Exam 6: Mixing Pure Strategies

-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, PETROX's expected payoff is:

Frans asked his mother, Greta, to bake him an apple pie. After baking the pie, Greta tells Frans to slice the pie any way he likes, but that he must give his brother, Hans, the first choice of slices. The only other condition is that the slices must be divided into quarters. The most likely guiding principle for determining the Nash equilibrium strategy profile for this game is the:

-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." The pure-strategy Nash equilibrium for this game is: I. {ABEC, IGDB}. II. {ACEB, IHFC}. III. {ABEC, IHFC}. IV. {ACEB, IHFC}. Which of the following is correct?

-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 mixed strategy?

-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, the mixed-strategy Nash equilibrium strategy profile for this game 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 receiver's optimal mixing rule is:

-Consider the game in Figure 6.1. What is the success rate of the defense if the offense adopts its optimal mixing rule?

-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. Suppose that both players adopt his or her optimal mixing rule. The receiver's success rate will be:

-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." Suppose that Acre adopts its optimal mixing rule. Its success rate will be:

The Nash equilibrium existence theorem guarantees that:

-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. The optimal mixing rule for the defense is:

-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. The mixed-strategy Nash equilibrium for this game is:

-Consider the game in Figure 6.1. The dominant strategy for the offense is to:

A pure strategy is:

Frans asked his mother, Greta, to bake him an apple pie. After baking the pie, Greta tells Frans to slice the pie any way he likes, but that he must give his brother, Hans, the first choice of slices. The only other condition is that the slices must be divided into quarters. The most likely Nash equilibrium strategy profile for this game is:

-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 defense is:

-Suppose that two individuals play a game of tennis. The situation depicted in Figure 6.5summarizes the probabilities that the receiver will successfully return a serve that isdirected to his backhand or forehand. The mixed-strategy Nash equilibrium for this game is:

-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 mixed-strategy Nash equilibrium for this game is:

-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 adopts its optimal mixing rule. What is the success rate of the offense?

-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." Suppose that Ilia adopts its optimal mixing rule. Its success rate will be: