(Two Point Conversion in Football Game) It is the closing seconds of a football game, and the losing team has just scored a touchdown. Now down by only one point, the team decides to go for a two-point conversion that, if successful, will win the game. The offense chooses among three possible running plays: run wide left, run wide right, and run up the middle. The defense decides between defending against a wide run and a run up the middle. The payoff to the defense is the probability that the offense does not score, and the payoff to the offense is the probability that it does score. The payoff matrix is given by the following table. Offense Run Up Middle Run Wide Left Run Wide Right Defend against Wide Run 0.6, 0.4 0.4, 0.6 0.5, 0.5 nse 0.6, 0.4 Defend against Middle Run 0.3, 0.7 0.3, 0.7 5.

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5.
(Two Point Conversion in Football Game)
It is the closing seconds of a football game, and the losing team has just scored a
touchdown. Now down by only one point, the team decides to go for a two-point
conversion that, if successful, will win the game. The offense chooses among three
possible running plays: run wide left, run wide right, and run up the middle. The
defense decides between defending against a wide run and a run up the middle. The
payoff to the defense is the probability that the offense does not score, and the payoff to
the offense is the probability that it does score. The payoff matrix is given by the
following table.
Offense
Run Up Middle
Run Wide Left
Run Wide Right
Defend against Wide Run
Defense
0.6, 0.4
0.4, 0.6
0.6, 0.4
Defend against Middle Run
0.3, 0.7
0.5, 0.5
0.3, 0.7
Find all Nash equilibria (in pure and mixed strategies).
Transcribed Image Text:5. (Two Point Conversion in Football Game) It is the closing seconds of a football game, and the losing team has just scored a touchdown. Now down by only one point, the team decides to go for a two-point conversion that, if successful, will win the game. The offense chooses among three possible running plays: run wide left, run wide right, and run up the middle. The defense decides between defending against a wide run and a run up the middle. The payoff to the defense is the probability that the offense does not score, and the payoff to the offense is the probability that it does score. The payoff matrix is given by the following table. Offense Run Up Middle Run Wide Left Run Wide Right Defend against Wide Run Defense 0.6, 0.4 0.4, 0.6 0.6, 0.4 Defend against Middle Run 0.3, 0.7 0.5, 0.5 0.3, 0.7 Find all Nash equilibria (in pure and mixed strategies).
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