In this assignment there are two professional tennis players. Player one, who we will call Chrissy is going to be returning the serve of player two, who we will call Martie.

If Chrissy hits down the line and Martie tries to cover cross-court then Chrissy will win 80 percent of the time and lose 20% of the time. If Chrissy hits down the line and Martie chooses to cover down the line then Chrissy will win only 50 % of the time.

If Chrissy hits cross-court and Martie tries to cover down the line then Chrissy will win 90 percent of the time and lose 10% of the time. But if Chrissy hits cross-court and Martie covers for cross-court then Chrissy will win only 20% of the time and lose 80% of the time.

a.) Create a normal form for this game and solve for PSNE

b.) Solve for p and q in a mixed strategy approach and list the optimal strategy for each player for each scenario.

c.) plug the p and q back into the Expected Payoff formula and report on the expected payoff for Chrissy.

d.) Test my claim in the video by changing the mix for Martie and then calculate the optimal mix for Chrissy to achieve the highest win percentage.

this is done by changing the q in the equation after the calculus solution for the new q you choose to assign to Martie. Lets say you change it from 60 to 40. Then solve the original formula for q.

-100q + 60 = 0 becomes -100q + 60 = 20. This becomes -100q + 40 = 0

Now you have to add the 20 to the equation for p so the equations remain equal

-100p + 70 = 0 becomes -100p + 90 = 0

and p becomes 90%. That is the optimal response from Chrissy.