Question

3. Novak Djokovic and Rafael Nadal are two professional tennis players playing a match. Suppose Djokovic has just volleyed. (A volley is when a player hits the ball before it bounces on their side of the court. This usually occurs close to the net.) In response, Nadal has two options. He can try a down the line shot (hitting the ball straight down the sideline) or a cross-court shot (hitting the ball diagonally into Djokovic’s court). Djokovic knows that these are Nadal’s two options and thus must choose to cover either the cross court short or the down the line shot. If Djokovic covers the cross court shot, Nadal has an 80% chance of success with the down the line shot and a 20% chance of success with a cross-court shot. If Djokovic covers the down the line shot, Nadal has a 50% chance of success with the down the line shot and a 90% chance of success with a cross-court shot.

The payoff matrix for this game is below.

	Down the line (DL)	Cross Court (CC)
Down the line (DL)	.5, .5	.8, .2
Cross Court (CC)	.9, .1	.2, .8

a. Find the best response function for Nadal.

b. Find the best response function for Djokovic.

c. Find all Nash Equilibria.

Answer 1

Best response function for Nadal,

If Djokovic covers the down the line shot, is cross court shot as chances of success is higher (90%) than down the line shot(50%)

If Djokovic covers the cross court shot, is down the line shot as chances of success is higher (80%) than cross court shot(20%)

Best response function for Djokovic

If Nadal plays down the line shot, is down the line shot as chances of success is higher (50%) than cross court shot(20%)

If Nadal plays cross court shot, is cross court shot as chances of success is higher (80%) than down the line shot(10%)

Nash Equilibria doesnt exist in this case.