Question

Little Kona is a small coffee company that is considering entering a market dominated by Big Brew. Each company's profit depends on whether Little Kona enters and whether Big Brew sets a high price or a low price:
Big Brew
High Price Low Price
Little Kona Enter $2 million, $3 million
Little Kona Don't Enter ($0,$7)millions ($0,$2)millions

a. Does either player in this game have a dominant strategy?
b. Does your answer to part (a) help you figure out what the other player should do? What is the Nash equilibrium? Is there only one?
c. Big Brew threatens Little Kona by saying, "If you enter, we're going to set a low price, so you had better stay out." Do you think Little Kona should believe the threat? Why or why not?
d. If the two firms could collude and agree on how to split the total profits, what outcome would they pick?

Answer 1

Answer and explanation:

a) If Kona enters, Big Brew would want to maintain a high price. If Kona does not enter, Big Brew would want to maintain a high price.

Thus, Big Brew has a dominant strategy of maintaining a high price.

If Big Brew maintains a high price, Kona would enter. If Big Brew maintains a low price, Kona would not enter.

Thus, Kona does not have a dominant strategy.

b) Because Big Brew has a dominant strategy of maintaining a high price. Kona should enter. There is only one Nash equilibrium, which is, Big Brew will maintain a high price and Kona will enter.

c) Little Kona should not believe this threat from Big Brew because it is not in Big Brew's interest to carry out the threat. If Little Kona enters. Big Brew can set a high price, in which case it makes $3 million, or Big Brew can set a low price, in which case it makes $1 million.

Thus, the threat is an empty one, which little Kona should ignore; Little Kona should enter the market.

d) If the two firms could successfully collude, they would agree that Big Brew would maintain a high price and Kona would remain out of the market. They could then split a profit of $7 million.