It is now time to get a little deeper into how strategy work,
to examine strategic behavior into some more depth.
First of all, in some games,
we have seen that playing first gives you an advantage.
Like for example in tic-tac-toe,
if you play first, you have better chances to not lose.
In other games, playing first gives you a disadvantage.
Like for example, rock-scissors- paper.
Even if you play with a kid,
going first will make you lose every single time.
So, what makes a difference between these two games?
Let's bring it to economic games, assuming oligopoly.
We have different theories to examine oligopolies,
that there is a different strategic relevance
between the choice of variables of the players.
First of all, it could know,
as your rival increases their quantity, what do you want to do?
How do you want to adjust your quantity?
Most likely, of course you know the answer, but most likely,
what you're going to do is you are going to move to
the opposite direction from where your opponent moves.
If you don't do that, you are both going to lose.
In Bertrand, as your rival increases the price, what do you want to do?
You want to move to the same direction with a change of your rival's change of variable.
So, we see here that you want to move to different directions in
each of two different games according to what the choice variable is.
Also, in these two games,
you will see that in Bertrand,
you will never want to set the price first.
Because if you set the price first to B, let's say,
the other player will come up and set their prize to B minus something small,
minus epsilon in order to undercut you,
and they will steal all your demand.
So therefore, you don't want to go first.
In Cournot, if you go first,
you turn it into the Stackelberg model,
and then, you have a higher profit.
So, you see that strategic relevance plays a huge role.
How your variables, the choice of variables,
either if it's price,
or quantity, or quality,
or research, or anything that you compete.
How these variables are strategically
related is what makes the difference in competition. Be careful.
Not every competition is the same.
Not every competition gives you the same results.
Not every competition follows the same mechanics.
Competition and price?
Very different than the competition in quantity.
You want to reply in different ways,
and you want to know how you should reply
into these kinds of factions in different models.
So, strategic variables seem to be related in a causative manner.
Your opponent does something,
this causes you to want to reply in some way.
And these causative manner can be either towards the same direction,
that is a positive relationship between the variables,
or inversely, that is a negative relation between the variables.
So, what of the two is it going to be?
Let's examine strategic substitutability and strategic complementarity,
because it will be very important for
a generalized theory of protection of your territory.
In Cournot, we have seen that the reaction functions are negatively sloped.
That is, an increasing quantity of your rival will
optimally make you decrease your own quantity.
So, you want to move to the opposite direction,
that's why you have a negative slope.
When the reaction functions are downward sloping,
doesn't matter if it's quantity or if it's another variable.
You say reaction functions or downward sloping,
we say that the actions of firms are strategic substitutes.
We call them substitutes because if your opponent wants to go up,
you substitute by decreasing.
If your opponent wants to go down,
you substitute by increasing.
So, you substitute what the other does,
therefore, they are called strategic substitutes.
In Bertrand style competition,
reaction functions are positively sloped.
This means that any increase in price or any other variable that is
related in a positive way with your variable has positive reaction functions,
should be optimally addressed by the same direction move in your control variable.
That is, when the reaction functions are upward sloping,
firms compliment each others action.
You increase, they increase.
You decrease, they decrease.
So, they both go towards the same direction.
Therefore, we call them strategic complements.
As I said before, be careful.
It will make a very big difference to what the correct reaction is,
if your competition in your business
happens in a way that you have strategic substitutability,
or if you have strategic complementarity.
If you're in a market that has strategic substitutability,
and you play as if the variables are strategic complements,
believe me, your rivals will love that because they are going to make much more money.
Okay, so be careful here because these are crucial factors in competition.
So, we will return with how the strategic substitutability and complementarity can to
be taken in context that will give you a strategic effect, right after this.