Let's now get to the most interesting part.
Let's try to understand how real businesses see competition.
I will want to remind you,
something that we said in the previous lecture, the prisoner's dilemma.
And we're going now to revisit the prisoner's dilemma and
see deeply how it affects our discussion.
So, you had the boy and a girl that there are
separate cells and they try to understand what they should do,
if they should confess,
o r they should deny.
We said that the Nash equilibrium here is that they will both confess, however,
they would love to collude and that they both deny,
so they get less years in jail.
But we said also that this is not a Nash equilibrium because if they both agreed to deny,
then when they sign their final statements,
they might want to betray the other person and confess while the other person denying.
So, they have a cheating solution that will
make the double-denial to not be an equilibrium.
So, the prisoner's dilemma is much more than an example,
much more than a simple game.
It's a philosophical device that makes the point that self-interest,
if you pursue your own ambition only,
you might end up to a social sub-optimal.
This is in direct contradiction to what Adam Smith said
in the 1700 with his monumental book in economics,
that he said "Individual ambition serves the common good."
Here, we do not have that.
Individual ambition will make both of
these two agents to end up in the worse possible situation.
That is, both of them will confess and both of them they will get many years in jail.
In the game, acting towards your self-interest exposes you.
It leaves you open to the interest of the other person.
It makes you open to be exploited by the other person,
and you don't want that.
So, therefore, in the collusion outcome,
there is a deviation tendency for both players.
Both players want to leave the cell.
Both players have a strong tendency to cheat to
betray the agreement that they have with their counterpart.
This analysis is not only in the prisoner's dilemma.
The prisoner's dilemma can be applied in strategy and
strategic competition environment in real business all the time.
Let's see how, and let's see how the previous material that
we did today will actually come into the game here.
Nash versus collusion.
In our previous example with differentiated products,
we can't two different situations.
Firms could compete, they could compete with respect to differentiated quantity.
If both firms charge four,
then we saw that they make a profit of 18 each.
So, strategy is four.
They could compete by setting the price to be equal to four.
And then, the payoff is a profit,
which is 18 for each.
We saw, so that they can collude and by colluding,
they set the price of 5.5,
so the strategy now is to play 5.5,
and they will get a payoff of 20.25 each.
So, 20 and a quarter units for each firm,
much higher than if they compete.
By not competing, both firms doing better.
There is also another opportunity though.
And this is, what a firm decides to collude,
but the other firm decides to compete?
What if a firm charges 5.5 and the other firm charges four and undercuts?
What happens in this case?
So, if you resolve the problem,
you will see that if this happens,
then the firm who charges
more expensive losses lots of customers and gets a profit of 13.5.
And the firm who undercutted,
they can actually now have a much higher profit and enjoy 22.5 units.
So, the cheater gets a benefit.
The person who he cheated upon is in the worst situation ever.
So, they are going for a profit 20.25 by setting a price of 5.5.
And then, in the end of the period,
they look at their registry,
and they have only 13.5.
If you consider that these values can very easily be
millions of dollars or euros or whatever else currency they will use,
you understand that the change,
that the difference is actually huge.
So, what is going to happen here?
If we both agree to conclude,
there is a tendency of deviation.
They say, "Yes, 20.25 is better than 18,
but 22.5 is better than both."
So, cheating is a very strong incentive for both businesses here.
There is the competition outcome,
there is the collusion outcome,
and there is the cheating outcome.
If they both go for competing, they get 18.
If they both go for colluding,
they will get 20.25.
If one is convinced for colluding and the other cheats
by going for competing slightly undercuts,
then, in this case,
we will have different payoffs,
and the person who cheats gets much more.
The interesting is that most likely they will both cheat,
and they we'll end up to
the competitive solution because this is the essence of Nash equilibrium.
Nash equilibrium is not when we say we are going to compete.
Nash equilibrium is when we both tried to cheat,
we both try our best for ourselves,
and we end up in a sub-optimal situation.
Why not going for the collusion all together from the beginning?
Why not agreeing that let's collude,
it will be better for both of us, let's not cheat?
Don't forget that most of the times agreements can happen in front of others,
but decisions are made in your own privacy.
Final decisions are make in your own privacy.
So, you might have an agreement,
but then there is a tendency to cheat.
And even if you don't want to cheat,
even if you are not a cheater by ethical construction of yourself,
then, in this case, there is something else.
Charging 5.5 and then waiting for your opponent to do the same leaves you open,
exposes you to your rival.
You might end up instead of seeing these 20.25,
to see the 13.5,
and then as a manager in your firm,
it will be very difficult to explain this to your bosses, to the stakeholders.
So, therefore, firms usually try to protect themselves,
and they will always have a very strong tendency to get back to the competition case.
We should have a much stronger,
external reason that they will enforce collusion,
and this is something that we will examine very extensively in future lectures.
The prospect of collusion in general is as simple as it can get.
There is the competition point,
there is two cheating outcome,
and there is a collusive outcome.
So, why not set profit to
the maximizing collusion price and hope that everybody will follow?
Because if this is a one shot game,
and people do not care about their reputations,
and you don't have a chance to retaliate with a known empty threat in the future,
then this is not going to happen.
Because collusion is not a Nash equilibrium,
there are strong tendency to deviate.
You will want to deviate to cheating,
the other person will want to deviate to cheating,
and then in the end,
both together will find yourself competing to each other.
So, collusion level of price and output
is never on the optimal response curve and therefore,
you will end up on your optimal response only by competing.
Today's lecture showed you a lot about the static competition.
I tried to keep it as simple as possible.
However, we had several models.
What you have to do is,
as an economist, as someone who sees the economy,
who sees the business and understands them,
your duty is to be able to read behind those equations,
to understand what is the essence of equations.
We are not solving the equations for fun.
We don't have them there to seem smart.
Those equations have things to teach us,
and this is what we have to learn.
So, use the models to your advantage. See you in the next lecture.
