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 .70.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 .77.
B)run to the right side with probability .87.
C)run to the two sides with equal probability.
D)be sure to run to the right side.
E)run to the right side with probability .70.

Question

Quizplus · Accepted Answer

In a Nash equilibrium, both the offense and defense adjust their strategies based on the other's actions to reach a point where neither can benefit by changing their strategy unilaterally. Given Michigan's higher probability of gaining at least 5 yards when running to the right (.70) even if the defense also focuses on the right, the offense is incentivized to favor the right side. However, to prevent the defense from always defending the right, Michigan must mix its strategy to keep the defense guessing. The exact probability of .77 for choosing the right side is calculated based on the game's specific payoffs and the need to make the defense indifferent between defending left or right, leading to a mixed strategy Nash equilibrium.

The Old Michigan Football Coach Had Only Two Strategies, Run