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

B&R

Price high

$1500, $1500

$2000, $500

Price low

$500, $2500

$2000, $2000

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

As your question was not clear for the matrix value positions, I guess I've raken the right values in the right cell.

1. As seen dominant strategy is the strategy which is played irrespective what strategy the other player plays. We see B&R will always go for Advertising and that is its dominant strategy.

2.Sweet J will always go for advertising too, and that is its dominant strategy.

3.We have a nash equilibirum at both B&R and Sweet J choosing Advertising.