Deck 11: Dynamic Games With Complete

Question 1

An extensive-form game summarizes:

A) Players, strategies, discount rates, order of moves, intentions, and payoffs.
B) Players, arrangements, situations, and payoffs.
C) Players, arrangements, order of moves, and bids.
D) Players, situations, strategies, discount rates, and payoffs.
E) Players, stages, strategies, order of moves, and payoffs.

Answer 1

Players, stages, strategies, order of moves, and payoffs.

Question 2

A decision node:

A) May be the root or subroot of an extensive-form game.
B) Is where a player must decide how to move.
C) May lead to another decision node.
D) May lead to a terminal node.
E) All of the above are correct.

Answer 2

All of the above are correct.

Question 3

A solution to a multistage game may be arrived at through:

A) Deductive reasoning.
B) Inductive reasoning.
C) Backward induction.
D) Simplex method.
E) Maximin analysis.

Answer 3

Backward induction.

Question 4

A subgame equilibrium:

A) Is the solution to a trivial subgame.
B) Is the solution to a proper subgame.
C) Is a unique Nash equilibrium for a dynamic game.
D) Is always unique.
E) None of the above.

Question 5

A subgame-perfect equilibrium:

A) Is a Nash equilibrium to a multistage game.
B) Is a solution to a subgame in a multistage game.
C) Is a solution to any stage of a multistage game.
D) Can only exist in the presence of multiple Nash equilibria.
E) None of the above.

Question 6

A subgame-perfect equilibrium is:

A) An equilibrium to a multistage game.
B) A Nash equilibrium.
C) A equilibrium strategy profile in which no player can improve upon his or her payoff by switching strategies at any stage of a multistage game.
D) All of the above.
E) None of the above.

Question 7

A subgame-perfect equilibrium:

A) Is the solution to an extensive form game.
B) Can be found using the method of backward induction.
C) Is a Nash equilibrium for a sequential-move game.
D) All of the above.
E) None of the above.

Question 8

Terminal nodes:

A) Designate the end of a multistage game.
B) Identifies a player's move at any stage of a multistage game.
C) Are the same as subroots.
D) Are Nash equilibria.
E) None of the above.

Question 9

In multistage games, every decision node is:

A) The solution to a subgame.
B) A Nash equilibrium.
C) A subgame perfect equilibrium.
D) A subroot.
E) All of the above.

Question 10

-Consider the game depicted in Figure 11.1 in which player A moves first. This multistage game has how many trivial subgames?

A) 0
B) 1
C) 2
D) 3
E) 4

Question 11

-Consider the game depicted in Figure 11.1 in which player A moves first. This multistage game has how many proper subgames?

A) 0
B) 1
C) 2
D) 3
E) 4

Question 12

-Consider the game depicted in Figure 11.1 in which player A moves first. This multistage game has how many subgames?

A) 0
B) 1
C) 2
D) 3
E) 4

Question 13

-Consider the game depicted in Figure 11.1 in which player A moves first. The subgame perfect equilibrium for this game is:

A) {1 ? 2}.
B) {2 ? 3}.
C) {2 ? 1}.
D) {3 ? 2}.
E) {3 ? 1}.

Question 14

-Consider the game depicted in Figure 11.1 in which player A moves first. The payoffs for the subgame perfect equilibrium of this game are:

A) (100, 350).
B) (225, 250).
C) (150, 275).
D) (250, 125).
E) (250, 350).

Question 15

-Consider the game depicted in Figure 11.2 in which player A moves first. This multistage game has how many trivial subgames?

A) 0
B) 1
C) 2
D) 3
E) 4

Question 16

-Consider the game depicted in Figure 11.2 in which player A moves first. This multistage game has how many proper subgames?

A) 0
B) 1
C) 2
D) 3
E) 4

Question 17

-Consider the game depicted in Figure 11.2 in which player A moves first. This multistage game has how many subgames?

A) 0
B) 1
C) 2
D) 3
E) 4

Question 18

-Consider the game depicted in Figure 11.2 in which player A moves first. The subgame perfect equilibrium for this game is:

A) {1 ? 2}.
B) {2 ? 3}.
C) {2 ? 1}.
D) {3 ? 2}.
E) {3 ? 1}.

Question 19

-Consider the game depicted in Figure 11.2 in which player A moves first. The payoffs for the subgame perfect equilibrium of this game are:

A) (300, 225).
B) (250, 125).
C) (150, 240).
D) (175, 250).
E) (75, 350).

Question 20

-Consider game depicted in Figure 11.3 in which Left moves first. This multistage game has how many trivial subgames?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 21

-Consider game depicted in Figure 11.3 in which Left moves first. This multistage game has how many proper subgames?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 22

-Consider game depicted in Figure 11.3 in which Left moves first. This multistage game has how many subgames?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 23

-Consider game depicted in Figure 11.3 in which Left moves first. The subgame perfect equilibrium for this game is:

A) {Down}.
B) {Up ? Up}.
C) {Up ? Down ? Up ? Down}.
D) {Up ? Down ? Up ? Up}.
E) {Up 6 Down ? Down ? Down}.

Question 24

-Consider game depicted in Figure 11.3 in which Left moves first. The payoffs for the subgame-perfect equilibrium for this game are:

A) (3, 2).
B) (1, 4).
C) (2, 3).
D) (2, 2).
E) (1, 5).

Question 25

-Consider again the multi stage-game in Figure 11.4 in which Homer moves first. The subgame perfect equilibrium for this game is:

A) {Bart 6 Lisa}
B) {Bart 6 Maggie}
C) {Lisa 6 Bart}
D) {Maggie 6 Maggie}
E) This game does not have a subgame perfect equilibrium.

Question 26

-Suppose that an industry consists of two firms: Magna Corporation and Summa Corporation. Each firm produces an identical product. Magna and Summa are considering whether to expand (None) their production capacity for the next operating period. If the decision is to expand, the two firms must decide whether the expansion should be Moderate or Extensive. The tradeoff confronting each firm is that expansion will result in greater output that will lower the selling price of the product in the market. The normal form of this game is summarized in Figure 11.5. If larger payoffs are preferred, which firm has a strictly dominant strategy?

A) Magna Corporation.
B) Summa Corporation.
C) Both companies.
D) Neither company.
E) Cannot be determined from the information provided.

Question 27

-Suppose that an industry consists of two firms: Magna Corporation and Summa Corporation. Each firm produces an identical product. Magna and Summa are considering whether to expand (None) their production capacity for the next operating period. If the decision is to expand, the two firms must decide whether the expansion should be Moderate or Extensive. The tradeoff confronting each firm is that expansion will result in greater output that will lower the selling price of the product in the market. The normal form of this game is summarized in Figure 11.5. If larger payoffs are preferred, the Nash equilibrium strategy profile for this game is:

A) {None, None}.
B) {Moderate, Moderate}.
C) {Extensive, Extensive}.
D) {Moderate, Extensive}.
E) {None, Moderate}.

Question 28

-Suppose that the game depicted in Figure 11.5 is modeled as a multistage game with Magna Corporation moving first. The subgame perfect equilibrium for this game is:

A) {Extensive 6 None}
B) {Moderate 6 None}
C) {None 6 Extensive}
D) {Moderate 6 Moderate}
E) {None 6 None}

Question 29

-Suppose that the game depicted in Figure 11.5 is modeled as a multistage game with Magna Corporation moving first. The payoffs to both companies from a subgame perfect equilibrium are:

A) (25, 10).
B) (30, 15).
C) (10, 25).
D) (20, 20).
E) (25, 25).

Question 30

-Consider the one-time, noncooperative, static game depicted in Figure 11.6. If larger payoffs are preferred, which player has a strictly dominant strategy?

A) P1
B) P2
C) Both players
D) Neither player
E) Cannot be determined on the basis of the information provided.

Question 31

-Consider the one-time, noncooperative, static game depicted in Figure 11.6. If larger payoffs are preferred, which player has an iterated strictly dominant strategy?

A) P1
B) P2
C) Both players
D) Neither player
E) Cannot be determined on the basis of the information provided.

Question 32

-In the game depicted in Figure 11.6, which of the following strategy profiles is a Nash equilibrium:
I. {A, D}.
II. {A, F}.
III. {B, E}.
IV. {C, F}.
V. {C, D}.
Which of the following is correct?

A) I only.
B) II only.
C) III only.
D) III and IV only.
E) II and V only.

Question 33

-Suppose that the game depicted in Figure 11.6 is modeled as a sequential move game in which P1 moves first and the payoffs are (P2, P1). The subgame perfect equilibrium for this game is:

A) {F ? A}.
B) {D ? B}.
C) {D ? C}.
D) {E ? C}.
E) {F ? C}.

Question 34

-Suppose that the game depicted in Figure 11.6 is modeled as a sequential move game in which P1 moves first and the payoffs are (P2, P1). The payoffs to both players are:

A) (3, 9).
B) (4, 2).
C) (9, 3).
D) (8, 4).
E) (7, 7).

Question 35

-Suppose that the game depicted in Figure 11.6 is modeled as a sequential move game in which P2 moves first and the payoffs are (P2, P1). The subgame perfect equilibrium for this game is:

A) {A ? F}.
B) {C ? D}.
C) {B ? D}.
D) {B ? F}.
E) {C ? F}.

Question 36

-Suppose that the game depicted in Figure 11.6 is modeled as a sequential move game in which P2 moves first and the payoffs are (P2, P1). The payoffs to both players are:

A) (9, 3).
B) (3, 9).
C) (2, 4).
D) (8, 6).
E) (7, 7).

Question 37

-Refer to Figure 11.7. If larger payoffs are preferred, which player has a strictly dominant strategy?

A) Player A
B) Player B
C) Both players
D) Neither player
E) Cannot be determined on the basis of the information provided.

Question 38

-Refer to Figure 11.7. If larger payoffs are preferred, which player has an iterated strictly dominant strategy?

A) Player A
B) Player B
C) Both players
D) Neither player
E) Cannot be determined on the basis of the information provided.

Question 39

-In the game depicted in Figure 11.7, what is the Nash equilibrium strategy profile for this game?
I. {A1, B1}.
II. {A3, B1}.
III. {A3, B3}.
IV. {A2, B3}.
V. {A2, B2}.
Which of the following is correct?

A) I only.
B) II only.
C) III only.
D) I and IV only.
E) II and V only.

Question 40

-Suppose that the game depicted in Figure 11.7 is modeled as a sequential move game with Player A moving first and the payoffs are (Player A, Player B). The subgame perfect equilibrium for this game is:

A) {A3 6 B3}
B) {A2 6 B1}
C) {A1 6 B3}
D) {A3 6 B1}
E) None of the above. This game has multiple subgame perfect equilibria

Question 41

-Suppose that the game depicted in Figure 11.7 is modeled as a sequential move game with Player A moving first and the payoffs are (Player A, Player B). The payoffs for this game are:

A) (5, 2).
B) (2, 3).
C) (2, 4).
D) (3, 2).
E) None of the above are correct.

Question 42

-Suppose that the game depicted in Figure 11.7 is modeled as a sequential move game with Player B moving first and the payoffs are (Player A, Player B). The subgame perfect equilibrium for this game is:

A) {B3 6 A3}
B) {B2 6 A1}
C) {B1 6 A3}
D) {B3 6 A2}
E) None of the above.

Question 43

-Suppose that the game depicted in Figure 11.7 is modeled as a sequential move game with Player B moving first and the payoffs are (Player A, Player B). The payoffs to both players are:

A) (5, 2).
B) (4, 1).
C) (4, 4).
D) (3, 2).
E) None of the above are correct.

Question 44

A player has a first-mover advantage:

A) If he or she is able to obtain a payoff that is no worse than if all players moved simultaneously.
B) Will always obtain the highest possible payoff.
C) Only in games in which all players have dominant strategies.
D) Only in games in which none of the players have dominant strategies.
E) None of the above.

Question 45

According to the Stackelberg duopoly model, if both firms in the industry face identical demands and identical total production costs, then:

A) The Stackelberg leader will produce more than the Stackelberg follower.
B) The Stackelberg follower will produce more than the Stackelberg leader.
C) The Stackelberg leader and Stackelberg follower will produce identical output.
D) The outcome is identical with that predicted by the Cournot model.

Question 46

If both firms in a duopolistic industry face identical demands and identical total production costs, then:

A) Total industry output predicted by the Stackelberg duopoly model will less than total industry output predicted by the Cournot duopoly model.
B) Total industry output predicted by the Stackelberg duopoly model will greater than total industry output predicted by the Cournot duopoly model.
C) Total industry output predicted by the Stackelberg duopoly model will be the same as total industry output predicted by the Cournot duopoly model.
D) None of the above. It is more appropriate to compare the Stackelberg duopoly model with the Bertrand duopoly model.

Question 47

In the case study "Sun Country versus Northwest Airlines," Sun Country's error was:

A) Failing to use backward induction.
B) Ignoring Northwest's possible reaction to its decision begin regularly scheduled nonstop service to Boston, New York, Washington, D. C., Los Angeles, and seven other destinations.
C) Assuming that Northwest would continue to charge competitive prices.
D) Answers b and c are correct.
E) All of the above.