Reference no: EM132587189

In a tennis game the server chooses to aim the ball to the left or to the right of the receiver. If the ball lands to the right of the receiver, she will respond to it with a forehand stroke (assuming she is right handed), and if it lands to her left, she will respond with a backhand stroke. The receiving player must decide whether to prepare for a forehand stroke or a for a backhand stroke at the very moment the server makes her serve, since the ball travels very fast. Suppose that when the server aims right she wins the point 10% of the times if the receiver responds with a forehand, and 70% of the times if the receiver responds with a backhand. Alternatively, when the server aims left she wins the point 80% of the times if the receiver responds with a forehand, and 40% of the times if the receiver responds with a backhand. This situation is a simultaneous constant-sum game (hint: set the constant equal to 100).

(a) Represent the game in strategic form (matrix).

(b) Determine the security strategies and maxmin payoffs for each player.

(c) Find the mixed strategy Nash equilibrium of this game.