Question

strategies and games
Q7 & Q11

4.7
Show that posting a price of 0 dollars and posting a price of 6 dollars are both dominated strategies. What
about the strategy of posting a price of $4? $5?

4.11
Argue that the unique outcome to IEDS in this model is for both firms to price at 1 dollar.
There is a more general result about price competition that we have established in the course of the previous
five questions.

In any model of duopoly price competition with zero costs the IEDS outcome is the lowest price at
which each firm makes a positive profit, that is, a price equal to a dollar.
Let us investigate why price competition appears to be so beneficial for the customer! Suppose that our
earlier model is modified so that the demand curve is written more generally as
where D(p) is a downward sloping function, i.e., the quantity demanded at price (p - 1), D(p - 1), is larger
than the quantity demanded at price p, D(p). Denote the monopoly price pm and suppose, without loss of
generality, that it is 2 dollars or greater.

                 Left        Center     Right
Top          4, 5           1, 6          5, 6
Middle    3, 5           2, 5          5, 4
Bottom   2, 5           2, 0          7, 0

Answer 1

In the figure above, both A and B are competing in the business, both are trying to get their business strategy which can maximize their profit. Since the average cost is same both A and B attain maximum profit . In the case $4 and $5, it will lead to a collusion , it will be benefited only through iterated Elimination of Dominated Strategy.

In the perfect combination, the consumers and the producers will be benefited by maximum profit to the producer and the consumer surplus for customers. In the monopoly, it will be benefited to the producer. In the right 5,6. In the above game theory a maximum strategy is one chosen by a player to maximise the minimum gain that it can earn . In the monopoly , the producer who plays a maximum strategy assumes that the opposition will play the strategy that does the most damage. So he will choose the monopolist plays the right top strategy.