A famous Big Ten football coach had only two strategies, Run the ball to the left side of the line and Run the ball to the right side.The defense can concentrate forces on the left side or the right side.If the opponent concentrates on the wrong side, his offense is sure to gain at least 5 yards.If the defense defended the left side and the offense ran left, the offense gained only 1 yard.If the opponent defended the right side when the offense ran right, the offense would still gain at least 5 yards with probability .30.It is the last play of the game and the famous coach's team is on offense.If it makes 5 yards or more, it wins; if not, it loses.Both sides choose Nash equilibrium strategies.In equilibrium the offense
A)is sure to run to the right side.
B)will run to the right side with probability .59.
C)will run to the right side with probability .74.
D)will run to the two sides with equal probability.
E)will run to the right side with probability .70.

Question

Quizplus · Accepted Answer

In a Nash equilibrium, both the offense and defense will choose strategies that best respond to each other, given the probabilities of success. The offense will run to the right side with a probability that makes the defense indifferent between defending the left or the right side. Given the payoff structure, where running right has a .30 probability of gaining at least 5 yards even if defended, and running left guarantees only 1 yard if defended, the offense's strategy involves mixing plays to keep the defense guessing. The correct probability balances the expected outcomes, making it .59 to the right, as it aligns with the strategic mixing required to achieve a Nash equilibrium.

A Famous Big Ten Football Coach Had Only Two Strategies