4. Suppose a football offense has two choices: run or pass. Likewise, the defense has two choices: run defense of pass defense. In parts (a) and (b), assume that the two teams must make their decisions simultaneously. If the offense runs the ball, and the defense plays a run defense, the offense loses 2 yards. If the offense passes the ball, and the defense plays a pass defense, the pass is broken up, and the offense gains 0 yards. If the offense passes the ball, and the defense plays a run defense, the offense gains 5 yards. Finally, if the offense passes the ball, and the defense plays a run defense, the offense gains 8 yards. These payoffs are summarized as

Defense RunDefense Pass

Offense Run-2,+2+5,-5

Offense Pass+8,-80,0

where the first number in each cell denotes the offense's payoff, and the second number represents the defense's payoff.

a) Dose any pure strategy Nash equilibria exist? If so, what are they?

b) Now suppose that the defense is very fast, and is able to react to whatever play the offense calls. This changes the game to a sequential structure, with the offense moving first and the defense moving second. What is the most plausible Nash equilibrium in this sequential game? (That is, what play does each team call?)