More on three yard football. The following table gives the strategies and payoffs for the first play.

Visitors 6 on the line 7 on the line 8 on the line 9 on the line

fade -2 -1 1 -1

slant 1 0 2 1

run up the middle 2 -1 2 2

run wide 1 -2 -1 -1

Write out the best response for the home team and the visitors.

Home team   Visitors

6 on line ______ fade _______

7 on line ______ slant _______

8 on line ______ run middle _______

9 on line ______ run wide _______

What are the Nash equilibrium strategies?

Home _______________ Visitors _______________

Will the home team win the game on the first play?

Yes No

Marquise Brown, the power forward for Enormous State has two post moves: the jump hook with the left hand and the newly learned drop step. His defender must anticipate one move or the other. The probability that Marquise makes the shot is given in the table.

Defender

Anticipate Jump hook Anticipate Drop step

Jump hook 0.3 0.9

Marquise

Drop step 0.6 0.2

Is there a Nash equilibrium in pure strategies? Explain briefly.

Determine the optimal mixing probability for Marquise.

What is the probability that he makes the shot.