Game theory, Avinash, an example of an economic game in a book?

Question

Mathematics

In Avinash's book Game Theory, an example of an economic game between two companies is given. Based on this example, a table of payoffs for each side was compiled. Can someone explain the formula in this example? I don’t understand the moment how a company that lowered the price could make a profit less than the one that remained at the same price?
Quote from the book:

Let's analyze this concept using the price game between
Rainbow's End and BB Lean as an example. In Chapter 3, they only had two
price options for the shirt: $70 and $80. Each company
was strongly tempted to lower that price. Now let's increase
the number of choices by allowing them to change the price by
one dollar in the lower price range, from $42 to $38.
The previous example says that if both companies
charge $80, they will each sell 1,200 shirts. If
one of the companies lowers the price by one dollar and the other leaves it
unchanged, then the company that lowered the price will attract 100
buyers: 80 buyers who switched from any other
companies, and 20 new ones - these may be buyers who decide
to purchase a shirt that they would not have bought at a higher price.
If both companies cut the price by one dollar, existing customers
will not change their habits, but each company will have 20
new customers. Therefore, if both companies charge
$42 instead of $80, they each get 38 × 20 = 760 customers
over and above the original 1,200. In this case, each company sells
1,960 shirts and makes a profit of (42–20) × 1,960 = $43,120.
Performing similar calculations for other price combinations, we get
the following payoff table for this game:

Answer 1

If you plot the income difference between companies, you will see that it is a downward parabola. Accordingly, she has a maximum point of earnings. The limiting factor on the left is low value added and on the right is competition.