Question

Tessio In the Godfather, Michael Corleone (the head of one Mafia family would like to meet with Don Tessio (the head of a second Mafia family). Don Tessio is concerned that if he agrees to meet the Corleones will kill him. We can think of their problem as a game. First, Don Tessio decides whether or not to agree to meet. If he does not accept the invitation, suppose the Tessios and the Corleones each get a payoff of zero. If he does accept the invitation, then the Corleones will decide whether or not to kill him. If they decide to kill him, then the Corleones get a payoff of 60 and the Tessio family gets a payoff of -40; if they do not kill him, then each gets a payoff of 20. This game is illustrated by the decision tree on the right Use backward induction to figure out how this game will be played. The Nash equilibrium is for Tessio and for the Corleones if Tesslo meets. Meet Don't Meet Corleone T: 0 C: 0 Kill Don't Kill The Bocchicchio family had a well-deserved reputation for ruthlessness. They had a simple code of vengeance: if you were responsible for the death of a member of their family, they would kill a member of yours, regardless of the cost to them. Suppose that when Michael invites Don Tessio to meet, he also hires a member of the Bocchicchio family to go to Tessio's house. There, the "hostage will be guarded by Tessio's men. If Don Tessio does not return safely, Tessio's men will kill the hostage. The Bocchicchio family, seeking revenge will blame Michael Corleone for the death, since he made the promise that Don Tessio will not be harmed, and will eventually kill Michael. If Michael and Don Tessio are both killed, each family gets a payoff of - 40. Use backward induction to determine how this game will be played. The Nash equilibrium is for Tessio and for the Corleones if Tessio meets. T: -40 C: 60 T: 20 C: 20 Tessio Meet Don't Meet Corleone T: 0 C: 0 Kill Don't Kill T: -40 C: -40 T: 20 C: 20

Answer 1

1. In game 1, using backward induction Corleone will kill. Knowing this Tessio will choose ‘Don’t play’.

Thus the Nash equilibrium is for Tessio Don’t meet and corleones kill if tessio met.

2. In second game, using backward induction

The Nash equilibrium is for Tessio to meet and for the corleones to Dont kill if tessio meet