Consider the Matching Pennies game:

Suppose Player A always uses a pure strategy that selects heads, and Player B always uses a pure strategy that selects tails. Is this outcome a Nash equilibrium?
A) Yes, both players have no incentive to change their actions.
B) No, Player A would want to switch to tails.
C) No, Player B would want to switch to heads.
D) No, Player B would want to switch to tails.

Question

Consider the Matching Pennies game:

Suppose Player A always uses a pure strategy that selects heads, and Player B always uses a pure strategy that selects tails. Is this outcome a Nash equilibrium?
A) Yes, both players have no incentive to change their actions. 
B) No, Player A would want to switch to tails. 
C) No, Player B would want to switch to heads. 
D) No, Player B would want to switch to tails.

Quizplus · Accepted Answer

If Player A switches to tails, he would always lose, and if Player B switches to heads, he would always win. Therefore, Player A has an incentive to switch to tails, making this not a Nash equilibrium.

Consider the Matching Pennies Game