-Consider the game in Figure 6.1. The optimal mixing rule for the offense is:
A) Randomly pass the ball 50 percent of the time.
B) Randomly run the ball 50 percent of the time.
C) Randomly defend against the pass 50 percent of the time.
D) Randomly defend against the run 50 percent of the time.
E) Answers a and b are correct.

Question

-Consider the game in Figure 6.1. The optimal mixing rule for the offense is:
A) Randomly pass the ball 50 percent of the time. 
B) Randomly run the ball 50 percent of the time. 
C) Randomly defend against the pass 50 percent of the time. 
D) Randomly defend against the run 50 percent of the time. 
E) Answers a and b are correct.

Quizplus · Accepted Answer

In a mixed strategy Nash equilibrium, each player randomizes over their strategies in such a way that the opponent is indifferent between their options. For the offense in a game like the one described, mixing between passing and running the ball 50 percent of the time each makes the defense indifferent between focusing on defending against the pass or the run, thus making answers A and B correct, which is summarized in option E.

-Consider the Game in Figure 6