Use the following case from question
Two siblings,Sarah and Tom are playing a simultaneous hit and tell game.Sarah can hit Tom or not and Tom can tattle on Sarah or not.Relative to no hitting and no tattling,if Sarah hits Tom,and he tattles they both experience a loss of 10.Not telling,gets Tom a bruise,a loss of 5 but Sarah gains 5.If he tattles untruthfully,he gets a gain of 5 and Sarah loses 5.If they get along,no one gets anything
-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

Question

​Use the following case from question
Two siblings,Sarah and Tom are playing a simultaneous hit and tell game.Sarah can hit Tom or not and Tom can tattle on Sarah or not.Relative to no hitting and no tattling,if Sarah hits Tom,and he tattles they both experience a loss of 10.Not telling,gets Tom a bruise,a loss of 5 but Sarah gains 5.If he tattles untruthfully,he gets a gain of 5 and Sarah loses 5.If they get along,no one gets anything
-​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

Quizplus · Accepted Answer

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.

​Use the Following Case from Question

Use the Following Case from Question