Question

A town has two repair shops, Blue and Red. Each shop must decide whether it will remain open on Sunday or be closed on that day. The payoffs, which are in dollars, are provided in the normal form below. This is a static, or one-shot, game.

			Red
		Open	Closed
		Sunday	Sunday
	Open Sunday	8,000	7,000
Blue		4,000	7,000
	Closed Sunday	10,000	12,000
		3,000	6,000

Assuming the shops make their decisions simultaneously:

(A) Which shop is the most profitable in the Nash equilibrium?

(B) Does the shop you identified in part (A) have a dominant strategy? If so, what is it?

(C) What should this shop do? Explain your answer.

(D) Is this an example of a prisoners’ dilemma.

Answer 1

A) Blue is the most profitable in the Nash equilibrium. This is perhaps because it's payoff are greater in every condition when compared with its rival. This can be seen from the fact that in every cell profit are at least as much as the profit earned by Red

B) yes it has a dominant strategy and it to remain closed on Sunday. For every strategy selected by the rival if Blue remains closed on Sunday, it has a higher profit of 10000 and 12000 compared to its profit of 8000 and 7000 when it opens.

C) because it has a dominant strategy of closed on Sunday, Blue should remain closed on Sunday.

D) No. This is not an example of a prisoners’ dilemma because here the selected outcome (closed, closed) has a overall higher profit at 18000 (12000 + 6000). This is a Pareto efficient outcome, unlike prisoners’ dilemma game where the selected outcome has lower profits for both.