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## Oligopoly and game theory

# Game theory worked example from AP Microeconomics

AP.MICRO:

PRD‑3 (EU)

, PRD‑3.C (LO)

, PRD‑3.C.1 (EK)

, PRD‑3.C.2 (EK)

, PRD‑3.C.3 (EK)

, PRD‑3.C.4 (EK)

, PRD‑3.C.5 (EK)

, PRD‑3.C.6 (EK)

## Video transcript

- [Instructor] What we have
here is a free response question that you might
see on an AP microeconomics type exam that deals with game theory, and it tells us Breadbasket and Quicklunch are the only two sandwich
shops serving a small town. So, we're in an oligopoly situation where we only have a few firms. Each shop can choose to set a high price, or a low price, for sandwiches. The payoff matrix below shows
the daily profits for each combination of prices that
the two shops could choose. The first entry shows
Breadbasket's profits, and the second entry shows
Quicklunch's profits. Assuming that both shops
know the information shown in the matrix, answer the following. So, just to make sure I
understand what's going on here, this is saying that for example
if bread, Breadbasket can either choose to charge
high prices or low prices. Quicklunch can either
choose to charge high prices or low prices. If Breadbasket chooses high prices and Quicklunch also chooses high prices, then what this tells us is the first one is Breadbasket's profit
per day would be $105, while Quicklunch's profit
per day would be $110, and then this is a
situation where Breadbasket is low and Quicklunch is high price, and then Breadbasket would make 120, and Quicklunch would make
80, and then when Quicklunch has low prices we can see
what are the profit of either when Breadbasket charges high prices or Breadbasket charges low. So, with that out of the way, let's try to answer these questions. Does each shop have a dominant strategy to set a high price, a dominant
strategy to set a low price, or does it have no dominant strategy? So, pause the video and
try to figure that out, and just as a bit of
a hint, or a reminder, a dominant strategy is
a strategy of regardless of what the other player
does you would still be better off to make that choice. So, a dominant strategy
of setting a high price would be regardless of
whether the other player decides to set a high or
low price a high price would always make sense for you. So, pause the video and try
to see if you can answer that. All right, now let's see what Breadbasket's situation is here. So, if we think, Breadbasket
of course can either choose to go high or low. Now, if Quicklunch goes high,
what should Breadbasket do? Well, then we are in
this column over here, and these two numbers are for Breadbasket, and so if Quicklunch goes
high then Breadbasket could go high and charge
105, or it could go low and charge 120. So, if Quicklunch goes high,
Breadbasket should go low. So, let me write this,
Quicklunch, Quicklunch, if it chooses to go high, then Breadbasket should go low. Now, what happens if
Quicklunch chooses to go low? Well, if Quicklunch chooses to go low, the two options for Breadbasket
are either $40 of profit per day if they have a high price, because a lot of their
business would go to Quicklunch in that situation, or
they could go low price and make $75 per day. So, even if Quicklunch goes
low it still makes sense for Breadbasket to go low. So, Breadbasket goes low. So, we see that Breadbasket,
no matter what Quicklunch does, it makes sense for Breadbasket to go low. So, Breadbasket has a dominant strategy to set a low price. So, the dominant, dominant strategy to set, let me write that
a little bit clearer, set low price. All right, now, Quicklunch,
so, we could do the same type of analysis based on what
Breadbasket might choose to do. So, if we see, okay, if
Breadbasket goes high, what should Quicklunch do? Well, let's see, then Quicklunch should, so, if Breadbasket goes high, Quicklunch, should it go high or low? So, it would have the option of $110, or it would have an option of $130. So, if Breadbasket goes high, Quicklunch is better off going low. So, let me write that down. Quicklunch should go low. And if Breadbasket goes low
what should Quicklunch do? So, if Breadbasket goes low,
Quicklunch can either make 80 if it goes high or 70 if it goes low. So, in this situation
if Breadbasket goes low it makes sense actually
for Quicklunch to go high and make the 80. So, Quicklunch would go high. So, Quicklunch has no dominant strategy. It doesn't make sense for
them to always go low, or always go high regardless
of what Breadbasket is doing. Depending on Breadbasket,
it might make sense for them to go low if
Breadbasket goes high, or high if Breadbasket goes low. So, no dominant, dominant strategy. If the two shops do not
cooperate on setting prices, what will be the profit for each shop? Well, actually, just pause the video. See if you can answer that
before we work through it. Well, we already know that Breadbasket has a dominant strategy to set a low price. So, Breadbasket is gonna
go low, regardless. So, that we're going to end up
in this row right over here, and if we are in that situation
where Breadbasket goes low regardless we know that it
makes sense for Quicklunch to go high, because they
could either make 80 or 70. Well, they're gonna go high,
and so we're going to end up in this column right over here. So, if the two shops do not
cooperate on setting prices, the profit of each shop would
be Breadbasket would be making $120 a day and Quicklunch
would be making $80 a day. And this is a Nash
equilibrium, because on its own no firm can change its decision
to optimize its prices more, because if you are in this,
if you are in this cell right over here, Quicklunch can't change Breadbasket's decision. So, Quicklunch could say
I'm either gonna make 80 or I'm gonna make 70, so,
it wouldn't make any sense for them to switch away,
and then Breadbasket, they can't make the
decision for Quicklunch. They can say, hey, we're
either gonna make 120 or we're gonna make 105. And so, since we can't change
what Quicklunch is doing, well, of course we're going
to choose to make 120. So, people will stay in
this bottom left cell (mumbles) a Nash equilibrium. All right, so the next part
they ask us, or they tell us, the town government is concerned that food prices are too high. It decides to give a daily
subsidy of $20 to any shop that chooses to set a low
price for its food items. Redraw the payoff matrix under the government subsidy system. So, like always, pause this video, and go through that exercise. It'll be interesting. All right, now, let's do this together. So, we have Breadbasket,
and I'll try to write bread, actually, let me draw
my little matrix first. So, it's a two by two. So, almost done with my matrix. And one more. That wasn't near the middle. There you go, right around there. Still, maybe there. And then we have that there. And then we have high, low, high, low, and then you have Quicklunch. If I were actually doing this on the test maybe I'd write this a little bit lower so it's a little bit neater,
and then this is Breadbasket. And let's see. It's giving a daily subsidy of $20. So, if we could just do
that, that adds to the profit of a firm that is selling at low prices. So, if they're both at high prices, that's not, they're not going to be able to get that subsidy from the government. So, we're still going to be at 105 and 110 for Breadbasket and
Quicklunch respectively. Now, if Breadbasket stays
high in this situation, well then, they're still
only going to make $40. But in this situation right over here Quicklunch is going to get a $20 subsidy because they are choosing to go low. So, they're going to make 130 plus 20. So, I'll write that in a different color. So, I will put that in
and I'll put this in red. So, 130 plus 20. They're going to make $150
because they're choosing to go low price here. That's what qualifies you for the subsidy, and in this situation if
Breadbasket goes low price they're going to make 120,
what they would have made in that situation, plus 20. So, this is going to be 140. But this is a situation
where Quicklunch is charging a high price. So, they're not going to get the subsidy. So they're still going to make $80. And then this cell is both
of them charging a low price. So they're both gonna get
$20 more than what you see right over here. So, Breadbasket would make $95, $95, and Quicklunch is going to
make $90 in this situation. And let's see, they ask us more questions. They say using your redrawn payoff matrix answer each of the following. Would Quicklunch choose to set
a high price or a low price? Explain using specific values
from your redrawn matrix. So, pause the video and
see if you can answer that. All right, so we're going
to look at Quicklunch now, and we could do the same type of analysis to see if they have a dominant strategy. We could say, okay, if
Breadbasket goes high, goes high, what is Quicklunch going to do? So, if Breadbasket goes
high, now in this situation Quicklunch will either
go high and make $110 or it could go low and make 150. So Quicklunch is going to
go low in this situation, and if Breadbasket goes
low Quicklunch canmake $80 if it goes high or it could
make $90 if it goes low. So once again, Quicklunch
is going to go low. So, Quicklunch, Quicklunch now has dominant, dominant strategy for low price, for low price. And I could try to explain this out. If Breadbasket goes high,
I'll write it out here. Normally you have a little
book to write this in, but, if bread, I'll abbreviate,
Breadbasket goes high Quicklunch is rational to
make $150 instead of 110, would want to make $150 versus 110 by going low. If Breadbasket goes low, goes low, Quicklunch makes $90 versus, versus $80 by going low. All right, would the profits
for Breadbasket increase, decrease, or stay the same? Explain with a comparison to
your answer in part B one. Use specific values. So, before subsidy,
actually pause this video and try to do this as well. Before subsidy, oh, now
we'll do it together. Before subsidy, Quicklunch,
or I should say Breadbasket, Breadbasket was making,
and we have it up here. So, if the two shops do not
cooperate on setting prices, what will be the profit of each shop? We saw Breadbasket would make $120, 'cause that was that
Nash equilibrium state. After subsidy, after subsidy, so, let's look at it. We still have, Breadbasket
still has a dominant strategy to go low, because if Quicklunch goes high Breadbasket would wanna
make the 140 instead of 105, and if Quicklunch goes low
Breadbasket would wanna make 95 instead of 40. But now they both have a
dominant strategy for going low. So, we're going to end
up in this bottom right, this bottom right cell. After subsidy, both have
dominant, dominant strategy to go low, resulting in $95 profit for Breadbasket. And so, $95 is less than $120. So, Breadbasket's profit goes,
or I should say it decreases, decreases, and we are done.

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