Three tennis players want to enter a tennis tournament. There is room left in the tournament for one doubles team and one singles player. Each player may apply for only one slot-a singles slot or a doubles slot. Each player knows there are two other applicants, but doesn't know who they are so there is no chance for communication.

If one player applies for the singles slot, she gets it. If two players apply for the singles slot they cut cards and each has a 50% chance of getting it. if all three apply for the singles slot, each has a 33 1/3 % chance of getting it.

If one player applies for the doubles team, she doesn't play in the tournament. If two players apply for the doubles team, they are in. If three apply for the doubles team, they cut cards and each of the three has a 66 2/3 % chance of getting into the tournament.

a. Put the game in normal form. Make sure that the top left cell of matrix one where Player 3 plays Singles, is labled S for player 1 and S for player 2. This is so we are all all looking at the same picture.

b. Find the pure strategy Nash equilibria using the underlining method.

c. Show (S,S,S) is Nash using the definition method. Show (S, S, D) is not Nash using the definition method.

d. What would you do if you were one of the players?