Two football teams play against each other. The offense can choose to pass or run, and the defense can choose to defend against either the pass or run. Depending on the combination of choices, the payoff matrix below shows the average number of yards gained or lost on each play. Since the number of yards gained by the offense equals the number of yards given up (or lost) by the defense, the payoffs to the offense and defense are the same value but opposite in sign. Each cell shows the average gain by the offense (the value on the left) and the average loss by the defense (the value on the right). Defense Pass defense Run defense Pass 3, -3 10, -10 "\"' Run a. e In What is the Nash equilibrium for this game? lThere is no Nash equilibrium in pure strategies There is no Nash equilibrium using pure strategies because each side wants to anticoordinate with the other. There is, however, a Nash equilibrium using mixed strategies, where each side allows chance to partially dictate their strategy (nding this strategy is outside the scope of this course, but the intuition of being unpredictable is easy to see). Suppose the offensive coach chooses Pass 50% of the time and Run 50% of the time, i.e.. ips a coin to decide. The defensive coach chooses Pass defense 65% of the time and Run defense 35% of the time. What is the probability that the play is a Pass against a Run defense resulting in a big gain for the offense? |:| percent. If the offensive coach flips the coin and it decides on a Pass play, what is their expected value of Passing given the opponents mixed strategy? :I. What is their expected value of a Run play? . {Enter your responses rounded to two decimal places.)