Question

B&R and Sweet J are two competitors that sell flavored ice cream in a market where they are the only two sellers. Both companies are considering what actions to undertake in the following week. The profit of each firm depends on the other firm’s decision. The payoff matrix shown here gives each firm’s daily profits. The first entry in each cell of the payoff matrix is B&R’s profit, and the second entry is Sweet J’s profit. Sweet J Advertise Do not advertise $1500, $1500 $2000, $500 $500, $2500 $2000, $2000 B&R Price high Price low A) Do we have a dominant strategy for B&R? Explain. B) Do we have a dominant strategy for Sweet J? Explain. C) Is there a Nash Equilibrium? Explain. D) What is the stable profit margin of each company?

Answer 1

		Sweet J
		Advertise	Do Not Advertise
B&R	Price High	$1500 , $1500	$2000 , $500
Price Low	$500 , $2500	$2000 , $2000

A) For B&R, pricing High gives a better payoff when Sweet J does not advertise and it gives the same payoff as pricing low when Sweet J Does not Advertise. So for B&R the dominant strategy is to Price High

B) For Sweet J, irrespective of B&R's strategy, Advertising gives a better payout than Not Advertising. So Sweet J's dominant strategy is Advertising.

C) If B&R Price High and Sweet J Advertise, then there is no way for either player ti improve their payoff by changing their own strategy if the other player does not change. So this is a Nash Equilibrium.

D) The stable profit margin of both the companies is $1500. It is the dominant strategy which each player will be playing and there is no incentive for anyone to shift their strategies. So the resultant outcome will be for B&R to price High and Sweet J to advertise leading to a profit of $1500 for each company.

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