So, I finished writing
up the exam so I can tell you a little
bit more about it. The exam's going to
be, probably around 55% of it is game
theory related. And some key things
I want to point out now that you can
focus on, because I will appear on the
exam in some form, is firstly, mixed
Nash equilibria. Know how to find the
mixed Nash equilibria, the probability
that player 1 does action 1, and
the probability that play 2, just action,
you know, Q, etc. That's important. Secondly, how to find
in infinite games and stochastic
games the cutoff point, whether it
be the interest rate or the probability
that the game ends. Knowing that is going
to be important. And the other thing
I'll point out as well is
understanding what sub -games are. If I gave
you a game tree, if you are able to
figure out how many sub -games there are, that
will help. and also just a general understanding
of what sub-game perfect national
equilibrium is. You don't need to go too deep
into that one, though. Then around 10% to
15% of the exam, more close to 10%,
will be on the oligopoly models
that we've discussed up until
the end of Monday. As I think I said
in this class, none of that will
be mathematical, so you don't need to
derive any reaction functions, even though
I really wanted to put that on the exam.
I didn't. It's more going to be about the
assumptions in these different models and
what are the implications that come out from
these assumptions. And we will do a
kahoot today, so hopefully that will
refresh your memory there. And the
remainder third will be on the market
structures that we spoke about a
few weeks back now. Any questions regarding
the exam itself? Great. I've been
a little bit slack. I apologise
about that. I will put out a
practice exam soon. just finishing
writing up the questions i'll
hold the revision section in
class on monday and then i'll release
the room where i'm doing the two-hour
revision before the exam so hopefully that's
enough housekeeping and we're all
on the same page there but yeah
don't hesitate to reach out if you
have questions so we finished up by
looking at the um the the stackelberg
oligopoly model and the stackelberg is the exact
same as our Cournot oligopoly model in that
both firms choose the amount of output to
produce that determines the output, the price
and the market and the profit. The key
difference is in Cournot, all firms are
choosing their output quantity at the same time
whereas in Stackelberg it's sequential.
There's a leader, the first one that
chooses their output and then the second firm
is essentially reacting to that so the second
firm's reaction function is the exact
same as in core noise the only difference is
the first firm doesn't take into account
the quantity produced by the followers but
rather they only in the end care about the
marginal cost so as you can see here what ends
up happening in these Sackleberg oligopolies
is that the leader will always produce
more output than the follower they're
essentially strong arm in the follower because
they have this first mover advantage. And
importantly, the price in the market is the
same for both firms. One firm can't sell at
one price and another firm sells at another
price. They have to sell at the same price.
So what will happen here is the profit for
the leader is going to be much larger than
the profit for the follower. And I'll show
that again shortly. So that was what we went
over with Sackleberg. And now I kind of want
us to switch gears a little bit and rather
than thinking about quantity and how
much to produce let's start thinking about
prices how much do you price your products
out and we're going to test this out by playing
a little bit of a game you know me I like
my games where all of you are going to be in
this duopoly environment it's going to be
you and one other person in this class
and you both are selling your products essentially
it costs you three dollars to make one
of these products and you price them anywhere
between $3 and $15. And the way this market works is the consumers have perfect
information and there are no transaction
costs, so they know everything
about your pricing. And what they'll
do is they're going to buy from whoever
prices it the lowest. So if you
price it at $10 and the other person
prices it at $9, then all the consumers
will buy from the person who prices it
at $9, and none of the consumers will buy
from the person who prices it at $10. If two people
price it at the same, if they
both price at $10, then the way it works
is consumers will 50 % go to one and 50% go
to the other. You'll have this 50% there's
going to be 10 rounds, you're going to be
mapping the same person throughout, and as
with the other games, whoever makes the most
money at the end will get a little bit, will
get a little prize. So if you go to
veeconlab.com, BLGR30, you can get started.
The instructions will clear a few
things up as well. You can ask questions. If you're on your phone, you can turn
it to the side. It's much easier to read. So someone asked in
the other class, yes, you're matched with
another person in this class. It's not
an AI or a robot. People are starting to
put in their prices. Yeah, there's 10
rounds and you're matched with
the same person. Yeah, Eric, in the instructions,
let me check. Also, then sometimes, you know, with
these things, the matching doesn't
properly work. Eric, if it isn't
working for you, just tag along
with the SNX. What's your name
again, sorry? Moses. Yeah, just like Eric's hand. Oh, no,
it's working. Okay, you got it. Okay. What did you get? $109. I think you're
in the lead. I think that's
pretty good. Okay. Irwin's currently in
the lead with $109.5. dollars? But I think
someone will beat you. They're finishing up
a little bit of a game at the moment. Yeah,
we'll talk about it. Oh, you can see
my name on it. I have access to
it every weekend. I'm a big brother. Okay. DK, what did you get? I guess it's a number
of years. I think it's like 133. So
DK's on 133, so that's the leading
number at the moment, and that is higher
than what everyone got in the other
class and we had twice as many people, so
really well done. So as people are
continuing and finishing up, and if you're still
leading at the end, you can come up and
get a prize from me at the end of class,
but please keep going. DK, what was
your strategy? How did you make
so much money? So in the first round, what price did you do? Um, I think I did like, I think I did like $6,
like I just did like the average, and then
minus $2, and then like, I don't know.
It's nice, it's nice. Who didn't do well?
Did anyone not do well? Michael, what did
you, what did you get? Um, I got $22. $22, so more than $100
less in DK. Why did you only get $22? What
happened? I feel like I set my prices too
high in the beginning. Yeah. I expected the
person to do maybe like $12 or something, so I
did like $9, but then it was the opposite,
and they kept going down, I kept going just
like one over them. Okay, so you were
at $4, yeah? Yeah. Isabel, is it the
same with you? It was pretty much the same.
Whoever the other seller was kept it at $4, so
I had to kind of stay the same level. So you
were at $4 as well. Yeah, I saw a lot of
$4s happening there. Right, so everyone's
finishing up. Yeah, DK, amazing job.
I don't know how you made that much money.
So this is a game, this is known as the
Bertrand oligopoly, and unlike Cournot, the
key difference here is rather than choosing
the quantity to produce as you all just did
yourselves, you choose what price to set.
That's the variable that you can change price
rather than quality. So firms in this
market produce identical products at
a constant marginal cost. They have
the same marginal cost in the game
that you played. And as I said,
consumers have perfect information and
there's no transaction cost. So they'll
just buy from whoever charges the lowest.
And barriers to entry exist so other
firms can't enter into the market.
So this is a game. So can someone
tell me what's going to happen
in this game? Is there a Nash
Equilibrium? And the hint is,
people already kind of talked
about what it is. Eric. So why? Yeah, why? That's what I
said about. OK. Sure, I mean, that's
a tautologist answer, but it is right.
Christian, what's up? So you could 100 cut
anybody without losing money. Yeah. If you
do it 3, you won't pay any money. Yeah,
yeah, exactly. So if you set a really high
price at like $12, what that means is
if you both set it at $12, you both split the
market, you both make positive profits, but
you're incentivized to go lower to $11
because then you capture the whole market and
you make more of a profit. and what that
means is if you go to 11 then your opponent
is incentivized to go to 10 and then your
incentivize to go to 9 so on and so forth
until you're all the way down to four dollars
in our game at least so four dollars is is
the Nash equilibrium in our game but in
reality when your prices are more granular when
you can go to like decimals in the sense
what happens is the price ends up equaling
the marginal cost that's what the Nash
equilibrium is imagine if could go to decimals
you could go in three dollars and one cent
it would be better to do that than four
dollars because then you capture the whole market
etc so you keep going down until both firms
price their product at the marginal cost
this is assuming the marginal cost is the
same for both parties as it was in our game
but this price wall ends up in this actually
socially efficient level of output it's
the same marginal revenue equals marginal
cost as in a competitive market so as you'll
see our different assumptions about
oligopoly have different outcomes for the welfare
of society so this is a graph of prices from
melbourne australia and this is our petrol
market we call gas petrol and these are
the big plays we have bp caltex coals woolies
7-eleven and this is the wholesale price
of petrol and what is going on here so the
graph on the previous page unpacks the mechanisms
that drive prices up and down published
by burn at all 2023 it shows the average
price for each major retailer around Melbourne
so the companies listed represent more
than 50% of the market share they're essentially
an oligopoly they're all the big players
in this market most of them are the supermarket
chains that add a gas station in the
vicinity of their store at their stores and
the market later in the area calls is the one
that initiates the price cycles so what
you can see here is this weird pattern the price
is lifted by coals by like 20 cents a litre
up here and all the others collude and go
up with them with this higher price but then
you can clearly see between october one
and november one over a month there's this
undercutting phase you can see this step function
essentially where one you know a firm
lowers their price so they all do and they keep
undercutting each other like with this
logic in the Bertrand equilibrium model all
the way until they're pretty much at the
wholesale price November 1. Then somehow they're
able to collude again and go back to
the high price and then the undercutting
phase begins again and this is not just
over like a couple months this is years
worth of data that show this pattern.
So we have this really weird situation
where these cycles reflect tacit collusion
that these firms somehow have a way to
collude on a high price but it's imperfect
because as soon as they get to this high
price point they're incentivized to start
undercutting each other. I think it's just
pretty incredible how these cycle repeats each
other and it happens in a lot of oligopoly
markets as well. Yeah Tava? Yeah, so there's a little
bit of Stackelberg in that sense but
it's different because what they're
changing is price and not quantity so they're
altering the prices which is the key
part of the Bertrand model and we can
see the other part of the Bertrand model
is this undercutting phase as well so
we see that there, how they lead
this collusion is another question
entirely I think the paper speaks about
it a bit more I think it's quite
interesting how they're able to do
it like that though yeah yeah but when
it's when it's that low how much of the market
share you actually like capturing at these
small profits you're probably better off
in the short run at least colluding as
well so there is as we know benefits to
colluding it's just unstable but yeah there
are also friction cost think about like when
you all drive around there's probably some
gas stations you go to more than others
because of proximity things so there are
kind of some frictions in the market as well
that probably lead to more collusion so
these models are very basic foundations
that we use to conduct our research and our
analysis so as you can see the ideas are
pretty strong here but there's probably other
factors as well that like point to why
this collusion happens alright, so the last
thing I want to do is just compare the
oligopoly models, so across all of them,
actually I should say Sweezy is a
little bit different Sweezy doesn't allow
us to do this sort of analysis so
we're only going to compare the other
three with Sweezy, all I want you to remember
is two things, the assumption in
Sweezy is that other firms will match
your price decreases but not your price
increases, and as a result of
that assumption we have this
kinked demand curve and thus it kinked
marginal revenue curve. And the implication of
this is that there's a large area where your
marginal cost decreases but you're not actually
incentivised to produce more. Because
if you produce more, the price lowers, other
firms match this lower price, and you end
up with less profit. So that's the weird
implication of SWEASY. That's all I need you
to remember for SWEASY. I do like saying
SWEASY, clearly. Alright, so let's
compare the others. So if they face this
following inverse demand function where price
equals a thousand minus quantity, where quantity
is made up of the quantity produced by both
firms, and both firms face the same
marginal, the same cost function of four times
the quantity produced. so what do the different
oligopoly models say that will happen in
the market so i'm not going to do the math
again we did it last class and as i said
on the exam i'm not allowed to ask you the
math so let's just go through the implications
we can derive the reaction function of
both firms here so it's just taking the the
total revenue minus the total cost and then
taking the derivative of that and then isolate
in terms of q1 and as you can see their
reaction function depends on the output
of the other firm firm two and same for firm
two to firm one the next step in solving this
model is you substitute this equation into
q2 then you can solve q1 once you have q1
you can plug it into q2 you have q2 add q1
and q2 together you've got your quantity once
you have your quantity you can figure out
your price because it's just a thousand
minus quantity and then you can figure out
profit as well those are the steps for those
wondering but as you can see the outcome here
is both firms produce 332 units each which
means there's 664 units in the market so
the price is 336 dollars and both firms earn
110 224 dollars each okay so let's compare
this to stackelberg so in stackelberg if
you remember there's a leader who sets their
output first and then the followers set it
so the followers are reacting to the leader
they're using reaction functions and the
followers reaction function is the exact
same as in corno 498 minus a half times q1 exact
same thing here the difference is the leader's
decision regarding output do you remember
what we ended up deriving is the leader
takes into account a which is this intercept
here so a thousand plus their own
marginal cost function, sorry, the other
firm's marginal cost function, which is 4,
minus 2 times their own marginal cost
function, which is 4, divided by 2 times B, which is just
the slope of this here,
which is just 1. And that's how we get their output,
which is 498. So as you can see,
in this market, the leader is producing
much more than the follower overall
there's more quantity in the market compared
to in the um uh um the the corno oligopoly
and the profits are quite distinct from each
other the leader makes 124 000 which is more
than what they're making corno so there
is his first mover advantage so they're
making 14 grand more and the follower is much
worse off so they're making essentially
fifty thousand dollars less and because the
price is lower it's 253 dollars here
instead of um 336 what's going on is the leader
can kind of extract as much surplus as they
can which makes the other sellers worse
off but what this means is the um sackelberg
outcome is better for consumers than it is
for produces lower prices yeah yeah that's
like a law I mean there are ways we can
do marginal cost so it's dicey but the law
is that if they have the same marginal the
same cost function first mover always produces
more always produces more and they both
sell at the same price those are the key
features key features then we have bertrand
and if you remember they'll keep undercutting
prices until price equals the marginal
cost that's the national equilibrium here and
as a result if price is fall we can solve
for quantity quantity is going to be 996 and
given symmetric firms each firm gets half
the market so they each sell 498 units but
because the price which is the marginal revenue
equals the marginal cost they're not making
any money on each sale so they're earning
zero economic profits and this is an
efficient market this is the exact same outcome
as in a competitive market essentially there's
no dead weight loss here and finally we
have our collusive outcome when our corno
firms act as a monopoly and split the profits
so in this case the price is going to be
the highest at 502 and each firm is going to
earn 124 000 dollars and two cents which is
interestingly the same profit as the leader
in the stackelberg so both firms are better
off colluding than they are in the corner
equilibria but can someone tell me daniel is
this a stable outcome in collusion be stable
in the in the short yeah so the the
technical answer here is you're on the you're
on the right path the technical answer here
is it's um not in actual equilibria in
like the one-shot version you have an incentive
to cheat because you'll make more
however as we learned in these stochastic games
or infinite games using these trigger
strategies you can actually sustain collusion
but when i ask you like an oligopoly
question like this i'm not talking about you know
infinite or stochastic you know situations
the assumption is that you know this
isn't a stable um situation and firms will
defect on each other okay finally
contestable markets so we've talked about
the firms in the market but we've
always just assumed barriers to entry
into these markets. So let's talk about
this a bit more. So a contestable
market involves the strategic interaction
among existing firms and potential
entrants into a market. A market is
considered contestable if all the
following hold. All producers have access
to the same tech. Consumers respond
quickly to price changes. Existing firms cannot
respond quickly to entry by lowering price,
and there are no sunk costs. If this is
the case, there are economic profits to be
had, and firms will want to enter into the
industry because they can capture some of
these economic profits. However, if some
of these don't hold, you're
going to have non-contestable
markets. So for example, existing firms cannot
respond quickly to entry by lowering price.
This is a strategy done all the time by, you
know, for example, a famous one is OPEC, That
if there's a competitor that joins the market,
they just lower their prices so low so quickly,
it's not sustainable for another firm
to keep their entry and they drop out. This
also actually serves as a really strong
signal and a threat to anyone considering
entering the market in the future that we can drop
our prices so quickly that it's not profitable
for you to enter. Also, the idea that there are no sunk costs. A lot of the time,
costs are sunk. So, for example, let's say
you want to join the food truck industry.
Buying the food truck isn't free. That's the
sunk cost. You might have to spend like
$100,000 on it, for example. And if you
resell it and you exit the market, you might
only get $80,000 back. So, $20,000 is sunk. And because of that,
you need to take that into account when
deciding to enter. So, if there are no
sunk costs, all you need to think about is
this marginal revenue versus marginal
cost. But when you're considering the sunk
cost as well of entering, that changes the
calculus a little bit. If different producers
have access to different technology, that's
how we get to these more monopolistic
situations as we showed, more economies of
scale, patents, other tech features, network
effects are ways to stop other firms
entering essentially. So, this is what kind of
allows for certain markets to be contestable
and others not. If these conditions
do hold, if the market is
contestable, we end up with the perfect
competition outcome where price equals
marginal cost and firms earn zero
economic profits. So, that's all I
have for today. We're going to do the Kahoot
now. I should also say we're not going to
have class on Friday. Use that as a time
to study for the exam. I'll release
a practice exam hopefully tomorrow
afternoon and yeah and no one beat DK's
$133 I'm guessing okay sorry DK you
got you got sniped okay so wait what
price were you doing yeah okay you
don't have to out yourself stuff
like that. So this is why in
experiments, incentives matter. So in this case,
the incentive is only for the
person who maximise their income and
won the game. So you can do that
sort of behaviour. But what if, for example,
I actually paid you the money you earned, do
you think you would have behaved a bit
differently if you got in cash whatever money
you got on your screen? Yeah. Okay. Fair enough. I
would assume that if there was real money
on the line, depending on your earnings
and it wasn't zero sum, that only
one person won and everyone lost, people
would have behaved a little bit
differently, I assume. Everyone in? Is it a sustainable
strategy? I know it wouldn't be
sustainable, but if they both did 15, what
would you have got? If you both did 15, I can't remember what
the demand curve was, but the issue
is, in the last round, you're
incentivized to do 14, and that rolls back
in the same way. Yeah, that's why
this, like, task solution in these
petrol markets is also really
interesting. Okay, I'm gonna
start us off. Six questions. Which of the following
is not one of the four oligopoly models
covered in this topic? Sweezy, Corneau,
Bertrand, Marshallian. Come on, give me 100%. Okay. Yeah, Marshallian, yes.
I mean, yeah, I can't really comment on this
one. just it's not a oligopoly model ah in
an oligopoly managers can ignore the
decisions of rival firms when making their own
choices true or false 100 fantastic now
i'm happy well done everyone ah in the
sweezy model each firm believes that rivals
will match both price increases and
decreases match price increases but not price
decreases match price decreases but not
price increases ignore all price changes
let's see if you were listening earlier
yeah great majority of you got that right yep
that's the assumption maybe match price
decreases but not price increases for
those of you got that wrong now's the time
to remember this one firms in a corno oligopoly
always earn higher profits by colluding
than by competing. Okay, so this is
true. So if they both collude, by definition,
they both earn higher profits than if they
both don't, essentially, if they play the
call, no equilibrium. It's a different
question to say, is this a stable outcome or
not? But the whole point is the payoffs
are higher for both when they collude.
And that's what we get at with this
interesting situation. And it is essentially
a prisoner's dilemma at the end of
the day okay penultimate question in a
stackelberg oligopoly the key difference
from corno is that firms compete on
price instead of quantity one firm
chooses output before the others firms produce
differentiated products there are
no barriers to entry majority of you got
that right so firms competing on price
instead of quantity that's bertrand so in stackelberg
it's the exact same as corner except it's
a sequential game where one firm moves
first okay who's in the lead who's um sunny
frog nice have you won one before okay cool um
i mean you're only 23 points up so it's
pretty close all right last round bertrand
competition with identical products in constant
marginal cost drives price down to marginal
cost. True or false? Quick on the
trigger there. Majority got that
right? Yeah, that's true. As we showed,
they undercut until we get to
the marginal cost. Oh, wow. Did you get the
right answer? Oh, you got the right
answer and you got overtook that. You must
have been lightning on the trigger there.
Congratulations. Okay, that's it.
Enjoy your extra ten minutes in the sunshine,
and I will not see you on Friday, but
I'll see you on Monday. Yes, have a letter,
and we can work away. Yeah, of course. Do you want anything
yet? I want one of the go-goes. Okay,
what do you want? You can have koala
kangaroo, stress ball, produce, stress
ball, or a candy bar. Okay, I'll give
you your choices. Do I have any
other variety left? No one likes pre
-masketeers, apparently. No worries. And also, yeah,
so your email. I reckon we do
a little bit. My assumption is
you're going to do well on this exam. Yes. I
need like six years. And then you won't
have the bottle. So you're going to
do it during all week of finals for you?
Yeah. Okay, correct. No worries. Eric, what's up? Are those empty slides
important? I wasn't here on Kono. I completely
don't understand what's going on, but
I'll try my best. Somehow, it's
overcorrected. I don't know how to do that.
Yeah, so the intuition is more important at
the end of the day. So you can get to it
with the graphs, but yeah, the math, like,
go over the video. Okay, and for the
announcement... Were you here on Monday? Yeah,
would you say the math we did for Kono? It
probably is important. Oh, that's the right
part. Yeah, that's what you derive,
but you don't need to know it for the
exam, but I think it helps with the
intuition more, because the graphs
are an absolute mess. I don't like the
graphs. See, Mark? Yeah, it's just no lines. Yeah, yeah, and they're not that informative, yeah. And for the
announcement you make, what do you
mean by derived? Does that mean like no
compilation or still compilation, but just
no? For the oligopoly models, there's no
derivations. No derivations. Yeah, so none of that
math is necessary. I just want you to
know the assumptions of each of the models
and the implications. So there's no
calculations going on? On the exam, there's
going to be a lot of calculations in
the banking research. But not for the
all-calculation? No. No equation
at all? No. No equations? No equations. Just the concept. So the game theory,
we're supposed to know all types of
games and everything related to it? Yeah,
everything we covered. surprises. No
worries. Okay, see ya. Oh wait, your prize. What do you want? Are there the same
options? Yeah, kangaroo, koala,
stress ball, choppy. Nice. There you go,
congratulations. What's your name,
sir? Parv. Parv, okay, brilliant. Congratulations,
Parv. Thank you. See you. See you. Are you going to
post questions again? When I
finish writing them? Yeah, I'll try it
tomorrow afternoon. Oh, okay. Yeah, yeah. Got it. So, just to
make sure again, the derivation
you've been, it's been like
every equation Yeah, the
equations, I won't ask you to do
anything mathematical with the oligopoly model. See Eric. Moses, you good?