SERVER
Forehand Backhand
Forehand 9,1 0,10
RECEIVER
Backhand 0,10 6,4
This game is like the Tennis Game in Dixit and Nalebuff, except that if the Receiver is surprised, he never succeeds in returning the serve.
1_1 What is the Nash equilibrium probability of Forehand for the Server?
A. Between 0 and .2, inclusive.
B. Greater than .2 but less than .5.
C. Between .5 and .7, inclusive
D. Greater than .7
B. CORRECT. If the Server chooses that probability of Forehand, the Receiver cannot advantage of his choice.
If the server chooses the equilibrium probability of .4, then
Receiver's Payoff (Forehand) = .4 (9) + .6(0) = 3.6 < Receiver's Payoff (Backhand) =.4(0) + .6 (6) = 3.6.
To derive that value of .4, you need to choose a mixing probability X for the Server such that the Receiver does no better from Forehand than from Backhand. To do that, you solve
Receiver's Payoff (Forehand) =X (9) + (1-X)(0) = Receiver's Payoff (Backhand) =X(0) + (1-X) (6).
Return to Self Test 2.