​What would be the Nash equilibrium of this simultaneous game?

A) ​Hit,Tell
B) Not hit,Tell
C) Hit,Not tell
D) ​Both B&C

In order for a Nash equilibrium to exist, each player's strategy must be optimal given the other player's strategy.

If Sarah hits Tom, Tom's optimal strategy would be to tattle because tattling minimizes his loss from the hit. Therefore, Sarah's optimal strategy would be not to hit because hitting results in a loss for both players. This gives us the strategy pair (Not hit, Tell), which is a Nash equilibrium.

If Sarah does not hit Tom, Tom's optimal strategy would be to tattle in order to gain 5, which means Sarah's optimal strategy would be to not tell and avoid the loss. This gives us the strategy pair (Not hit, Not tell) which is also a Nash equilibrium.

Since the game has two Nash equilibria, the answer is D, both B and C.