The old Michigan 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 either on the left side or the right side of Michigan's line.If the opponent concentrates on the wrong side, Michigan is sure to gain at least 5 yards.If the defense defended the left side and Michigan ran left, Michigan would be stopped for no gain.But if the opponent defended the right side when Michigan ran right, Michigan would still gain at least 5 yards with probability .60.It is the last play of the game and Michigan needs to gain 5 yards to win.Both sides choose Nash equilibrium strategies.In Nash equilibrium, Michigan would

A) run to the right side with probability .71.
B) run to the right side with probability .83.
C) be sure to run to the right side.
D) run to the two sides with equal probability.
E) run to the right side with probability .60.

In a Nash equilibrium, each player's strategy is optimal given the other player's strategy. Here, Michigan's optimal strategy involves mixing between running left and right in such a way that the opponent is indifferent between defending left or right. Given the information, if Michigan runs right, they have a 0.60 chance of gaining at least 5 yards even if the opponent defends right. To make the opponent indifferent, the probability of running right (p) must be such that the expected gain from defending either side is equal. If Michigan runs left and the opponent defends left, Michigan gains nothing. If Michigan runs right and the opponent defends right, Michigan still has a 0.60 chance of gaining 5 yards. The opponent will mix their defense strategy to make Michigan indifferent between running left or right, leading to a situation where Michigan's probability of choosing right maximizes their minimum guaranteed gain, which is achieved by running to the right side with a probability of 0.71, making the opponent indifferent and establishing a Nash equilibrium.