Deck 12: Game Theory

Question 1

Use the following to answer questions 10-11:
Table 12.5
(Table 12.5) Payoffs represent profits in millions of dollars. What is ESPN's dominant strategy?

A) none
B) run the Brett Favre cover story
C) run the Tim Tebow cover story
D) run either cover story

Answer 1

A

Question 2

A simultaneous game:

A) requires that both participants play exactly the same strategy at the same time.
B) involves at least one participant playing a random strategy after first observing the opponent's strategies.
C) necessitates participants revealing their strategy at the same time without knowing the strategy of their opponent.
D) requires both players to base their strategy on backward induction.

Answer 2

C

Question 3

Use the following to answer questions 19-20:
Table 12.12
(Table 12.12) The payoffs are profits in millions of dollars. If Firm 1 follows a maximin strategy, the outcome of this game is:

A) (20 , 20).
B) (8 , 8).
C) (-20 , 15).
D) (-1 , 10).

Answer 3

D

Question 4

Which of the following statements is (are) TRUE?

A) I and II
B) I, II, and III
C) I and III
D) III

Question 5

Use the following to answer question:
Table 12.4
(Table 12.4) Payoffs are profits in thousands of dollars. Which of the following statements is TRUE?

A) This game has no Nash equilibrium.
B) Horizon's dominant strategy is high price.
C) The Nash equilibrium occurs when both companies choose the low-price strategy.
D) There are two Nash equilibria, (80 , 80) and (65 , 65).

Question 6

Use the following to answer question:
Table 12.6
(Table 12.6) Payoffs represent profits in thousands. What is the Nash equilibrium?

A) (20 , 20)
B) (17 , 17)
C) (14 , 14)
D) (19 , 10) or (10 , 19)

Question 7

Use the following to answer question:
Table 12.3
(Table 12.3) The payoffs represent profits. If Cape North and Imperial both choose their dominated strategy, Cape North will earn a profit of _____ and Imperial will earn a profit of _____.

A) $154; $154
B) $120; $120
C) $75; $180
D) $75; $75

Question 8

Use the following to answer questions 13-14:
Table 12.7
(Table 12.7) Payoffs represent profits in millions of dollars. What is Owens Corning's dominated strategy?

A) no expansion
B) small expansion
C) large expansion
D) none

Question 9

Use the following to answer questions 10-11:
Table 12.5
(Table 12.5) Payoffs represent profits in millions of dollars. In a Nash equilibrium, Sports Illustrated will run the _____ cover story and ESPN Magazine will run the _____ cover story.

A) Brett Favre; Brett Favre
B) Brett Favre; Tim Tebow
C) Tim Tebow; Brett Favre
D) Tim Tebow; Tim Tebow

Question 10

Use the following to answer question:
Table 12.1
(Table 12.1) Randy and Todd are playing a simultaneous game. Randy's dominant strategy is _____. and Todd's dominant strategy is _____.

A) Bottom; Left
B) Top; Left
C) Bottom; Right
D) Top; Right

Question 11

Use the following to answer questions 13-14:
Table 12.7
(Table 12.7) Payoffs represent profits in millions of dollars. The Nash equilibrium:

A) does not exist.
B) occurs when both firms choose small expansion.
C) occurs when both firms choose large expansion.
D) occurs when both firms choose no expansion.

Question 12

Use the following to answer questions 19-20:
Table 12.12
(Table 12.12) The payoffs are profits in millions of dollars. The Nash equilibrium of this game is:

A) (20 , 20).
B) (8 , 8).
C) (-20 , 15).
D) (-1 , 10).

Question 13

Use the following to answer question:
Table 12.11
(Table 12.11) The payoffs represent dollars won or lost. Which of the following statements is TRUE?

A) The Nash equilibria are (1, -1) and (-1 , 1).
B) The dominant strategy for Player B is pick odd number.
C) In mixed strategy, the Nash equilibrium is for both players to randomly select their strategy with a 50% probability.
D) The pure-strategy equilibrium is (odd number, even number).

Question 14

Use the following to answer question:
Table 12.2
(Table 12.2) Thelma and Louise have been arrested for a crime. In this simultaneous game, the payoffs represent years in jail. Louise's dominated strategy is ______ while Thelma's dominated strategy is _________.

A) Confess; Deny
B) Deny; Deny
C) Deny; Confess
D) Confess; Confess

Question 15

Use the following to answer question:
Table 12.9
(Table 12.9) Payoffs represent profits in thousands of dollars. In this game, the Nash equilibria are:

A) (210 , 250) and (180 , 180).
B) (50 , 50) and (20 , 20).
C) (210 , 250) and (50, 50).
D) (20 , 20), (50, 50), and (180 , 180).

Question 16

The _____ model is an example of a simultaneous game, while the _____ model is an example of a sequential game.

A) Cournot; Stackelberg
B) Cournot; Bertrand
C) Bertrand; Cournot
D) Stackelberg; Bertrand

Question 17

Use the following to answer question:
Table 12.8
(Table 12.8) Payoffs represent profits measured in thousands of dollars. Which of the following outcomes represent(s) a Nash equilibrium?

A) II and I
B) II
C) II and III
D) III and IV

Question 18

Which of the following is (are) the elements of every game?

A) I, II, III, and IV
B) I, II, and III
C) IV
D) I and II

Question 19

Use the following to answer question:
Table 12.10
(Table 12.10) The table shows the payoffs from the game rock-paper-scissors. Which of the following statements is (are) TRUE?

A) II and III
B) I and III
C) III
D) I and II

Question 20

Suppose that Fizzy Soda and Townie Soda must choose whether to advertise their soft drinks. In a Nash equilibrium, both firms choose to advertise and earn weekly profits of $80,000. Which of the following statements is (are) TRUE?

A) I
B) II and III
C) I, II, and III
D) I and II

Question 21

Big Earth and District 13 are two producers of neodymium, a rare earth. If they agree to restrict output, each firm earns $100 million per year. If both firms expand output, each firm earns $50 million per year. If one firm restricts output and the other firm expands output, the firm that expands output earns $150 million per year and the other firm earns only $30 million per year. Assume that Big Earth and District 13 will compete infinitely, with each firm following a grim trigger strategy. Which of the following statements is TRUE?

A) If d = 0.50, Big Earth is indifferent between agreeing to restrict output and expanding output.
B) If d = 0.40, Big Earth would be better off restricting output.
C) If d = 0.90, Big Earth is indifferent between agreeing to restrict output and expanding output.
D) If d = 0.75, Big Earth would be better off by expanding output.

Question 22

Use the following to answer question:
Table 12.13
(Table 12.13) The payoffs represent dollars. If both players follow their maximin strategy, the outcome of this game is:

A) (-500 , -500).
B) (15 , -25).
C) (25 , -15).
D) (0 , 0).

Question 23

Use the following to answer question:
Figure 12.4
(Figure 12.4) The outcome of this game is:

A) (9 , 10).
B) (14 , 9).
C) (6 , 8).
D) (12 , 3).

Question 24

Use the following to answer question:
Table 12.15
(Table 12.15) The table shows the strategies of two players playing prisoner's dilemma. What is player A's strategy?

A) tit-for-tat
B) grim reaper
C) hammer and sickle
D) positional leadership

Question 25

Use the following to answer questions 26-28:
Table 12.16
(Table 12.16) The payoffs represent profits measured in thousands of dollars. In this infinitely repeated game, Firm A and Firm B are both using grim trigger strategies; they agree to charge a high price in period 1. If Firm A has a change of heart and decides not to charge a high price in period 1, what is Firm A's expected payoff from cheating? Assume that d = 0.9.

A) $165,000
B) $2 million
C) $315,000
D) $580,000

Question 26

Use the following to answer question:
Table 12.19
(Table 12.19) The payoffs represent profits in thousands of dollars. Which of the following statements is (are) TRUE?

A) I and III
B) II
C) II and III
D) I, II, and III

Question 27

Use the following to answer question:
Figure 12.3
(Figure 12.3) Which figure corresponds to the following normal-form game?

A) panel a
B) panel b
C) panel c
D) panel d

Question 28

Use the following to answer question:
Table 12.18
(Table 12.18) The payoffs represent profits measured in thousands of dollars. In this infinitely repeated game, the two schools agree to cooperate and not offer financial aid. Each school follows a grim trigger strategy. At what value of d is the Motor City Art School indifferent between upholding and cheating on the agreement?

A) 0.5
B) 0.7
C) 0.75
D) 0.9

Question 29

Use the following to answer question:
Table 12.20
(Table 12.20) Payoffs represent profits in millions of dollars. Which of the following statements is (are) TRUE?

A) I and III
B) II
C) II and III
D) I, II, and III

Question 30

Use the following to answer questions 26-28:
Table 12.16
(Table 12.16) The payoffs represent profits in thousands of dollars. Suppose that two firms are playing an infinitely repeated game. In period 6, Firm B decides it will no longer cooperate with Firm A. If Firm A is using a grim trigger strategy, Firm A will choose:

A) a low price in period 7 and all future periods.
B) a low price in period 7 and a high price in all future periods.
C) to set price below marginal cost and drive Firm B out of the market.
D) to maintain a high price in all future periods.

Question 31

Which of the following games is solvable by backward induction?

A) II
B) IV
C) I and III
D) I and IV

Question 32

Use the following to answer question:
Figure 12.5
(Figure 12.5) The outcome of this game is for:

A) Firm B to choose strategy 3.
B) Firm A to choose strategy 1 and then Firm B to choose strategy 3.
C) Firm A to choose strategy 2.
D) Firm A to choose strategy 1 and then Firm B to choose strategy 4.

Question 33

Use the following to answer question:
Figure 12.2
(Figure 12.2) Two firms are considering whether to expand their production capacity. Which of the following statements is TRUE?

A) The outcome is (10 , 6) or (6 , 10).
B) There is no first-mover advantage.
C) Neither firm expands its production capacity.
D) There is a first-mover advantage.

Question 34

Use the following to answer question:
Figure 12.1
(Figure 12.1) The Nash equilibrium of this game is:

A) Low , Up.
B) Low , Down.
C) High , Up.
D) High , Down.

Question 35

Consider a simultaneous game for two players. Each player has a choice between two strategies, Friend and Foe. If both players play Friend, each wins $1,000. If both play Foe, they win nothing. If one plays Foe and the other plays Friend, the Foe wins $2,000 and the Friend wins nothing. Which of the following statements is (are) TRUE?

A) I and II
B) I, II, and III
C) II and III
D) II

Question 36

Use the following to answer questions 26-28:
Table 12.16
(Table 12.16) The payoffs represent profits measured in thousands of dollars. In this infinitely repeated game, Firm A and Firm B are both using grim trigger strategies; they agree to charge a high price in period 1. If Firm A charges a high price for all periods, what is its expected payoff? Assume that d = 0.9.

A) $720,000
B) $3 million
C) $364,000
D) $200,000

Question 37

Use the following to answer question:
Table 12.17
(Table 12.17) The payoffs represent profits in millions of dollars. In this infinitely repeated game, Firm A and Firm B agree to cooperate and not offer warranty coverage. Each firm follows a grim trigger strategy. At what value of d is Firm A indifferent between keeping the agreement with Firm B and cheating on it?

A) 0.2
B) 0.4
C) 0.6
D) 0.8

Question 38

Use the following to answer question:
Table 12.14
(Table 12.14) The payoffs represent profits in millions of dollars. Suppose that this simultaneous-move game is played once in each period for 3 periods. In period 1, the outcome will be _____, and in period 2, the outcome will be _____.

A) (6 , 6); (4 , 4)
B) (4 , 4); (4 , 4)
C) (2 , 7); (6 , 6)
D) (6 , 6); (6 , 6)

Question 39

Use the following to answer question:
Figure 12.6
(Figure 12.6) Which of the panels correctly illustrates trimming the branches?

A) panel a
B) panel b
C) panel c
D) panel d

Question 40

Suppose that Ben and Tim are playing a finitely repeated flag game. The game starts with 7 flags in the ground, and the players take turns removing the flags. A player must remove either 1, 2, or 3 flags per turn. The player who takes the last flag out of the ground, whether it is by itself or in a group, wins the game. Assume that Ben decides first on how many flags to remove. How many flags should Ben remove on his first turn to guarantee that he will win the game? Use backward induction.

A) 1
B) 2
C) 3
D) either 1 or 2

Question 41

The lesson from Dr. Strangelove is that:

A) your enemies must know about your doomsday machine if it is to serve as a credible deterrent to attack.
B) to win at love you must sometimes make implausible promises to your lover.
C) prisoner's dilemma can be avoided by making side payments to your opponent.
D) forward induction is never superior to backward induction.

Question 42

Use the following to answer question:
Figure 12.9
(Figure 12.9) Brad may threaten to play strategy _____ if Sly plays strategy _____.

A) B; A, in an attempt to move the game's outcome from (10 , 3) to (7 , 4)
B) B; B, in an attempt to move the game's outcome from (10 , 3) to (7 , 4)
C) B; A or B
D) A; A, in an attempt to move the game's outcome from (1 , 2) to (10 , 3).

Question 43

Use the following to answer question:
Table 12.26
(Table 12.26) payoffs are in thousands of dollars.

Question 44

At one time, tobacco companies vigorously fought lawsuits by their current and former customers, even though the cost of defending the lawsuits exceeded the amount of money demanded by the smokers. What type of strategic behavior were tobacco companies using?

A) excess capacity
B) reputation
C) grim reaper
D) MAD

Question 45

Use the following to answer question:
Table 12.30
(Table 12.30)

Question 46

Use the following to answer question:
(Table: Lemonade)
(Table: Lemonade)
Answer the following questions.
a. Who are the players?
b. What strategies does each player have?
c. Identify any dominant strategies.

Question 47

Use the following to answer question:
Figure 12.7
(Figure 12.7) Suppose that Player A promises a $2 side payment to Player B if Player B chooses Pass. As a result of the side payment, the game's outcome will change from:

A) (2 , 10) to (10 , 9).
B) (5 , 0) to (8 , 11).
C) (5 , 0) to (7 , 2).
D) (2 , 10) to (8 , 11).

Question 48

Consider the following game: Find the mixed-strategy Nash equilibrium.

Question 49

Use the following to answer question:
Table 12.23
(Table 12.23)

Question 50

According to Goolsbee and Syverson, how did incumbent airlines respond to the entry of Southwest Airlines?

A) They raised airfares just before Southwest's arrival and then cut airfares when Southwest began operating.
B) They lowered airfares just before Southwest's arrival and then raised airfares when Southwest began operating.
C) They began cutting airfare as early as 1 to 2 years before Southwest began operating from the same airport.
D) They kept airfares unchanged before Southwest's arrival and then lowered airfares when Southwest began operating.

Question 51

Use the following to answer question:
Table 12.22
(Table 12.22) Payoffs, represent profits in millions of dollars. In this simultaneous game, TriStar and New Line Cinema both decide the genre of their summer movie release. TriStar prefers to release a superhero movie and New Line Cinema releases a comedy. TriStar enters into an irrevocable contract that will provide penalty payments to theater chains if it releases a summer comedy. These penalty payments serve as a credible commitment to TriStar's desire to release a superhero movie. How large do these penalty payments have to be to convince New Line Cinema that TriStar will release a superhero movie?

A) between $1 million and $5 million
B) greater than $5 million
C) at least $90 million
D) less than $95 million

Question 52

Use the following to answer question:
Table 12.24
(Table 12.24) Payoffs represent profits in millions of dollars.

Question 53

Use the following to answer questions 47-48:
Figure 12.10
(Figure 12.10) In the figure, payoffs are profits in millions of dollars. Suppose that Feely cannot develop an antibedbug mattress because of Mealy's patented technology. Should Mealy develop and release its antibedbug mattress?

A) Yes, Mealy will earn $4 million and Feely will earn $9 million.
B) Yes, Mealy will earn $13 million and Feely will earn $3 million.
C) Yes, Mealy will earn $6 million and Feely will earn $4 million.
D) No, Mealy will earn larger profits by not releasing the mattress.

Question 54

Use the following to answer question:
Table 12.25
(Table 12.25) Payoffs represent profits in millions of dollars.

Question 55

Use the following to answer question:
Figure 12.8
(Figure 12.8) Which of the following is an example of a noncredible threat?

A) O's Groceries tells the Food Palace that it is committed to entering the market.
B) Food Palace tells O's Groceries that it will build a large store whether or not O's Groceries enters the market.
C) Food Palace tells O's Groceries that it will build a small store if O's Groceries enters the market.
D) O's Groceries tells the Food Palace that it will not enter the market.

Question 56

Use the following to answer questions 47-48:
Figure 12.10
(Figure 12.10) Payoffs are profits in millions of dollars. Should Mealy Mattress develop its antibedbug mattress if Feely Mattress promises not to develop its own antibedbug mattress?

A) Yes, Feely's promise is credible, and Mealy's profits would increase from $6 million to $13 million.
B) Yes, Feely's promise is credible, and Mealy's profits would increase from $4 million to $13 million.
C) No, Feely's promise is not credible, so Mealy should not develop the antibedbug mattress and should earn $6 million.
D) No, Feely's promise is not credible, so Mealy should develop the antibedbug mattress and earn $13 million.

Question 57

The game has two players, each with three strategies.
a. Identify and list any dominant strategies.
b. Using the check method, find all pure Nash equilibria in the game.

Question 58

Use the following to answer question:
Table 12.28
(Table 12.28)

Question 59

Use the following to answer question:
Table 12.21
(Table 12.21) Payoffs represent profits in millions of dollars. Which of the following statements is (are) TRUE?

A) I, II, and III
B) II and III
C) I and III
D) I

Question 60

The table contains letters that represent payoff values. If the strategy combination (B , Y) is a Nash equilibrium, then prove that the strategy combination (A , X) must also be a Nash equilibrium assuming there are no dominant strategies. Assume that no two letters will take on the same value.

Question 61

The following game:

A) has no mixed-strategy equilibria.
B) has a mixed-strategy equilibrium in which Row plays Up with 0.5 probability and Down with 0.5 probability.
C) has a mixed-strategy equilibrium in which Column plays Left with 0.5 probability and Right with 0.5 probability.
D) has a mixed-strategy equilibrium in which answers B and C both hold.

Question 62

The following game:

A) has no mixed-strategy equilibria.
B) has a mixed-strategy equilibrium in which Row plays Up with 0.5 probability and Down with 0.5 probability.
C) has a mixed-strategy equilibrium in which Column plays Left with 0.5 probability and Right with 0.5 probability.
D) has a mixed-strategy equilibrium in which answers B and C both hold.

Question 63

Which of the following statements about mixed strategies is FALSE?

A) They enable the player to randomize her actions.
B) They always exist in an equilibrium when there are at least two pure-strategy equilibria in a game.
C) They always involve some positive probability on every available strategy.
D) They can exist in equilibrium in games that do not have any pure-strategy equilibria.

Question 64

Suppose that you are playing an infinitely repeated game. You and your opponent agree to restrict output each period to maximize discounted profit. For each period, you and your opponent have to touch a button on a computer screen that selects the level of output, namely, restricted or unrestricted output. Once the button is touched, the output is locked in for the period and cannot be changed. If your opponent has a shaky hand, would you rather use a grim trigger strategy or a tit-for-tat strategy?

Question 65

Use the following to answer question:
Table 12.31
(Table 12.31)

Question 66

Construct the decision tree for the following game. There are two players; each may choose 1, 2, or 3 straws at each turn. The game begins with a total of 5 straws. The object of the game is to take the last straw or straws. Assume that a player either wins $1 or loses $1. Find all Nash equilibria.

Question 67

Use the following to answer question:
(Table: Lemonade)
(Table: Lemonade) Abe and Sarah operate lemonade stands in the same neighborhood. Payoffs are in quarters . This can also be extended: c + ad + cd² + ad³. . . = (c + ad)/(1 - d²).

Question 68

Use the following to answer question:
Table 12.33
(Table 12.33) Two firms have formed an agreement to restrict output. They are playing an infinitely repeated game in which output decisions must be made every period. Both firms are using grim trigger strategies.

Question 69

Use the following to answer question:
Figure 12.12
(Figure 12.12)
a.
What is the Nash equilibrium of this game?
b.
Is it credible for the United States to threaten to blow up the world if China invades Taiwan?

Question 70

Consider two players in the following game. For what values of the discount rate would a grim trigger strategy ensure cooperation between the two players if they play forever?

Question 71

Consider the following game. Either of the two players can choose to stop the game or continue it at any point. If a player continues the game, she loses $1, and $2 is added to her opponent's payoff. The game is played for 10 rounds. Construct the decision tree for this game.

Question 72

Use the following to answer question:
Table 12.32
(Table 12.32) Two firms have formed an agreement to restrict output. They are playing an infinitely repeated game in which output decisions must be made every period. Both firms are using a grim trigger strategy. At what value of d (discount rate) would Firm A be indifferent about keeping the agreement or cheating on the agreement?

Question 73

Consider two players with the following decision tree: What is the Nash equilibrium?

Question 74

The following game:

A) has no mixed-strategy equilibrium.
B) has a mixed-strategy equilibrium in which Row plays Up with 0.5 probability and Down with 0.5 probability.
C) has a mixed-strategy equilibrium in which Column plays left with 0.5 probability and right with 0.5 probability.
D) has a mixed-strategy equilibrium in which answers B and C both hold.

Question 75

Use the following to answer question:
Table 12.36
(Table 12.36)

Question 76

Consider a game in which a person called the proposer is given $200. The proposer must choose to split the money with a person called the responder. The money must be split in one of three ways:
(1) Proposer keeps $199; responder gets $1.
(2) Proposer keeps $100; responder gets $100.
(3) Proposer keeps $50; responder gets $150.
The responder can either accept or reject the proposer's offer. If the responder rejects the offer, both players get nothing. Illustrate this game in extensive form. Using backward induction, what is the outcome of this game?

Question 77

Answer the following questions.

Question 78

Use the following to answer question:
Figure 12.11
(Figure 12.11)

Question 79

Use the following to answer question:
Table 12.35
(Table 12.35)

Question 80

Use the following to answer question:
Table 12.34
(Table 12.34) Represent the normal-form game as a sequential game, with Firm A making the first decision. What is the outcome of this game?