Question

4)    Big Brew is a large coffee house in a medium-sized town. Little Kona is thinking of entering this market to compete with Big Brew. Big Brew has threatened to drop price to keep Little Kona out of the market. The payoff table is shown below:

		Little Kona
		Enter	Not enter
Big Brew	Cut price	3, -2	9, 0
	Don’t cut price	7, 5	14, 0

a.      Are there dominant strategies for either of the firms? If so, what are they?

b.      In a one-shot simultaneous-choice game, what is the Nash Equilibrium?

c.       Show a sequential game tree where Little Kona moves first to either enter or not enter, and then Big Brew moves second to either cut price or not cut price. Indicate the Nash equilibrium in this game. Why is the outcome different in this game compared to the original game?

Answer 1

Ans for a)

Yes we can see that above game has strictly dominant strategy for Big Brew and that is Dont Cut Price because 7>5 and 14>9

Little Kona has no dominant strategy avilable

Ans for b)

In one shot simultaneous game we have Nash Equilibrium equals to (Dont cut Price, Enter)

Ans for c)

Again if we investigagte the tree diagram we can see that NAsh Equilibrium for above game is the same as above simultaneous game

As if Little Kona plays Not to enter then she will hve certain payoff of 0 but if she chooses to enter than she knows that Big Brew will choose higher playoff and that is 7. In this scenario Little Kona will have positive payoff equals to 5

Therefore Nash Equilibrium is (Dont Cut Price, Enter)