The Coach of the Offensive Football Team Has Two Options

Essay

The coach of the offensive football team has two options on the next play.He can run the ball or he can pass.His rival can defend either against the run or against the pass.Suppose that the offense passes.Then if the defense defends against the pass, the offense will make zero yards, and if the defense defends against the run, the offense will make 25 yards.Suppose that the offense runs.If the defense defends against the pass, the offense will make 10 yards, and if the defense defends against a run, the offense will gain 2 yards.
a.Write down a payoff matrix for this game.
b.Is there a Nash equilibrium in pure strategies for this game? If so, what is it? If not, demonstrate that there is none.