A famous American 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 0.50. 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.
Is there a Nash equilibrium in pure strategies in this game? Explain why or why not.
What is the probability that the offense will run to the left?
What is the probability that the offense will run to the right?
What is the probability that the defense defends the left hand side?
What is the probability that the defense defends the right hand side?
Explain in words what the expected outcome will be.