Exam 6: Mixing Pure Strategies

-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 both groups adopt is optimal mixing rule, the Knot Head's expected payoff 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. Suppose that both players adopt his or her optimal mixing rule. The servers's success rate will be:

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

-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 offense is:

-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 Knot Head's optimal mixing rule?

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

-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 both groups adopt is optimal mixing rule, the Egg Head's expected payoff is:

A two-player, two-strategy, noncooperative, zero-sum, static game has _____ Nash equilibria.

-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 defense is:

-Consider the oil-drilling game in Figure 6.6. Payoffs are in millions of dollars. PETROX's optimal mixing rule 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 dominant pure strategy for the offense is: