Complex Theory

 

Acelancer

Question 1

If a player in a game has a dominated strategy, then

    A. he or she should definitely use it.
B. his or her opponents must have a dominated strategy as well.
C. he or she will never find it optimal to choose it.
D. it must be part of a Nash equilibrium.

 

Question 2

The next two questions are based on the following game: Which of the following is true?

A. A dominant strategy for Firm A is “do not invest”.
B. There does not exist a dominant strategy for Firm A.
C. A dominant strategy for Firm B is “invest”.
D. None of the above

 

Question 3

What is the Nash equilibrium of the game?

A. (invest, invest)
B. (do not invest, do not invest)
C. (invest, do not invest)
D. A and B

 

Question 4

Consider the following information for a static game. If you advertise and your rival advertises, you each will earn $5 million in profits. If you choose not to advertise and your rival chooses not to advertise, you will each earn $10 million in profits. However, if one of you advertises and the other does not, the firm that advertises will earn $15 million and the firm that does not advertise will earn $1 million. Assuming that each player cares only about his or her own profits, the Nash equilibrium is

A. for each firm to advertise.
B. for neither firm to advertise.
C. for your firm to advertise and the other not to advertise.
D. None of the above.

 

Question 5

A coordination problem arises whenever:

A. there is no Nash equilibrium in a game.
B. there is a unique Nash equilibrium but it is not very desirable.
C. there are multiple Nash equilibria.
D. each player has a dominant strategy.

1 points

Question 6

Consider an industry with a small number of firms with market power. Suppose they sell identical products and have identical cost of production. If each firm posts a price without knowing the prices posted by its rivals, and it is impossible for them to collude, then

A. Firms will charge prices equal (or almost equal) to the marginal cost of production.
B. Firms will make zero (or close to zero) economic profits.
C. Firms will have incentives to invest in product differentiation.
D. All of the above.

1 points

QUestion 7

The next three questions are based on the following game: Which of the following are Nash equilibrium payoffs in the one-shot game?

  A. (0, 0)
  B. (100, 100)
  C. (-20, 250)
  D. (250, -20)
     

Question 8

Which of the following are the Nash equilibrium payoffs (each period) if the game is played only 2 times (and both players know this)?

A. (0, 0)
B. (100, 100)
C. (-20, 250)
D. (250, -20)

 

Question 9

Suppose the game is repeated over and over again, with players not knowing when it will be the last time they will play the game. If players use trigger strategies and value future payoffs sufficiently highly, then how much can each player earn per period?

A. (0, 0)
B. (100, 100)
C. (-20, 250)
D. (250, -20)
     

Question 10

The next two questions are based on the following information: Suppose the market for computer chips is dominated by two firms: Intel and AMD. Intel has discovered how to make superior chips and is considering whether or not to adopt the new technology. Adoption would entail a fixed setup cost of F but would increase revenues. However, if Intel adopts the new technology, AMD can easily copy it at a lower setup cost of F/2. If Intel adopts and AMD does not, Intel would earn $20 in revenues while AMD would earn $0. If Intel adopts and AMD does likewise, each firm will earn $7 in revenues. If Intel does not adopt the new technology, it will earn $3 and AMD will earn $2. Each firm cares only about its own profits. The extensive form representation of the game is shown below. Suppose F = 16. Then, using backward induction, what prediction do we obtain?

 

A. Intel will not adopt the new technology.
B. Intel will adopt the new technology, and so will AMD.
C. Intel will adopt the new technology, and AMD will not adopt it.
D. All of the above.

Question 11

Suppose F = 5. Then, using backward induction, we obtain the following prediction:

A. Intel will not adopt the new technology.
B. Intel will adopt the new technology, and so will AMD.
C. Intel will adopt the new technology, and AMD will not adopt it.
D. None of the above.

 

Question 12

Using backward induction, what prediction do we obtain for this game?

A. Player 1 chooses T and Player 2 chooses D.
B. Player 1 chooses T and Player 2 chooses U.
C. Player 1 chooses B and Player 2 chooses L.
D. None of the above.

Question 13

The next three questions are based on the following table: Which of the following is true?

 

A. M is a dominant strategy for player 1.
B. C is a dominated strategy for player 2.
C. L is a dominant strategy for player 2.
D. U is a dominated strategy for player 1.

Question 14

Iterated elimination of dominated strategies yields the following prediction:

A. (M, C).
B. (D, L).
C. (M, R).
D. (U, R).

Question 15

The Nash equilibrium of the game is:

A. (M, L).
B. (D, C).
C. (U, R).
D. (C, D).