5 Crime and Punishment

Ben and Jerry are two partners-in-crime, who have robbed a bank. Ben got caught and is questioned by the police. He has got three options: to stay silent, confess, or tell the police that it was Jerry. Jerry can either remain at home, go to the police and blame Ben, or kill Ben's dog and cat. Ben feels good about confessing if Jerry does not do anything against him and feels good going to the police otherwise. Jerry on the other hand would hate to kill Ben's dog and cat, but would indulge in the revenge if Ben went to the police. For Jerry it is bad if Ben goes to the police. Ben is on the left and Jerry is on top, and their payos are on the left / right.

Jerry

Home Police Kill

Ben

Silent -2 / 4 -4 / 3 -5 / -5

Confess -1 / 5 -5 / 6 -7 / -5

Police -3 / -3 -2 / -2 -4 / -1

Find the Nash equilibrium in pure strategies when

1. Ben and Jerry move at the same time, not knowing what the other does.

2. Ben moves rst, then Jerry can observe this and subsequently makes his choice.

3. Jerry moves rst, then Ben can observe this and subsequently makes his choice.