10 Consider the following simplified version of football.On each play the offense chooses to run or pass. At the same time, the defense chooses to play a run defense or pass defense. The number of yards gained on each play is determined by the reward matrix in Table 18. The offense’s goal is to maximize the average yards gained per play.

a Use Problem 9 to show that the offense should run 10/17 of the time.

b Suppose that the effectiveness of a pass against the run defense improves. Use the results of Problem 9 to show that the offense should pass less! Can you give an explanation for this strange phenomenon?

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TABLE 18 Defense Offense Run Pass Run 1 Pass 10 08 8