Question

Duopoly Game. Assume an infinitely repeated game between DELL and Apple. The payoff matrix shows the price options ($1,000 or $900) for a given computer model for DELL and Apple. The numbers in the cells are profits in millions of dollars per month. The first entry in the cell is Apple’s profits and the second entry is DELL’s profits.     

  

		DELL
		$1,000	$900
Apple	$1,000	10, 10	5, 15
	$900	15, 5	7.5, 7.5

Answer the following questions:

1. Assume that you are DELL’s manager and know that Apple is charging $1,000 for the PCMAX computer.  Explain your pricing decision and why you would do it. Explain why you would not charge the lower price.

2. Given the answer to question 2.1, are you colluding with Apple’s manager?

3. You are DELL’s manager and do not know Apple’s price for the PCMAX. However, you want to charge $1,000 for the computer. What would you do to make Apple to engage in indirect collusion, so you would charge the higher price and, at the same time, avoid losing money?

Answer 1

1. If Apple is charging $1,000 for the PCMAX, DELL should sell for  $900 so as to earn higher profits. Selling at a lower price would only reduce my own revenue, hence the product is sold lower than Apple's to be able to attract its customer base

2. At this point, we are not colluding with Appl'es manger and are competing with it.

3. However, if apple's prices are unknown, and I have to charge $1000, the better way would be to sell at 900 initially, such that profits are shared between the two. This would make Apple realize that DELL can sell at 900 too, and when DELL increases its price to 1000, Apple would also prefer to increase his own prices and not stay at 900. The idea is to make Apple realize that Dell can sell at lower prices too and competition would not benefit either player