Question

Duopoly Game. The payoff matrix shows the price options ($1,000 or $900) for the computer model PCMAX 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

Assume that this is a simultaneous one-shot game and answer the following questions:

1. Explain the outcome of the game given the dominant strategy of both players.

2. Explain the Nash equilibrium.

3. Assume that you are the DELL’s manager, would you ask Apple’s manager to have lunch together to discuss the pricing options and seek an agreement on charging the higher the price?

Answer 1

1. In a simultaneous game, both Dell and Apple are playing the one-shot game. Given the strategy of Dell, the dominant strategy of Apple $900 and given strategy of Apple, the dominant strategy of Dell is $900.

2. Nash equilibrium is the best response of each player given whatever other player does. Each player plays its dominant strategy as the best response which is ($900, $900)

3. Given Dell and Apple discuss together about the pricing option to charge high price would like to cooperate at $1000 when the game is played for a longer period of time.