OK,  back at it again.  This is chapter
14, part two.  This is the continuation of
our oligopoly presentation.  We are going
to take a look at simultaneous games in
game theory.  Simultaneous games can be a
little tricky to work out, so I'm going
to help you through it in this
presentation.  In your chapter you will
also find a section on sequential games.
I find most students don't have any real
difficulty following the sequential
games. it makes a lot more sense.
Simultaneous games on the other hand
tend to trip you up a little bit.  Let's
go ahead and just work through some of
the basics of these games.
Alright the easiest way to usually learn
these simultaneous games is to just take
a look at them.  For starters let's get
lingo out of the way.  You are going to
have players,
these are usually firms.  In our example
here two airliners, British Airways and
Lufthansa.
Those firms are also going to be making
choices about strategies,  in our example
they're trying to choose between a high
price for a particular air route or a
low price.  How they do on those
strategies is going to depend on what
their competitor chooses, so you have a
payoff matrix.  Each one of these boxes
represents an intersection of two
different strategies by the players.
Those numbers will indicate how they do. 
In our example the way I have set this up
Lufthansa is always your upper left
corner... British Airways is always your
bottom right corner.   So, now you've got
the basics down: players, strategies, payoffs.
How does this help us actually
understand what firms are going to do?
Firms are always thinking about what
their competitors are likely to do,
because they would like to choose the
best choice, given what a competitor
is going to do.  The only problem is they
don't know for sure what that competitor
is going to do.  Game theory helps us to
see the choices in front of them and
also which choices likely make sense for
them.  So let's go ahead and do Lufthansa
in green and we'll make British Airways
the red.
Okay if Lufthansa is planning ahead
and wants to know what they should do
if British Airways were to choose a high
price, then they're going to go ahead and
they're going to say,  "Alright well if
British Airways puts me in the left
column I've got to choose between 1.2
million and 1.6 million. Of course 1.6
million is the more attractive choice,  so if
British Airways were to choose hi
Lufthansa would be better off if they
had chosen the low.  Now British Airways
also may choose to go with a low price,
and if British Airways chooses to go
with a low price that puts Lufthansa in
in the right hand column....and they're now
thinking if British Airways were to
choose a low price would I be better off
choosing a high price or would I be
better off choosing a low price.
Obviously 800,000 is better than zero, so
it looks as though Lufthansa is actually
going to choose a low price no matter
what British Airways does.  We're going to
refer to that as a dominant strategy.  Now
it turns out that British Airways is
actually going to look at this in almost
the exact same way since the payoff
matrix is symmetrical.  If Lufthansa were to choose a hi price British
Airways has got to choose between a high
price or a low price.  They're better off
with a low price,  one point six million
is bigger than 1.2 million.  If Lufthansa were to go low
then of course British Airways would
prefer to make $800,000 with a low price
than to lose all of their customers if
they had a high price.   They're going to
choose a low price no matter what as
well.   It looks as though both of them
have dominant strategies.  When you get to
circled results in the same box.  This is what we refer to as a
Nash equilibrium.  Occasionally you'll
hear referred to as a non-cooperative
equilibrium.  This is basically indicating
that neither player can do better by unilaterally changing their play.  Given what
the other player is doing they've chosen
the best outcome for themselves.  This is
basically a likely outcome for the
entire game.  One of the things that will
present itself as curious here is that
both of them have ended up choosing a
low price when they couldn't cooperate
with the other player.  The reason that's
curious is because, of course, you have
got this scenario here which obviously
would have been better for both of them. When you get a result where individual
firms acting in a profit maximizing way
actually leads to them both making less
money than they could have if they were
cooperating we refer to this as a
prisoner's dilemma.   So is there a way out
of this prisoner's dilemma?  There's a
couple of ways.  One you can break the law
and you can cooperate.  If you both have a
conversation and cooperate then you
would both choose to take a high-price.
That will put you in trouble with the
law though.. possible felonies if
you get caught. The other way that it can
be done is with signaling, and signaling
would also be illegal but it's much more
difficult to prove.  So if Lufthansa and
British Airways have been at this for
quite some time we would expect that
British Airways and Lufthansa
are operating here.
If Lufthansa all of the sudden out of the blue
decided to change from a...[sorry this
should say low]... from a low price to a
high price they're going to start taking
a loss...
well not a loss they're going to make
zero money.  British Airways can look at
this and assume a couple of things.  One
Lufthansa is suddenly stupid or two
Lufthansa is trying to tell them
something.  If they don't think Lufthansa
is stupid, then British Airways may read
this move to a high price as an
invitation for British Airways to also
move to a high price.  IF British
Airways picks up on that signal and they
both raise the airline ticket price to
$600 apiece, then of course they are
going to end up escaping the prisoner's
dilemma and they did it without ever
actually having a conversation with each
other.  This frustrates authorities to no
end.   Very, very difficult to prove
collusion when there isn't a paper trail
or conversation where they're discussing
how they're going to do it, still illegal
but practically very difficult to solve
for the authorities.  Another common theme
that will pop up here is a price
leadership model or a coupon price
matching scheme.  If in fact one of these
competitors agrees to match a low price
from another competitor no matter what.
That pretty much is sending a signal out
to the other competitor that they should
just leave their prices high.  That's a
way that they can also avoid this and it
looks a whole lot like competition.
Interestingly enough it's probably
anti-competitive.  In any event you can
escape the prisoner's dilemma if you can
find a way to cooperate or as we're
discussing here
tacitly collude.
All right time for you all to try.  Here's two games I want
you to figure out where the Nash
equilibrium are going to be, if there is
going to be a Nash equilibrium, and I'll
go ahead and walk you through the
solutions here in a second.  So pause this
presentation try em out yourselves... when
you've got answers start it up again.
Okay let's go ahead and work through
this.  Pepsi's on the top left.
Coke's on the bottom right.  They've got to
start planning around possible
strategies from their competitors.  Coke
is going to start asking themselves what
if Pepsi chooses not to advertise... and if
Pepsi chooses not to advertise then Coke
is going to be worried about this row
only.  Coke could either choose to not
advertise or to advertise.  500-million is
better than 450.  Now if Pepsi chooses to
advertise then Coke only has to
worry about the bottom row, and of course
300 million is better than 200 million.
So it turns out that Coke actually has a
dominant strategy to advertise no matter
what Pepsi might do.  Pepsi is actually
going to be in the same boat, because if
Coke chooses not to advertise, then Pepsi
is thinking about what would they be
best off doing.  The answer is
advertising.... and if Coke chooses to
advertise they only have to worry about
this right column and of course 300
million is better than 200 million.
They're also going to want to advertise.
This is another prisoner's dilemma.
They're going to end up both choosing to
advertise, and they're going to make less
money than if they were both not
advertising.  Okay let's look at this
example over here on the right... and
you've got two oil-producing nations,
Saudi Arabia and Nigeria.....And their
output decisions are going to influence
the world price of oil.  In other words
it's an interdependent scenario.  What one
of them does impacts the other.  So if you
start thinking about this you could have
the Saudis and they could be wondering
well if Nigeria were to go with low
output then what would I be best off
doing? low output or high output? They're
going to be better off doing low output. 
if Nigeria were to go with high output
the Saudis would start wondering well
once again low or high?  Turns out that
low
is a dominant strategy for them.  They're
always going to be better off no matter
what Nigeria does as long as they go
with low output.  Nigeria on the other
hand is going to start thinking what if
Saudi goes with low output.  If Saudi goes
with low output, then Nigeria starts
wondering do I go low or do I go high.  It
turns out they're going to be able to be
better off if they choose high output.  If
the Saudis go with high output... Nigeria
once again is better off choosing high
output.  Turns out that Nigeria has a
dominant strategy to go for high output;
whereas, the Saudis have a dominant
strategy to go low output.  This of course
one of the reasons why people will say
that the agreement between these nations
to limit oil production has consistently
failed, because some of the smaller
nations in OPEC,  or the oil controlling
exporting countries all have an
incentive to cheat on that agreement.  Only
the largest producers stand the most to
gain from keeping output low.  There's a
couple of solutions for you. I want you
to realize that.. that right there is a
Nash... let's not forget that!.... and here's
how you kind of work through them.  Let me
know if you have questions.
