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ECON 223 Term Test

19 September 2018

Q1. In game theory, a situation in which one firm can gain only what another firm loses is called

1) a nonzero-sum game.

2) prisoners' dilemma.

3) zero-sum game.

4) predation game.

Note: Use the following game to answer questions 2-4.

Two companies, Alpha and Beta, are trying to choose spending on research and development. They can choose either high spending or low spending. If both companies choose low spending, they will both earn $10 million per year. If both companies choose high spending, they will both earn $5 million per year. If one chooses high and the other low, the company that chooses high spending will earn $20 million, while the company that chooses low will earn $2 million. The companies must make their decision without knowledge of the other's action.

Q2. This game is best described as:

1) Non-cooperative, zero sum.

2) Non-cooperative, non-zero sum.

3) Cooperative, zero sum.

4) Cooperative, non-zero sum.

Q3. A dominant strategy for firm Alpha would be:

1) Always choose a low level of R&D.

2) Always choose a high level of R&D.

3) Choose low if Beta chooses low and high if Alpha chooses high.

4) There is no dominant strategy for Alpha.

Q4. The equilibrium in this game is going to be, expressed as (Alpha's strategy; Beta's strategy):

1) (High; High)

2) (Low; Low)

3) (Low; High)

4) (High; Low)

Q5. The point where the game starts in an extensive form game is called

1) Decision Tree

2) Initial Node

3) Strategy

4) Terminal Node

Note: Answer ALL questions. Each question is worth 6 marks. Part B is worth 18 marks. Write your answers clearly on the answer booklet provided.

1) What is the basic structure of a game?

(6 marks)

2) What is the difference between an extensive form game and a strategic form game?

(6 marks)

3) How is a dominated strategy different from a dominant strategy?

(6 marks)

Note: Answer ALL questions. Each question is worth 13 marks. Part C is worth 52 marks. Write your answers clearly on the answer booklet provided.

Q1. A business strategic situation has two players: the employee (Raquel) and the employer (Vera). Raquel has to choose whether to pursue training that costs her $1,000 or to not train which has zero cost. Vera has to decide whether to pay a fixed wage of $10,000 to Raquel or share half the revenues of the enterprise with Raquel. The revenues of the business are positively affected by both training and revenue sharing. With no training and a fixed wage total revenue is $20,000, while if either training or profit sharing is implemented the revenue rises to $22,000. If both training and revenue sharing are implemented the revenue is $25,000.

a. Construct the pay-off matrix. (2 Marks)

b. Are there any dominant strategy equilibria? Explain your answer. (3 Marks)

c. Is it possible to find the solution of the game with Iterated Elimination of Dominated Strategies? Why or why not? (4 Marks)

d. Are there any Nash equilibria for this game? Explain why or why not. (4 Marks)

Q2. a. A strategic form game involving three players is depicted below. Player 1 chooses the row (T or B), Player 2 chooses the column (L, M, or R), and Player 3 chooses

the matrix (W, X, Y, or Z).

W X

Y Z

Find all the strategies that survive iterated elimination of strictly dominated strategies. Show your working. (6 Marks)

b. Consider the following game.

Player 2

Player 1

Compute all the Nash equilibria for this game. Clearly show all your working.(7 marks)

Q3. a. Consider the following strategic situation concerning the owner of a firm (O), the manager of the firm (M), and a potential worker (W). The owner first decides whether to hire the worker, to refuse to hire the worker, or to let the manager make the decision. If the owner lets the manager make the decision, then the manager must choose between hiring the worker or not hiring the worker. If the worker is hired, then he or she chooses between working diligently and shirking.

A worker who is hired does not know if the manager or owner made the decision to hire them. But once a worker is hired, the worker makes a decision to work diligently or shirk, independent of who hired him. If the worker is not hired, then all three players get a payoff of 0. If the worker is hired and shirks, then the owner and manager each get a payoff of −1, whereas the worker gets 1. If the worker is hired by the owner and works diligently, then the owner gets a payoff of 1, the manager gets 0, and the worker gets 0. If the worker is hired by the manager and works diligently, then the owner gets 0, the manager gets 1, and the worker gets 1.

Represent this game in the extensive form (draw the game tree). (7 Marks)

b. Draw the strategic-form matrix of the following extensive-form game. Read the decision tree from left to right. The dotted line represents one information set. (6 Marks)

U 2, 1

1, 2

6, 8

4, 3

2, 1

D 8, 7

Q4. a). The game matrix as shown is of a game where Pam and Michael are deciding whether to invest in a small paper company or hold onto their money. The paper company will succeed if both invest in it but will fail if only one invests in it. The Payoffs represent profits received by Pam and Michael.

		Michael
		Invest	Don’t invest
Pam	Invest	2000,2000	0, 500
Pam	Don’t invest	500, 0	500,500

Identify any dominant strategies and any Nash Equilibria for this game. (7 marks)

b). Two mothers are deciding whether to vaccinate their children against measles. Each is trying to minimise the likelihood of their child getting measles. Payoffs represent the probability of mother 1’s child and mother 2’s child getting measles, respectively. The payoff structure for this game is shown in the following strategic form of the game: