
means is that I'm going to do the next
part just here is that big Q which equals Q1
plus Q2 equals 20 over 3 so you just add both
of them to we have the amount of output
in the market in total which means we can
figure out our price so remember the inverse
linear demand curve is price equals 10
minus Q we now know what Q is so 10 minus 10
so minus 20 on 3 and that's going to be
just equal to 10 on 3 so the price is going
to be 10 divided by 3, as is the
quantity of each firm produces, and the total
quantity of the market is 20 over 3. And
finally, to figure out a firm's profit, so
the profit of firm 1 just equals to price
times Q1, and this is just 10 over 3
times 10 over 3, which equals 100 on 9, or
I believe like 11.11 is the amount of profit that they're making. So it will be the same
for firm two as well. So they're both
making $11.11 in this environment. We know
how much each firm is producing. And we've got
all that through just figuring out the
maximizing output level. So what would happen
if these two firms colluded and acted
as a single entity, a monopoly, and
split the profits? Does anyone want to take a guess what
would happen? Michael. There would
be like one quantity? Yeah, that's how
we're going to go about it. But what
do you think is going to be the end result
for each firm? Do you think
there'll be better or worse? Do you think
there'll be more quantity or less
quantity in the market? Higher price,
lower price? Or will things
stay the same? Probably a higher price. Why? What's
your intuition? Because if
they're not, like, fighting with each
other anymore, they're just
going to set the price. Perfect.
Perfect intuition. Anyone else want to
jump in and share? So, if they're acting
as a monopoly is splitting the profits,
we're going to assume that big Q is just the
monopoly Q, and then we're just going to
split everything at the end. So, the inverse
demand function for the monopoly is going
to be 10 minus q we know that that cost
equals zero so that means total revenue equals
price times quantity which equals 10 minus
q multiplied by q and that means the
marginal revenue um sorry this just equals
10 q minus q squared so the marginal revenue
is just 10 minus 2q we know the marginal
cost equals zero so 10 minus 2q equals zero
and when we take this across q is going
to equal five so the quantity of of the
total market is going to be five units and if
you remember in our corno equilibria each
firm is producing 10 divided by 3 which is
like 3.33 if you add those together 6.66 so
if they're acting as monopoly there's less
quantity in the market overall so we know
the quantity we can figure out the price
the price is going to be five dollars ten minus
five so it's five dollars whereas in our
in our corner the price was three point three
three dollars so as as michael suggested
by them working together they can
collaborate and increase the price in the market
and finally we can figure out the total
profit so the total profit is going to be price
sorry total revenue i'm actually going
to go do it like this profit one equals total
revenue minus total cost which equals price
times quantity minus um total cost we know
total cost equals zero which makes it
easier five times five equals twenty five dollars
so acting as as one you know firm as a
cartel they make twenty five and if they split
the profits evenly they both get twelve
point five dollars and this is more than
the corno equilibria where they both made eleven
point one one dollars so the key thing here
is they would agree to each produce let's
say 2.5 units each out of the five so q1
equals 2.5 q2 equals 2.5 so both firms are
better off by colluding and acting as a
monopoly there is less quantity in the market
and a higher price so this goes very
similarly to the welfare effects of having a
monopoly is this stable is this an equilibrium
if I act as a cartel Kevin I saw
you squint your eyes there for a
second what are you thinking
yes yes why yes so by cooperating they
can do better than when they were
playing this corno equilibria but the
question is can either of them deviate from this
strategy of cooperation to do even better
and this is going back to our idea of
the prisoner's dilemma that if they renege
they can do better so what we can see
is now each firm is producing 2.5 units
to get to this 5 units in our monopoly
output let's go back to our reaction
function of firm 1 so Q1 equals 5 minus q2 divided
by 2, which equals 5 minus 2
.5 divided by 2. So, if we hash this
out, then we will get, so if we times both
by 4, we get minus 10 divided by 8 and 40
over 8 minus 10 divided by 8 which equals 30
divided by 8 which equals 15 divided by
4 so as you can see 15 divided by 4 is
very close to 4 it's like I don't know 3.8
units or something like that so firm 1 is
incentivized to produce more than the grade
upon 2.5 each. And what this means is,
let's say firm 2's output is constant at 2.5,
so 2.5 over 4 is 10, so then we have
quantity equals 15 over 4 plus 10 over 4,
which equals 25 over 4. and then we can figure
out Firm 1's profit is going to be 10 minus 25 over 4
sorry, profit of Firm 1 multiplied by their new output which is 15 on 4. So I want to do a
quick calculation of that. It should be
higher than 12.5. It should be higher than
12.5. But as you can see they're not going
to stick to the same quantity. The quantity
that they produce is the one variable
that they can change, and when they have
this necessarily agreement, then you're
not actually incentivized to stick to the
agreement. You can actually produce more
and be better off, and we'll see that
graphically as well. So the key thing
in Cournot is we have this
Nash Equilibria, but both parties can
be made better off by cooperating. However,
both firms have an incentive to deviate
on that agreement. So, I just want to give
you a little bit of experimental evidence
on Corneau oligopoly. So, we looked
at a situation where there's
only two firms. So, what happens
when we increase the amount of firms
in the oligopoly? And theory predicts
that markets will become more and
more competitive. So, prices will
continue to decrease. There'll be higher
quantities in the market and lower profits
for each firm as we keep adding more in.
and the additional effect is just in
general collusion is easier with fewer
firms so imagine you're playing this game where
you're each a firm and you're playing
with one other person it's probably easier
to sustain collusion because all collusion
is in the end of the day is cooperation
with one other person then with multiple
other people just less people you need
to trust essentially so there's a
paper by Huck Norman and Oshler in 2004 and what they did was
they ran an experiment on this corno oligopoly
market and in each treatment what they
differed was how many firms there were in
this market so you can see the linear demand
curve they had was the price in the market
equals 99 minus the total quantity produced
each firm had a marginal cost of one
dollar for each unit they produced they did
25 rounds of this in fixed groups and as you
can see here here are the number of firms in
each of the treatments so as you can see as
the amount of firms increased so did the
amount produced in the market and what
this means is because the prices is inversely
related to quantity price was lower in the
market which resulted in less profits for
each of the firms so the theory bore out
here that the more firms you put in the market
at the more competitive it becomes, the closer
it gets, actually, to the perfect
competition equilibria. Interestingly, they
even ran some other sessions with only two
firms, and they found just by changing
the framing of the instructions, they could
actually do why with the collusion entirely,
by making it more neutral, instead of
about, you know, collusion in general so the reason why I went to these lengths
to show you how to go about finding the
Konoha equalilibrium through calculus
is even though I can't test you on the
calculus itself I do think it gives a
better intuition than the graphs I'm about
to show so they use something called
isoprophic curves which have a lot of
similarities to our difference curves, but
they get quite messy. So these are
the isoprophic curves for firm 1. As you can see this
is firm 1's reaction function, and this
is the monopoly output point for
firm 1. So firm 2 produces nothing,
this is where firm 1 should produce, and
because they'd be a monopoly that's
their highest profit. So the four key things
of these isoprophic curves is every point
on a given isoprofit curve yields firm
on the same level of profit so g a h all
give the profit of of profit zero curve
the closer the profit curve is to the monopoly
output point the higher the profit so as
you move down towards here the higher the
profits for firm one so isoprofit curve
one gives you higher profit than isoprofit
curve zero and isoprofit curve two gives
you more profit than the other two curves
so on and so forth. Importantly the isoprofit
curves reach their peak for firm one
when they hit the reaction function and
finally due to transitivity they can't intersect
with each other. We know that already
from different curves. So how will firm
one react to firm 2 producing at Q2 star
here. If this is firm 2's output then firm 1 can
produce it anywhere. So you can see they
can produce here at QA1. If that's
the case then they're going to hit this
isoprophic curve, curve A. They produce at B
then they'll be at B and as you can see
they'll produce at C. The reason why they'll
produce at C is because it's on the
isoprophic curve that's closest to monopoly
point so that's how they maximize their
profits using this isoprofit curve
framework and it's very similar to consumer
maximization when it comes to utility so
if you're producing anywhere above
isoprofit curve c so if you're producing here
on a then you can still lower your curve and
produce at a number of points and still
be making more of a profit so as you can
see as we bring these curves in so if we
did a curve in between here there would be
points where it would still intersect with
Q2 star so you could still produce that like
more of a profit so this is essentially
our tendency point so isoprofit curve C just
touches the horizontal line here Q2 this
is the maximum point so if we lower the
isoprofit curve anymore it would no longer be
touching Q2 and it's no longer feasible
you can't actually produce there because
you need to produce at a point where Firm 2
is producing our Q2. So that's why
it's always going to be at the
maximum point here. So these are Firm
2's isoprofit curves and it's a
similar concept. So QM2 is Firm 2's
monopoly output point where Firm 1 produces
0. We move vertically and this is where
Firm 2 will produce. And as you can see,
everything's the same. As we move close to
the monopoly point, more of a profit is
being made by Firm 2. So this is a
reaction function, the isoprofit goes on the
reaction function. So this is our
Cournot equilibria. As you can see, this
is the point, C, where both the reaction
functions intersect with each other, where they
equal each other. And you can see the isoprofit
curves are going for each other here
as well at this point. so what happens
if one of the firm's marginal
costs decline so as we know if you
find the right page so if we look at firm
one's reaction function if their
costs decrease that's going to mean
they end up producing more so as their
cost decrease they will produce more so
what that means is as you can see in this
case FIRM2's marginal cost is decreasing
so FIRM2 this reaction function is
going to move up and to the right and at
the new equilibrium point where they both
intersect FIRM2 is going to produce more
and because FIRM2 produces more as we
can see FIRM1 here will produce less as
FIRM2 produces more so we can see that
here at point F so compared to the
equilibrium point firm 1 will produce less
than before and firm 2 will produce more so
that's how it would change when the cost
changes and vice versa if firm 2's marginal
costs increase then it would move down
and to the left and at the new equilibrium
point firm 1 would produce more firm 2
would produce less so as we spoke about firms can do better
by colluding both of them make a high profit
we saw that mathematically however this isn't
a stable equilibria because both the firms
have an incentive to deviate and
because both firms are aware of this um reach
inclusive agreements is often very difficult
so this is where it gets a bit messy so
we have our corno equilibria at point c so
we have our two reaction functions this is a
reaction function of firm two reaction
function of firm one and the isoprofit curves
in there somewhere. But, as we can see, what both firms
can do is they can collude
here at point D. And at point D, when
they collude, as you can see, firm two's
isoprofit function touches point D
here, and this is closer towards
the monopoly point than the corner of
equilibrium. and it's the same for
Firm 1 for Firm 1 this is their point
of collusion in terms of the
isoprofit curve and it's closer to the
origin than the Kono equilibria so both
are better off however what happens if Firm
1 decides to cheat they agree to
this you know this collusive option
then Firm 1 deviates so what that means is
firm 2 is producing at D and then firm
1 is going to see what firm 2 is producing
and then see what they should produce
based on their reaction function and produce
at G instead of producing here at D
they're producing at G so when they both
collude they both produce here but by cheating
they can get back to their reaction
function produce at G and as you can see the
isoprophic curve for cheating is closer
to the origin than colluding so they have
the incentive to do this they make
themselves better off we saw this same thing
mathematically as well and this actually
makes firm 2 worse off so under the
illusion of cooperation firm 2 thinks this
is going to be their isoprophic curve
but it's going to end up being here
instead so they're doing much worse and
worse than what they would do at the
corner of equilibrium This is just a
prisoner's dilemma at the end of the day when
you think about it. The Kono
Equilibria is our equilibria in the
prisoner's dilemma. Both of them setting
a low price or producing a higher
amount of quantity. Now they're both better
off by cooperating and both setting a
high price or producing less, but then each
firm individually has an incentive
to produce more themselves or set a
lower price, essentially, and end up doing
better, getting 50 instead of 10, and
screwing over the other. So the Cournot
Equilibria is essentially a Prisoner's Dilemma.
And as we know in the Prisoner's Dilemma,
in the one-shot version, or in the
finite version, with a known outcome,
it's impossible to cooperate, pretty much.
But we know through things like trigger
strategies, in an infinite game, or
the stochastic games, cooperation is possible, thus collusion
is possible. Collusion and cooperation
are essentially the same thing at
the end of the day. We just call them
different things because we frame cooperation
as good for society and collusion as bad
for society. When firms collude, we get
our monopoly outcome. And our monopoly
outcome, as we showed a couple of topics
back, is bad for society in terms of
the welfare costs. So whether it's through
the graphics or the mathematics, the three
key takeaways really is is how you get to
this corner equilibrium where these reaction
functions intersect we can show how they
act as one firm and they collude they're
both better off but both firms have
an incentive to defect or cheat from this
collusive outcome and do better themselves
those are the key three things to
remember in the corner finally I just want to quickly go over
Stackelberg So Stackelberg is the exact same as Cournot. There's only
one difference. In Cournot, we're assuming
it's a simultaneous game. Both firms
are making decisions at the same time,
how much to produce. Stackelberg's different. Stackelberg, we
have one firm, which we call the leader, that makes a decision, and then after that, followers make
a decision. So this has a
sequential property to it. There's
a first mover, and then the
other movers. So a single firm,
the leader, chooses an output before
all other firms, and then afterwards
all other firms take as given
the output of the leader, and choose
outputs that maximize profits given the
leader's output. I'll get back to the
graph in a second. So once again,
we have the same linear
demand function, price equals A minus B
times quantity, where quantity is just the
quantity of all the firms in the market.
This is the duopoly version. The cost
functions are the same. The follower has the
exact same reaction function as firms
in our Cournot equilibria. This
is the exact same. A minus C2 divided by 2B minus Q1 divided by 2. However, the key
difference is how the leader
decides to produce. So I don't expect you
to know this or memorize this. If I ask any
questions about Stackelberg, it's going
to be based on intuition or I'll give you the
formula of Zuckerberg. So the leader takes
into account the follower's reaction
function in determining their total output.
So we know the follower's reaction
function is this. That's what Q2
equals. So as you can see,
profit equals Q1 multiplied by the
price, which is this whole thing, minus
the cost of firm 1. And once you go through
all the simplifying, you end up with
Firm 1 choosing the output of A plus the
cost of Firm 2 minus 2 times the cost of
Firm 1 divided by 2B. So Firm 1's decision
doesn't depend on the output decisions of
Firm 2. It just depends on understanding what
their costs are. Once you know that, you
can make a decision. and as we can see
graphically what this looks like is that there's a
first mover advantage you want to be
the first mover in sackelberg so if firm
one produces here at q1s then firm two's best
response is to produce here at this point here
qs2 and when we look at the isoprofit
curves for firm one the isoprofit curve for the
stackelberg equilibria this blue line here is
closer to the origin than the corno one
so by being the first mover they're making
more of a profit and it's the opposite for firm
two they're further away with the isoprofit
curve here compared to where they would be
at corno so the move order matters by knowing
the other player's reaction function you
can produce a certain amount to maximize how
much better off you are and make the other
firm worse off and finally we can show this
mathematically as well we have this inverse
demand function we have these cost functions
and using what we had before we can figure
out firm two's reaction function so this is
if we do the math this is going to be firm
two's reaction function 24 minus a half q1
the leaders output is just a plus the cost
of firm two minus two times the cost of firm
one divided by two b and we have all of that
here so this is the the the cost of firm
one the cost of firm two this is a and b is
going to be one here we plug it all in and we
get 24 then we know because the lead is
going to produce 24 units we put that into the
followers reaction function 24 here and we
end up with 12 so now you can see they're
producing different amounts the the lead is producing
a lot more which means the follower
has to produce less we can figure out the
market price by adding them both in and ultimately
we can figure out the profits of each
firm and firm one is going to do better than
firm two in terms of profits because they're
both facing the same price but firm one is
able to produce more and finally
bringing the idea of these different
forms of oligopoly and duopoly
together is um you've probably all
noticed like every time you blink
there's a new ai model on the market
and this is because they're all racing
each other to get to the best
capabilities they know based on simple theories
like this if you can be the market
leader this is going to result in better
profits and ending up in this corner is set
up where everyone's making decisions at
the same time you want to be the first move
you want to be the first to get to something
so you have these sort of race dynamics
in the ai industry so what this means is it
incentivizes getting the best ai model
capabilities no matter what the cost and
there's a lot of concerns regarding ai in terms
of how it's going to affect um you
know society in terms of the labor market in
terms of the information puts out there
the slop on social media and for a number
of people there are genuine concerns about
existential threats which we can go into
another time and the argument is a lot of
firms individually they care about this
but they know that due to this racing dynamic
if they try to play things safer another
firm is just going to race ahead and be
the first one to get to artificial general
intelligence and be the market leader in
this Stapleberg kind of setup so when they
view a market at more as the Stackelberg
kind of set up where the leader wins, the
first and something wins as has been the
case with a lot of technology first to
the atom bomb first to the moon etc have had
these Stackelberg race dynamics we get a
lot of incentives for producing goods no
matter what the cost so yeah this is probably
an issue how to solve it is an interesting
question, I know there are people that
are trying to get the CEOs of these
firms to sign these conditional statement
saying, I promise my company will slow
down if all the other companies also promise
to slow down. So there's conditional cooperation
type of thing. But yeah, the incentives
for racing are due to the rewards of
being the leader as we saw in Stackelberg
compared to Cornelow. Okay, brilliant. That's all I have for today. I'll see you all
on Wednesday. And yeah, don't
hesitate to reach out if you
have questions. I was wondering
if I could take a picture
of your Mac. Yeah, sure. Thank you. Just for like
a reference. No worries. Thank you. So this kind of
overlaps with game theory a little
bit? This is game theory. Yeah,
this is exactly what game theory
can be used for. Okay, awesome. So that's more like a fly version of it?
Yeah, exactly. As I said, it's
essentially a prison's dilemma when you
think about it. Yeah. Because you
either collaborate or you don't collaborate. And then you can also
cheat. which is yeah exactly exactly and you
end up with this condo equilibrium you know
both firms worse off than what they could
be but it's actually a situation where the
incentives work out well for society because
we know it's just hard for firms to collude
which is nice yeah and i mean okay i don't want
to sound like rude but like usually firms
like tend to cheat a lot i know that's why
we have antitrust but i'll show you an example
later of um uh gas companies in australia
and there's some really interesting price
patterns of how they start off by collude and then
they keep undercutting each other and then
they get to a point of like no profits
and then they collude again and it has this
same pattern it's really weird that's weird I
should look you like okay you're gonna
present on that yeah yeah I'll talk about it yes
I want to look into that yeah yeah I can send
you some cool blog posts on it awesome
because I feel like I want to understand yeah no
remember all the stuff we're teaching is very
basic in the sense that it's not all
encompassing obviously firms collude they can as
we talked about using things like green trigger
strategies you can collude with each
other when there's more firms in the market it's
harder to collude as well these things hold
it doesn't mean collusion is impossible right
this means that the conditions they be in
a certain way for the allowing um allowing
collusion yeah i know like in this case we
only like saw like a case of like two firms doing
it so yeah exactly exactly in one shot
environment as well exactly yeah also for the
exam next week it will be pretty much this
chapter game theory and yeah yeah thank you no
worries yeah hey guys how's Tennessee yeah
yeah yeah yeah just have a quick question
on what chapters current amanda is this is all
about the exam yeah so So up until the end
of today's lecture, so Bertrand won't be on
the exam, but Sweezy, Corneau, and Stapleberg will
be, but when you think about it,
Corneau and Stapleberg are just applications
of game figures, so it should help
in that regard. So it's like lectures? Topics 9, 10, and
11. 9, 10, 11. Okay. Thank you for your
time. No worries, guys. Thank you. Have a
good one. Thank you. You've been
watching Artemis? it's on netflix
isn't it i'm pretty sure they're streaming
it on netflix support the oh really oh that's
amazing so i said to her and i was like
okay which one is this they have a sailor
moon cat and apparently the cat's name is
artemis oh they named it after the sailor moon
cat or did they well they named it after
mythology wait so artemis is a roman or
greek um roman isn't it paul is definitely
greek yeah it's apollo and
artemis so then it's greek is
it diana because the original
program is apollo so they picked
artemis because because she's
Apollo's sister. Ah, yeah. Goddess of hunting
the wilderness while it transitions
in each other. Interesting.