-Consider the reduced form of the Sink-the-Battleship Game depicted in Figure 6.4 where 1 designates a "hit" and 0 designates a "miss." Suppose that Ilia adopts its optimal mixing rule. Its success rate will be:
A) 25 percent.
B) 50 percent.
C) 75 percent.
D) 100 percent.
E) None of the above.

Question

-Consider the reduced form of the Sink-the-Battleship Game depicted in Figure 6.4 where 1 designates a "hit" and 0 designates a "miss." Suppose that Ilia adopts its optimal mixing rule. Its success rate will be:
A) 25 percent. 
B) 50 percent. 
C) 75 percent. 
D) 100 percent. 
E) None of the above.

Quizplus · Accepted Answer

In a mixed strategy Nash equilibrium of a zero-sum game like Sink-the-Battleship, each player randomizes over their strategies in such a way that the opponent is indifferent between their own strategies. This typically results in each player having a 50 percent success rate when both are playing optimally, as neither can improve their outcome through unilateral deviation.

-Consider the Reduced Form of the Sink-The-Battleship Game Depicted in Figure