And the potential entrant enters, the incumbent makes $3.
It's also true that if the demand conditions are good, the incumbent
sets a high price, the entrant decides to enter, the entrant will make $1.
That's how you read these different payoffs.
So in each case you have a price and an entry, no entry combination.
And that determines the pay offs of the individual players in this game.
Okay, so now let's think about strategy for these players.
Suppose it's a good state of the world, let's look at the payoffs for
the incumbent.
If we go over here, the payoffs for the incumbent are,
if they set a high price, their payoff is 3 if the entrant enters,
and it is 10 if the entrant stays out.
On the other hand, if the state of the world is good, and
the incumbent sets a low price.
If the entrant enters, the incumbent will make $2.
And if the potential entrant stays out, they'll make $9.
Now why is this important?
It's important to look at these two numbers and these two numbers and realize
that in both cases the 3 here is bigger than the 2.
And the 10 is greater than the 9.
And that means no matter what the entrant decides to do, enter or
stay away, if the state of the world is good,
then the incumbent is better off setting the high price.
That is the best strategy for them, if it's a good state of the world.
It doesn't make sense for them to set a low price,
because no matter what that entrant firm does, whether they enter or
stay out, they make less money then whatever happens on the high price side.
So that's a kind of a dominate strategy for them.
On the other hand, let's think of a low state of the world,
so low demand conditions.
In that case, if the incumbent firm plays high, they make 1,
if the entrant enters, or 3 if they do not enter.
This is the pair, right,
that's associated with a high price in a low demand situation.