1. In football, the offense can either run the ball or pass the ball, whereas the defense can either anticipate (and prepare for) a run or anticipate (and prepare for) a pass. Assume that the expected payoffs (in yards) for the two teams an any given down are as follows: DEFENSE OFFENSE Run Pass Defend the Run 2,-2 11,-11 Defend the Pass 8,-8 -5,5 a. Show that this game has no pure-strategy Nash equilibrium. b. Find the unique mixed-strategy Nash equilibrium to this game. c. Explain why the mixture used by the offense is different from the mixture used by the defense. d. How many yards is the offense expected to gain per down in equilibrium?