Problem: Sibling Rivalry
Two siblings, Bratty Brenda and Tattling Tina are playing a simultaneous hit and tell game. Bratty Brenda can hit Tattling Tina or not and Tattling Tina can tattle on Bratty Brenda or not. Relative to no hitting and no tattling, if Bratty Brenda hits Tattling Tina, and she tattles they both experience a loss of 10. Not telling gets Tattling Tina a bruise, a loss of 5, but Bratty Brenda gains 5. If she tattles untruthfully, Tattling Tina gets a gain of 5 and Bratty Brenda loses 5. If they get along, no one gets anything.
• What is the Nash equilibrium of this simultaneous game?
• If Tattling Tina does not want to be hit, what strategy should she follow?