Consider a tennis match with 3 sets (just like in the lectures). The first player to win 2 sets wins the match. Let the probability of winning a set...

Serve to backhand

40

90

For instance, if Serena serves to the forehand and Venus anticipates a backhand, Serena is likely to win 80 percent of the time. Serena wants to maximize the probability that she wins, while Venus wants to minimize it.

a.    What is Venus's best response if Serena is serving to the forehand?

b.    What is Serena's best response if Venus is anticipating a forehand?

c.     Is there a dominant strategy for Serena? If yes, what is it? If no, explain why not.

d.    Is there a pure strategy Nash equilibrium in this game? If yes, what is it? If no, explain why not.

e.    Find the mixed strategy Nash equilibrium of this game.