Question 1

The Sink-the-Battleship Game:

Accepted Answer

A)  Does not have a Nash equilibria in pure strategies. The best way to choose a strategy is to flip a coin after all dominated strategies were eliminated. 
B)  Has a unique Nash equilibrium in pure strategies. Both combatants have a dominant strategy. 
C)  Has multiple Nash equilibria in mixed strategies. Both combatants have dominated strategies. 
D)  Has two Nash equilibria in pure strategies, even though neither side had a dominant strategy. 
E)  None of the above are correct. 
A)  Does not have a Nash equilibria in pure strategies. The best way to choose a strategy is to flip a coin after all dominated strategies were eliminated. 
B)  Has a unique Nash equilibrium in pure strategies. Both combatants have a dominant strategy. 
C)  Has multiple Nash equilibria in mixed strategies. Both combatants have dominated strategies. 
D)  Has two Nash equilibria in pure strategies, even though neither side had a dominant strategy. 
E)  None of the above are correct. A

Question 2

In a two-player, zero-sum, noncooperative, simultaneous-move, one-time games:

Accepted Answer

A)  Both players attempt to maximize the other player's minimum payoff, while minimizing their own maximum payoff. 
B)  Both players attempt to maximize the other player's maximum payoff, while minimizing their own minimum payoff. 
C)  Both players attempt to minimize the other player's minimum payoff, while maximizing their own maximum payoff. 
D)  Both players attempt to minimize the other player's maximum payoff, while maximizing their own minimum payoff. 
E)  None of the above are correct. 
A)  Both players attempt to maximize the other player's minimum payoff, while minimizing their own maximum payoff. 
B)  Both players attempt to maximize the other player's maximum payoff, while minimizing their own minimum payoff. 
C)  Both players attempt to minimize the other player's minimum payoff, while maximizing their own maximum payoff. 
D)  Both players attempt to minimize the other player's maximum payoff, while maximizing their own minimum payoff. 
E)  None of the above are correct. D

Question 3

-Professor Nash teaches game theory at Gigantic State University (GSU). Just prior to the final exam, Professor Nash announces that students who score in the top half of the class will receive an A, while students who score in the bottom half will receive an F.There are just two types of students at GSU: Egg heads and knot heads. The students must decide whether to study for the final exam or not study and party. The payoffs for this game are summarized in Figure 6.7. If larger payoffs are preferred, which group has a dominant pure strategy?

Accepted Answer

A)  Egg heads. 
B)  Knot heads. 
C)  Both groups. 
D)  Neither group. 
E)  This question cannot be answered without additional information 
A)  Egg heads. 
B)  Knot heads. 
C)  Both groups. 
D)  Neither group. 
E)  This question cannot be answered without additional information D

Question 4

-Suppose that a football team is down by 5 points and faces a 4th down with 1 yard to go with 1 second left on the clock. The offense can either run or pass the ball. The defense can either defend against the run or the pass. Refer to Figure 6.2 summarizes the probabilities of each team winning the game. The pure-strategy Nash equilibrium for this game is:
I. {Pass, Pass}.
II. {Run, Run}.
III. {Run, Pass}.
IV. {Pass, Run}.
Which of the following is correct?

Accepted Answer

A)  I only. 
B)  II only. 
C)  I and II only. 
D)  II and III only. 
E)  None of the above. 
A)  I only. 
B)  II only. 
C)  I and II only. 
D)  II and III only. 
E)  None of the above.

Question 5

-Consider the oil-drilling game in Figure 6.6. Payoffs are in millions of dollars. If both oil-drilling companies adopt its optimal mixing rule, GLOMAR's expected payoff is:

Accepted Answer

A)  $42 million. 
B)  $58 million. 
C)  $64 million. 
D)  $76 million. 
E)  None of the above. 
A)  $42 million. 
B)  $58 million. 
C)  $64 million. 
D)  $76 million. 
E)  None of the above.

Question 6

In a zero-sum game with pure strategies:

Accepted Answer

A)  The payoffs may be different, but must add up to zero. 
B)  The gain by one player is exactly equal to the loss of the other player. 
C)  A Nash equilibrium can always be found using the maximin decision rule. 
D)  A Nash equilibrium can always be found using a minimax regret decision rule. 
E)  Must have a focal-point equilibrium. 
A)  The payoffs may be different, but must add up to zero. 
B)  The gain by one player is exactly equal to the loss of the other player. 
C)  A Nash equilibrium can always be found using the maximin decision rule. 
D)  A Nash equilibrium can always be found using a minimax regret decision rule. 
E)  Must have a focal-point equilibrium.

Question 7

-Suppose that a football team is down by 5 points and faces a 4th down with 1 yard to go and 1 second left on the clock. The offense can either run or pass the ball. The defense can either defend against the run or the pass. Refer to Figure 6.3 summarizes the probabilities of each team winning the game. The dominant pure strategy for the offense is:

Accepted Answer

A)  Run the ball. 
B)  Pass the ball. 
C)  Pick a play at random with a higher probability of passing the ball. 
D)  Pick a play at random with a higher probability of running the ball. 
E)  None of the above. 
A)  Run the ball. 
B)  Pass the ball. 
C)  Pick a play at random with a higher probability of passing the ball. 
D)  Pick a play at random with a higher probability of running the ball. 
E)  None of the above.

Question 8

-Consider the oil-drilling game in Figure 6.6. The mixed-strategy Nash equilibrium for this game is:

Accepted Answer

A)  Both companies randomly drill emphasizing narrow wells. 
B)  Both companies randomly drill emphasizing wide wells. 
C)  Both companies to randomly drill with PETROX emphasizing wide wells and GLOMAR emphasizing narrow wells. 
D)  Both companies to randomly drill with PETROX emphasizing narrow wells and GLOMAR emphasizing wide wells. 
E)  None of the above. 
A)  Both companies randomly drill emphasizing narrow wells. 
B)  Both companies randomly drill emphasizing wide wells. 
C)  Both companies to randomly drill with PETROX emphasizing wide wells and GLOMAR emphasizing narrow wells. 
D)  Both companies to randomly drill with PETROX emphasizing narrow wells and GLOMAR emphasizing wide wells. 
E)  None of the above.

Question 9

-Suppose that a football team is 3 points behind and faces a fourth down and goal to go with seconds remaining on the clock. The offense can either pass or run the ball. The defense can either defend against the pass or defend against the run. Figure 6.1 summarizes the probabilities of winning or losing the game from any combination of strategy profiles. The dominant pure strategy for the defense is to:

Accepted Answer

A)  Defend against the run. 
B)  Defend against the pass. 
C)  Flip a coin and choose a play at random. 
D)  There is not enough information to answer this question. 
E)  None of the above. 
A)  Defend against the run. 
B)  Defend against the pass. 
C)  Flip a coin and choose a play at random. 
D)  There is not enough information to answer this question. 
E)  None of the above.

Question 10

-Suppose that a football team is down by 5 points and faces a 4th down with 1 yard to go and 1 second left on the clock. The offense can either run or pass the ball. The defense can either defend against the run or the pass. Refer to Figure 6.2 summarizes the probabilities of each team winning the game. Suppose that the defense adopts its optimal mixing rule. What is its success rate?

Accepted Answer

A)  Around 29 percent. 
B)  Around 46 percent. 
C)  Around 54 percent. 
D)  Around 67 percent. 
E)  None of the above. 
A)  Around 29 percent. 
B)  Around 46 percent. 
C)  Around 54 percent. 
D)  Around 67 percent. 
E)  None of the above.

Question 11

-Consider the oil-drilling game in Figure 6.6. Payoffs are in millions of dollars. GLOMAR's optimal mixing rule is:

Accepted Answer

A)  Randomly drill a narrow well 4 out of 5 times. 
B)  Randomly drill a wide well 1 out of 5 times. 
C)  Randomly drill a narrow well 3 out of 4 times. 
D)  Randomly drill a narrow well 6 out of 15 times. 
E)  Answers a and b are correct. 
A)  Randomly drill a narrow well 4 out of 5 times. 
B)  Randomly drill a wide well 1 out of 5 times. 
C)  Randomly drill a narrow well 3 out of 4 times. 
D)  Randomly drill a narrow well 6 out of 15 times. 
E)  Answers a and b are correct.

Question 12

-Consider the reduced form of the Sink-the-Battleship Game depicted in Figure 6.4 where 1 designates a "hit" and 0 designates a "miss." Acre's optimal mixing rule is to program its computer to:

Accepted Answer

A)  Randomly select IGDB one out of two times. 
B)  Randomly select IHFC one out of two times. 
C)  Randomly select IGDB one out of 3 times. 
D)  Randomly select IHFC one out of 3 times. 
E)  None of the above. 
A)  Randomly select IGDB one out of two times. 
B)  Randomly select IHFC one out of two times. 
C)  Randomly select IGDB one out of 3 times. 
D)  Randomly select IHFC one out of 3 times. 
E)  None of the above.

Question 13

-Professor Nash teaches game theory at Gigantic State University (GSU). Just prior to the final exam, Professor Nash announces that students who score in the top half of the class will receive an A, while students who score in the bottom half will receive an F. There are just two types of students at GSU: Egg heads and knot heads. The students must decide whether to study for the final exam or not study and party. The payoffs for this game are summarized in Figure 6.7. What is the Egg Head's optimal mixing rule?

Accepted Answer

A)  Randomly study 4 out of 9 times. 
B)  Randomly party 5 out of 13 times. 
C)  Randomly study 7 our of 10 times. 
D)  Randomly party 3 out of 8 times. 
E)  Answers c and d are correct. 
A)  Randomly study 4 out of 9 times. 
B)  Randomly party 5 out of 13 times. 
C)  Randomly study 7 our of 10 times. 
D)  Randomly party 3 out of 8 times. 
E)  Answers c and d are correct.

Question 14

-Suppose that a football team is down by 5 points and faces a 4th down with 1 yard to go and 1 second left on the clock. The offense can either run or pass the ball. The defense can either defend against the run or the pass. Refer to Figure 6.3 summarizes the probabilities of each team winning the game. Suppose that both players adopt its optimal mixing rule. What is the success rate of the defense?

Accepted Answer

A)  Around 39 percent. 
B)  Around 48 percent. 
C)  Around 55 percent. 
D)  Around 75 percent. 
E)  None of the above. 
A)  Around 39 percent. 
B)  Around 48 percent. 
C)  Around 55 percent. 
D)  Around 75 percent. 
E)  None of the above.

Question 15

-Consider the game in Figure 6.1. The optimal mixing rule for the defense is:

Accepted Answer

A)  Randomly pass the ball 50 percent of the time. 
B)  Randomly run the ball 50 percent of the time. 
C)  Randomly defend against the pass 50 percent of the time. 
D)  Randomly defend against the run 50 percent of the time. 
E)  Answers c and d are correct. 
A)  Randomly pass the ball 50 percent of the time. 
B)  Randomly run the ball 50 percent of the time. 
C)  Randomly defend against the pass 50 percent of the time. 
D)  Randomly defend against the run 50 percent of the time. 
E)  Answers c and d are correct.

Question 16

-Suppose that two individuals play a game of tennis. The situation depicted in Figure 6.5 summarizes the probabilities that the receiver will successfully return a serve that is directed to his backhand or forehand. The server's optimal mixing rule is:

Accepted Answer

A)  Randomly serve to the forehand 3 out of 14 times. 
B)  Randomly serve to the forehand 3 out of 7 times. 
C)  Randomly serve to the backhand 3 out of 14 times. 
D)  Randomly serve to the backhand 3 out of 7 times. 
E)  None of the above. 
A)  Randomly serve to the forehand 3 out of 14 times. 
B)  Randomly serve to the forehand 3 out of 7 times. 
C)  Randomly serve to the backhand 3 out of 14 times. 
D)  Randomly serve to the backhand 3 out of 7 times. 
E)  None of the above.

Question 17

-Consider the reduced form of the Sink-the-Battleship Game depicted in Figure 6.4 where 1 designates a "hit" and 0 designates a "miss." Ilia's optimal mixing rule is to program its computer to:

Accepted Answer

A)  Randomly select IGDB one out of two times. 
B)  Randomly select IHFC one out of two times. 
C)  Randomly select IGDB one out of 3 times. 
D)  Randomly select IHFC one out of 3 times. 
E)  Answers a and b are correct. 
A)  Randomly select IGDB one out of two times. 
B)  Randomly select IHFC one out of two times. 
C)  Randomly select IGDB one out of 3 times. 
D)  Randomly select IHFC one out of 3 times. 
E)  Answers a and b are correct.

Question 18

-Suppose that a football team is down by 5 points and faces a 4th down with 1 yard to go and 1 second left on the clock. The offense can either run or pass the ball. The defense can either defend against the run or the pass. Refer to Figure 6.3 summarizes the probabilities of each team winning the game. The optimal mixing rule for the offense is:

Accepted Answer

A)  Randomly pass 5 out of 9 times. 
B)  Randomly run 4 out of 9 times. 
C)  Randomly pass 2 out of 7 times. 
D)  Randomly run 5 out of 7 times. 
E)  Both c and d are correct. 
A)  Randomly pass 5 out of 9 times. 
B)  Randomly run 4 out of 9 times. 
C)  Randomly pass 2 out of 7 times. 
D)  Randomly run 5 out of 7 times. 
E)  Both c and d are correct.

Question 19

-Consider the game in Figure 6.1. The optimal mixing rule for the offense is:

Accepted Answer

A)  Randomly pass the ball 50 percent of the time. 
B)  Randomly run the ball 50 percent of the time. 
C)  Randomly defend against the pass 50 percent of the time. 
D)  Randomly defend against the run 50 percent of the time. 
E)  Answers a and b are correct. 
A)  Randomly pass the ball 50 percent of the time. 
B)  Randomly run the ball 50 percent of the time. 
C)  Randomly defend against the pass 50 percent of the time. 
D)  Randomly defend against the run 50 percent of the time. 
E)  Answers a and b are correct.

Question 20

In the Sink-the-Battleship Game:

Accepted Answer

A)  Both combatants had a dominant pure strategy. 
B)  One combatant with a dominant strategy, but the other combatant did not. 
C)  Neither combatant had a dominant strategy, even after dominated strategies were eliminated. 
D)  There were non-zero-sum payoffs. 
E)  None of the above. 
A)  Both combatants had a dominant pure strategy. 
B)  One combatant with a dominant strategy, but the other combatant did not. 
C)  Neither combatant had a dominant strategy, even after dominated strategies were eliminated. 
D)  There were non-zero-sum payoffs. 
E)  None of the above.

The Sink-the-Battleship Game:

In a two-player, zero-sum, noncooperative, simultaneous-move, one-time games:

-Consider the oil-drilling game in Figure 6.6. Payoffs are in millions of dollars. If both oil-drilling companies adopt its optimal mixing rule, GLOMAR's expected payoff is:

In a zero-sum game with pure strategies:

-Consider the oil-drilling game in Figure 6.6. The mixed-strategy Nash equilibrium for this game is:

-Consider the oil-drilling game in Figure 6.6. Payoffs are in millions of dollars. GLOMAR's optimal mixing rule is:

-Consider the reduced form of the Sink-the-Battleship Game depicted in Figure 6.4 where 1 designates a "hit" and 0 designates a "miss." Acre's optimal mixing rule is to program its computer to:

-Consider the game in Figure 6.1. The optimal mixing rule for the defense is:

-Suppose that two individuals play a game of tennis. The situation depicted in Figure 6.5 summarizes the probabilities that the receiver will successfully return a serve that is directed to his backhand or forehand. The server's optimal mixing rule is:

-Consider the reduced form of the Sink-the-Battleship Game depicted in Figure 6.4 where 1 designates a "hit" and 0 designates a "miss." Ilia's optimal mixing rule is to program its computer to:

-Consider the game in Figure 6.1. The optimal mixing rule for the offense is:

In the Sink-the-Battleship Game:

Introduction to Game Theory

Noncooperative, One-Time, Static Games

Focal-Point and Evolutionary Equilibria

Infinitely-Repeated, Static Games

Finitely-Repeated, Static Games

Static Games With Continuous Strategies

Imperfect Competition

Perfect Competition and Monopoly

Strategic Trade Policy

Dynamic Games With Complete

Bargaining

Pure Strategies With Uncertain Payoffs

Torts and Contracts

Auctions

Dynamic Games With Incomplete Information

Filters

Exam 6: Mixing Pure Strategies

The Sink-the-Battleship Game:

In a two-player, zero-sum, noncooperative, simultaneous-move, one-time games:

-Consider the oil-drilling game in Figure 6.6. Payoffs are in millions of dollars. If both oil-drilling companies adopt its optimal mixing rule, GLOMAR's expected payoff is:

In a zero-sum game with pure strategies:

-Consider the oil-drilling game in Figure 6.6. The mixed-strategy Nash equilibrium for this game is:

-Consider the oil-drilling game in Figure 6.6. Payoffs are in millions of dollars. GLOMAR's optimal mixing rule is:

-Consider the reduced form of the Sink-the-Battleship Game depicted in Figure 6.4 where 1 designates a "hit" and 0 designates a "miss." Acre's optimal mixing rule is to program its computer to:

-Consider the game in Figure 6.1. The optimal mixing rule for the defense is:

-Suppose that two individuals play a game of tennis. The situation depicted in Figure 6.5 summarizes the probabilities that the receiver will successfully return a serve that is directed to his backhand or forehand. The server's optimal mixing rule is:

-Consider the reduced form of the Sink-the-Battleship Game depicted in Figure 6.4 where 1 designates a "hit" and 0 designates a "miss." Ilia's optimal mixing rule is to program its computer to:

-Consider the game in Figure 6.1. The optimal mixing rule for the offense is:

In the Sink-the-Battleship Game:

Introduction to Game Theory

Noncooperative, One-Time, Static Games

Focal-Point and Evolutionary Equilibria

Infinitely-Repeated, Static Games

Finitely-Repeated, Static Games

Static Games With Continuous Strategies

Imperfect Competition

Perfect Competition and Monopoly

Strategic Trade Policy

Dynamic Games With Complete

Bargaining

Pure Strategies With Uncertain Payoffs

Torts and Contracts

Auctions

Dynamic Games With Incomplete Information

Filters