# In football the offense can either run the ball or pass the ball,

November 24, 2016

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. The defense wants to guess correctly to reduce the yards gained by the offense, whereas the offense wants its opponents to guess incorrectly so that it can gain more yards. Assume that the expected payoffs (in yards) for the two teans on any given down are as follows:

A) Show that this game has no pure strategy Nash equilibrium
B) Find the unique mixed strategy Nash equilibrium to this game
C) Explain what the mixture used by the offenses different from the mixture used by the defense
D) How many yards is the offense expected to gain per down in equilibrium

Defense
Anticipate Run Anticipate Pass
Offense Run 1, -1 5, -5
Pass 9, -9 -3, 3

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