Answer the following Question:

2. Your standard game theory question: American style football can be viewed as a zero sum game. A major objective of the game is for each team's offense to gain yardage against the opposing team's defense. Yardage gained by the offensive team is lost by the defensive team. Consider the following simplified version of a matchup between two specific teams. Team A has developed a payoff matrix that they think describes the yardage they will gain on each play against Team B's defense. On each play, Team A may choose to run or pass. At the same time, Team B may choose to defend against a running play or choose to defend against a passing play. The number of yards gained by Team A on each play is determined by the payoff matrix given below. Team A's objective is to maximize the average yards gained per play, while Team B's objective is to minimize the average yards lost per play. Team B (Defense) Run Pass Run 3 6 Team A (Offense) Pass 12 -8 a. Determine the optimal strategy and the average yards gained/lost per play for Team A's Offense and Team B's defense.| b. Given the payoff matrix above, suppose Team A continues to use the strategy from part a, but Team B unilaterally decides to defend against a running play 50% of the time and to defend against a passing play 50% of the time. How will this affect the average yardage gained per play for Team A? c. If Team A makes an adjustment, and they believe that this adjustment increases the yards that a passing play will gain against a run defense by 50%, should Team A pass more or less frequently? Justify your response