Chapter 11.3, Problem 25E

In Exercises 13–27, use the graphical method when the payoff matrix is a 2 × 2 matrix or can be reduced to one after removing rows or columns that are dominated. Otherwise, use the simplex method.

Tennis In the game of tennis, a skilled player strategically chooses to serve the ball to the left or to the right of the opponent. Accordingly, the person receiving the serve needs to decide whether the ball will go left or right. If the serve goes left and the receiver moves right, then the advantage goes to the server. On the other hand, if the ball goes left and the receiver is also moving in that direction, the advantage goes to the receiver. This situation has been modeled for professional players at Wimbledon using game theory. Suppose that for two hypothetical players, the fraction of the lime that a server wins a point is given in the following payoff matrix. Source: The American Economic Review.

(a) Find the optimum strategy for each player and the value of the game.

(b) Discuss the possible wisdom of using these mixed strategies, in light of the fraction of the lime that a particular strategy pays off for a particular player.