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

Answer 1

Answer: d) both B and C

Explanation: Nash equilibrium is a concept within game theory where the optimal outcome of a game is where there is no incentive to deviate from their initial strategy.

Because if Sarah hit Tom, they will both experience a loss of 10 points

Also, not telling gets Tom a loss of 5 but Sarah will gain 5.

This will keep both of them in a nash equilibrium.