Question

1. Describe each actor’s dominant strategy in each scenario. Indicate whether there is a Nash Equilibrium
   1. Suppose that Angelina and Brad own the only two professional photography stores in town. Each must choose between a low price and a high price for senior photo packages. The annual economic profit from each strategy is indicated in the table below:

Angelina

Low price                           High price

Brad	Low price	Angelina’s profit = $20,000 Brad’s profit = $20,000	Angelina’s profit = $4,000 Brad’s profit = $23,000
	High price	Angelina’s profit = $25,000 Brad’s profit = $5,000	Angelina’s profit = $22,000 Brad’s profit = $22,000

2. Suppose that Robert and Howard own the only two movie studios in California. Each producer must choose between a low budget and a high budget strategy for his next film. The economic profit from each strategy is indicated in the table below

Howard

Low budget             High budget

Robert	Low budget	Howard’s profit = $19,000 Robert’s profit = $19,000	Howard’s profit = $4,000 Robert’s profit = $24,000
	High budget	Howard’s profit = $25,000 Robert’s profit = $5,000	Howard’s profit = $21,000 Robert’s profit = $21,000

3. Suppose that two coal mining companies – Allied and Barclay – own adjacent land suitable for excavating coal mines. The profits that each firm earns depends on both the number of mines it excavates and the number of mines excavated by the other firm. The table below lists each firm’s individual profits:

Allied

Excavate one mine              Excavate two mines

Barclay	Excavate one mine	Allied’s profit = $9 million Barclay’s profit = $9 million	Allied’s profit = $11 million Barclay’s profit = $6 million
	Excavate two mines	Allied’s profit = $6 million Barclay’s profit = $11 million	Allied’s profit = $7 million Barclay’s profit = $7 million

Answer 1

a. Given that Brad choose low price, Angelina's best response is low price($20,000).
Given that Brad choose high price, Angelina's best response is low price($25,000).
So, Angelina's dominant strategy is low price as it is always chosen by her.

Given that Angelina choose low price, Brad's best response is low price($20,000).
Given that Angelina choose hgh price, Brad's best response is low price($23,000).
So, Brad's dominant strategy is low price as it is always chosen by him.

The NE is (Low price, Low price) = (Angelina’s profit = $20,000; Brad’s profit = $20,000) as their best response occur simultaneously at this set.

b. Given that Robert choose low budget, Harvard's best response is low budget(19,000).
Given that Robert choose high budget, Harvard's best response is low budget(25,000).
So, Robert's dominant strategy is low budget as it is always chosen by him.

Given that Harvard choose low budget, Robert's best response is low budget(19,000).
Given that Harvard choose high budget, Robert's best response is low budget(24,000).
So, Harvard's dominant strategy is low budget as it is always chosen by him.

The NE is (Low budget, Low budget) = (Harvard's profit = $19,000; Robert's profit = $19,000) as their best response occur simultaneously at this set.

c. Given that Barclay excavate one mine, Allied's best response is to excavate 2 mines($11 million).
Given that Barclay excavate two mines, Allied's best response is to excavate 2 mines($7 million).
So, Allied's dominant strategy is to excavate two mines.

Given that Allied excavate one mine, Barclay's best response is to excavate 2 mines($11 million).
Given that Allied excavate two mines, Barclay's best response is to excavate 2 mines($7 million).
So, Barclay's dominant strategy is to excavate two mines.

The NE is (Excavate two mines, Excavate two mines) = (Allied’s profit = $7 million; Barclay’s profit = $7 million) as their best response occur simultaneously at this set.