Consider the Matching Pennies game:

Suppose Player B always uses a mixed strategy with probability of 3/4 for head and 1/4 for tails. Which of the following strategies for Player A provides the highest expected payoff?
A) Mixed strategy with probability 1/4 on heads and 3/4 on tails
B) Mixed strategy with probability 1/2 on heads and 1/2 on tails
C) Mixed strategy with probability 3/4 on heads and 1/4 on tails
D) Pure strategy in which Player A always selects heads

Question

Consider the Matching Pennies game:

Suppose Player B always uses a mixed strategy with probability of 3/4 for head and 1/4 for tails. Which of the following strategies for Player A provides the highest expected payoff?
A) Mixed strategy with probability 1/4 on heads and 3/4 on tails 
B) Mixed strategy with probability 1/2 on heads and 1/2 on tails 
C) Mixed strategy with probability 3/4 on heads and 1/4 on tails 
D) Pure strategy in which Player A always selects heads

Quizplus · Accepted Answer

If Player A always chooses heads, then their expected payoff will be either 1 or -1.

If Player A chooses a mixed strategy, their expected payoff will be:

E(h, h) = -1
E(h, t) = 1/4*(-1) + 3/4*1 = 5/8
E(t, h) = 3/4*(-1) + 1/4*1 = -1/2
E(t, t) = 1

Therefore, the highest expected payoff for Player A is when they choose the pure strategy of always selecting heads.

Consider the Matching Pennies Game