Deck 12: Game Theory

Question 1

(Table: Polaris and Yamaha I) The payoffs represent profits in millions of dollars. Suppose that this simultaneous-move game is played once in each period for three periods. In period one, the outcome will be _____, and in period two, the outcome will be _____.

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

Answer 1

B

Question 2

Dennis and Denise are trying to decide whether to go hiking or biking this weekend. Depending on their choices, they might go together or they might go apart. Their payoffs in terms of their happiness are as follows. There exists a mixed-strategy Nash equilibrium when Denise chooses biking with a probability of ____.

A) 3/4
B) 2/3
C) 1/2
D) 1/4

Answer 2

C

Question 3

Which of the following statements is (are) TRUE?
I) A Nash equilibrium requires that each player have a dominant strategy.
II) A Nash equilibrium requires that each player have a dominated strategy.
III) A game can have more than one Nash equilibrium.

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

Answer 3

D

Question 4

(Table: Jack and Jill I) If Jack chooses to climb the hill and Jill brings the pail, Jack's payoff is ____.

A) 0
B) 10
C) 20
D) 30

Question 5

(Table: Lemonade) Andrei and Sonya operate lemonade stands in the same neighborhood. Payoffs are in quarters . The kids have formed an agreement to restrict output. They are playing an infinitely repeated game in which output decisions must be made every period and both of them are using tit-for-tat trigger strategies. If the discount rate is d = 0.4, then the players ____.

A) prefer to collude rather than not to collude
B) prefer not to collude rather than to collude
C) are indifferent between colluding and not colluding
D) not enough information is given in the problem to determine preference for collusion.

Question 6

(Table: TriStar Pictures and New Line Cinema I) 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 7

(Table: Firms 1 and 2 II) 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 8

(Figure: Firms A and B V) Which figure corresponds to the following normal-form game?

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

Question 9

(Table: Firms 1 and 2 III) Payoffs represent profits in millions of dollars. Firm 1's dominated strategy is ____.

A) up
B) down
C) left
D) right

Question 10

(Table: Owens Corning and GAF Capacity Expansion I) 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 11

(Table: Jack and Jill I) Jack's strategies are ____.

A) climb hill and don't climb hill
B) bring pail and don't bring pail
C) climb hill and bring pail
D) don't climb hill and don't bring pail

Question 12

Robert and Rosalie are deciding whether to request fish or chicken at a wedding that they will attend. If they order different meals, they can try each of the dishes by sharing. Their payoffs in terms of their happiness are as follows. There is a pure-strategy Nash equilibrium at ____.

A) Fish, Fish
B) Chicken, Fish
C) Chicken, Chicken
D) none of these answers

Question 13

Karoun and Kohar hope to be roommates and are choosing between two apartments. Their payoffs are as given in the table. There exists a mixed-strategy Nash equilibrium when Kohar chooses Apartment 1 with probability ____.

A) 1/3
B) 2/3
C) 1/8
D) 7/8

Question 14

(Table: Fresh Fruit Market and Spoiled Not Food I) Payoffs are in thousands of dollars. Spoiled Not Food's dominant strategy is ____.

A) build new store
B) remodel store
C) leave store as is
D) Spoiled Not Food does not have a dominant strategy.

Question 15

(Table: Firms A and B I) 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 one. If Firm A has a change of heart and decides not to charge a high price in period one, what is Firm A's expected payoff from cheating? Assume that d = 0.9.

A) $165,000
B) $150,000
C) $315,000
D) $180,000

Question 16

(Table: Jack and Jill I) If Jack chooses to not climb the hill and Jill brings the pail, Jill's payoff is ____.

A) 0
B) 10
C) 20
D) 30

Question 17

(Table: Players 1 and 2 II) 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 18

(Table: Jack and Jill I) If Jack chooses to climb the hill and Jill does not bring the pail, Jill's payoff is ____.

A) 0
B) 10
C) 20
D) 30

Question 19

Dennis and Denise are trying to decide whether to go hiking or biking this weekend. Depending on their choices, they might go together or they might go apart. Their payoffs in terms of their happiness are as follows. There exists a mixed-strategy Nash equilibrium when Dennis chooses hiking with a probability of ____.

A) 3/4
B) 2/3
C) 1/2
D) 1/4

Question 20

(Table: Jack and Jill I) If Jack chooses to climb the hill and Jill brings the pail, Jill's payoff is ____.

A) 0
B) 10
C) 20
D) 30

Question 21

(Table: Helicopter Rides I) 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 22

(Table: Lemonade) Andrei and Sonya operate lemonade stands in the same neighborhood. Payoffs are in quarters . The kids have formed an agreement to restrict output. They are playing an infinitely repeated game in which output decisions must be made every period and both of them are using tit-for-tat trigger strategies. If the discount rate is d = 0.1, then the players ____.

A) prefer to collude rather than not to collude
B) prefer not to collude rather than to collude
C) are indifferent between colluding and not colluding
D) Not enough information is given in the problem to determine preference for collusion.

Question 23

(Table: Players 1 and 2 III) Payoffs represent profits in millions of dollars. Which of the following statements is (are) TRUE?
I) In a simultaneous game that is played only once, the Nash equilibria are (80 , 100) and (70 , 40).
II) In a sequential game in which Player 1 moves first, the Nash equilibrium is (100 , 90).
III) In a simultaneous game that is played only once, the dominated strategy for Player 1 is Middle.

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

Question 24

Suppose that in a two-player game in which player A can move Up or Down, and player B can choose Left or Right. Payoffs for this game are given in the table: There is a pure-strategy Nash equilibrium at ____.

A) Down, Right
B) Up, Right
C) Down, Left
D) none of the above

Question 25

(Figure: Firms A and B VII) Which of the panels correctly illustrates trimming the branches?

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

Question 26

(Figure: Game A and B I) The outcome of this game is:

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

Question 27

Dennis and Denise are trying to decide whether to go hiking or biking this weekend. Depending on their choices, they might go together or they might go apart. Their payoffs in terms of their happiness are as follows. There is a pure-strategy Nash equilibrium at ____.

A) Hiking, Hiking
B) Hiking, Biking
C) Biking, Biking
D) none of these answers

Question 28

Suppose that, in a two-player game, player A can move Up or Down, and player B can choose Left or Right. Payoffs for this game are given in the table: There exists a mixed-strategy Nash equilibrium at which Player B plays Left with probability ____.

A) 2/3
B) 1/3
C) 1/4
D) 3/4

Question 29

(Table: Firms A and B XIII) In a simultaneous game, the Nash equilibrium is Firm A choosing ____ and Firm B choosing ____.

A) no expansion; no expansion
B) no expansion; expansion
C) expansion; no expansion
D) expansion; expansion

Question 30

(Table: Jack and Jill I) Jill's strategies are ____.

A) climb hill and don't climb hill
B) bring pail and don't bring pail
C) climb hill and bring pail
D) don't climb hill and don't bring pail

Question 31

(Table: Hitter and Pitcher I) A mixed-strategy Nash Equilibrium in this game is ____.

A) guess fastball, throw fastball
B) guess Curveball, throw curveball
C) guess fastball, throw curveball
D) Hitter randomly guesses fastball 50% of the time and Pitcher randomly throws fastball 50% of the time.

Question 32

Suppose that, in a two-player game, player A can move Up or Down, and player B can choose Left or Right. Payoffs for this game are given in the table. There exists a mixed-strategy Nash equilibrium at which Player A plays Down with probability ____.

A) 2/3
B) 1/3
C) 1/4
D) 3/4

Question 33

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.

Question 34

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?
I) This game has a mixed-strategy equilibrium.
II) This game has a pure-strategy equilibrium.
III) The Nash equilibrium is for both players to play Friend.

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

Question 35

(Table: Fresh Fruit Market and Spoiled Not Food I) Payoffs are in thousands of dollars. Fresh Fruit Market's dominant strategy is ____.

A) build new store
B) remodel store
C) leave store as is
D) Fresh Fruit Market does not have a dominant strategy.

Question 36

Kelly and Karl can vote for or against a public project. Their payoffs are given in the table: There is a pure-strategy Nash equilibrium at ____.

A) For, For
B) For, Against
C) Against, For
D) none of these answers

Question 37

(Table: Firms 1 and 2 IV) Payoffs represent profits in millions of dollars. The Nash Equilibrium in this game is ____.

A) up, left
B) down, left
C) up, right
D) down, right

Question 38

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 one to two 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 39

(Table: Fresh Fruit Market and Spoiled Not Food I) Payoffs are in thousands of dollars. The Nash Equilibrium in this game is ____.

A) build new store, build new store
B) remodel store, remodel store
C) leave store as is, leave store as is
D) There are no Nash Equilibria in this game.

Question 40

Dennis and Denise are trying to decide whether to go hiking or biking this weekend. Depending on their choices, they might go together or they might go apart. Their payoffs in terms of their happiness are as follows. There exists a mixed-strategy Nash equilibrium when Dennis chooses biking with a probability of ____.

A) 3/4
B) 2/3
C) 1/2
D) 1/4

Question 41

(Table: Firms 1 and 2 III) Payoffs represent profits in millions of dollars. Firm 1's dominant strategy is ____.

A) up
B) down
C) left
D) right

Question 42

Robert and Rosalie are deciding whether to request fish or chicken at a wedding that they will attend. If they order different meals, they can try each of the dishes by sharing. Their payoffs in terms of their happiness are as follows. There is a pure-strategy Nash equilibrium at ____.

A) Fish, Fish
B) Fish, Chicken
C) Chicken, Chicken
D) none of these answers

Question 43

(Table: Hanes and Fruit of the Loom T-Shirts II) Answer the following. The outcome of Hanes T-Shirt choosing $____ and Fruit of the Loom choosing $____ is a Nash Equilibrium in this game.

A) 8; 8
B) 8; 6
C) 4; 4
D) 4; 6

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

The following game has _____ pure-strategy equilibrium (equilibria) and (but) _____ mixed-strategy equilibrium (equilibria).

A) two; no
B) two; one
C) no; no
D) two; an infinite number of

Question 46

(Table: Detroit Art School and Motor City Art School I) 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 47

(Table: Simultaneous Game II) Tatyana and Lena have been arrested for a crime. In this simultaneous game, the payoffs represent years in jail. It should be noted that years in jail are something that someone would like to avoid or are considered negatively. Lena's dominated strategy is ______, while Tatyana's dominated strategy is _________.

A) confess; deny
B) deny; deny
C) deny; confess
D) confess; confess

Question 48

Suppose the payoffs for players A and B, given their respective strategies, are as in the table: There is a pure-strategy Nash equilibrium at _____.

A) Down, Right
B) Up, Right
C) Down, Left
D) none of the above

Question 49

(Table: Cape North and Imperial Strategies I) 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 50

(Table: Players A and B VII) In Table 1, ____ is a Nash Equilibrium.

A) (A, A)
B) (A, B)
C) (B, A)
D) (B, B)

Question 51

Karoun and Kohar hope to be roommates and are choosing between two apartments. Their payoffs are as given in the table. There exists a mixed-strategy Nash equilibrium when Kohar chooses Apartment 2 with probability ____.

A) 1/3
B) 2/3
C) 1/8
D) 7/8

Question 52

Suppose that, in a two-player game, player A can move Up or Down, and player B can choose Left or Right. Payoffs for this game are given in the table: There exists a mixed-strategy Nash equilibrium at which Player B plays Right with probability ____.

A) 2/3
B) 1/3
C) 1/4
D) 3/4

Question 53

(Table: Firms A and B I) 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 one. 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 54

(Table: Hitter and Pitcher I) The hitter's dominant strategy is ____.

A) guess fastball
B) guess curveball
C) throw fastball
D) The hitter has no dominant strategy.

Question 55

(Table: Jack and Jill I) If Jack chooses to not climb the hill and Jill does not bring the pail, Jill's payoff is ____.

A) 0
B) 10
C) 20
D) 30

Question 56

Imagine two friends, Marcus and Marty, who are providing goods for a bake sale. They can take either brownies or cookies, and payoffs (the profits that they will split) are as given in the table: There is a pure-strategy Nash equilibrium at ____

A) Brownies, Brownies
B) Cookies, Brownies
C) Cookies, Cookies
D) none of these answers

Question 57

(Table: Jack and Jill I) If Jack chooses to climb the hill and Jill does not bring the pail, Jack's payoff is ____.

A) 0
B) 10
C) 20
D) 30

Question 58

(Table: Hitter and Pitcher I) A pure-strategy Nash Equilibrium in this game is ____.

A) guess fastball, throw fastball
B) guess curveball, throw curveball
C) guess fastball, throw curveball
D) There is no pure-strategy Nash Equilibrium in this game.

Question 59

(Table: Firms A and B II) 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 60

(Table: Owens Corning and GAF Capacity Expansion I) 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 61

Which of the following games is solvable by backward induction?
I) a 3-period simultaneous game
II) an infinitely repeated simultaneous game
III) a 1-period simultaneous game
IV) a sequential game

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

Question 62

To solve for a mixed-strategy equilibrium in a two-player, two-strategy game (two-by-two game):

A) set the expected value of playing the first strategy for the first player equal to the expected value of playing the first strategy for the second player, and solve for the implied probability.
B) always set the probability half to the first strategy and half to the second strategy.
C) for each player, roll a die to assign the probability of the first strategy and then calculate the implied second probability using the formula that probabilities must sum to one.
D) for each player, set the expected value of playing the first strategy equal to the expected value of playing the second strategy and solve for the implied probabilities.

Question 63

Karoun and Kohar hope to be roommates and are choosing between two apartments. Their payoffs are as given in the table. There is a pure-strategy Nash equilibrium at ____.

A) Apartment 1, Apartment 1
B) Apartment 1, Apartment 2
C) Apartment 2, Apartment 1
D) none of these answers

Question 64

(Table: Firms A and B X) 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.
If d (discount rate) = 0.80, Firm B's expected payoff from following the agreement is ____.

A) 550
B) 500
C) 470
D) 430

Question 65

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 66

Consider the following game. The choices of ____ represent a Nash Equilibrium in this game.

A) Strategy A, Strategy A
B) Strategy A, Strategy B
C) Strategy B, Strategy B
D) none of the above

Question 67

The following game has:

A) two pure-strategy equilibria but no mixed-strategy equilibria.
B) two pure-strategy equilibria and one mixed-strategy equilibrium.
C) no equilibria.
D) two pure-strategy equilibria and an infinite number of mixed-strategy equilibria.

Question 68

The following game has a mixed-strategy equilibrium in which Row plays Up with probability _____ and Column plays Left with probability _____.

A) 1/3; 2/3
B) 2/3; 1/3
C) 2/3; 2/3
D) 1/3; 1/3

Question 69

(Table: Sports Illustrated and ESPN Magazines I) 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 70

(Table: Players A and B I) 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 to pick an 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 71

(Table: Players 1 and 2 I) The table shows the payoffs from the game rock-paper-scissors. Which of the following statements is (are) TRUE?
I) There is no pure-strategy Nash equilibrium.
II) The Nash equilibria are (rock, rock), (paper, paper), and (scissors, scissors).
III) The mixed-strategy Nash equilibrium is for each player to randomly select each strategy one-third of the time.

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

Question 72

Kelly and Karl can vote for or against a public project. Their payoffs are given in the table: There is a pure-strategy Nash equilibrium at ____.

A) Against, For
B) For, Against
C) Against, Against
D) none of these answers

Question 73

Suppose the payoffs for players A and B, given their respective strategies, are as in the table: There is a mixed-strategy Nash equilibrium when Player B chooses Left with probability ____.

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

Question 74

(Table: Lemonade) Andrei and Sonya operate lemonade stands in the same neighborhood. Payoffs are in quarters . The kids have formed an agreement to restrict output. They are playing an infinitely repeated game in which output decisions must be made every period and both of them are using tit-for-tat trigger strategies. If the discount rate is d = 0.33, then the players ____.

A) prefer to collude rather than not to collude
B) prefer not to collude rather than to collude
C) are indifferent between colluding and not colluding
D) Not enough information is given in the problem to determine preference for collusion.

Question 75

(Table: Lemonade) Andrei and Sonya operate lemonade stands in the same neighborhood. Payoffs are in quarters . The kids have formed an agreement to restrict output. They are playing an infinitely repeated game in which output decisions must be made every period and both of them are using tit-for-tat trigger strategies. If the discount rate is d = 0.2, then the players ____.

A) prefer to collude rather than not to collude
B) prefer not to collude rather than to collude
C) are indifferent between colluding and not colluding
D) Not enough information is given in the problem to determine preference for collusion.

Question 76

Suppose the payoffs for players A and B, given their respective strategies, are as in the table: There is a mixed-strategy Nash equilibrium when Player A chooses Down with probability ____.

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

Question 77

(Table: Hanes and Fruit of the Loom T-Shirts II) Answer the following. The outcome of Hanes T-Shirt choosing $____ and Fruit of the Loom choosing $____ is a Nash Equilibrium in this game.

A) 8; 8
B) 8; 6
C) 6; 8
D) 6; 6

Question 78

Suppose the payoffs for players A and B, given their respective strategies, are as in the table: There is a mixed-strategy Nash equilibrium when Player B chooses Right with probability ____.

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

Question 79

Suppose the payoffs for players A and B, given their respective strategies, are as in the table: There is a mixed-strategy Nash equilibrium when Player A chooses Up with probability ____.

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

Question 80

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?
I) Neither firm has incentive to change its advertising strategy, given the strategy choice of its rival.
II) If Townie Soda decided to stop advertising, its profits would fall below $80,000.
III) If both firms stopped advertising, it is possible that each firm could earn profits greater than $80,000.

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