Bonnie and Clyde are players in a classical prisoner's dilemma. Captured by police, they are separated and

Question:

Bonnie and Clyde are players in a classical prisoner's dilemma. Captured by police, they are separated and each is offered the following deal: If nobody talks, there is enough evidence to convict them on a lesser charge, and each will get 3 years in jail. If one sells out the other on the primary charge, the one that talked will serve 1 year and the one that didn't will serve 20 years. If they both sell out the other, they will each serve 10 years. Payoffs for this scenario are presented on the right:

a. What is the Nash equilibrium in this prisoner's dilemma game? Is the outcome a great one for either player?
b. Suppose that, in the squad car on the way to the station, Bonnie tells Clyde, "If you rat me out, I'll have my peeps break your kneecaps." Assuming that Clyde is indifferent between spending 7 years in prison and having his kneecaps broken, redraw the payoffs in the game to reflect Bonnie's strategic move.
c. How does Bonnie's strategic threat alter the outcome of the game? Explain.
d. Suppose Clyde knows that Bonnie is a sadist, who would willingly pay a year in jail for the pleasure of breaking his kneecaps no matter what Clyde does. Will Bonnie's threat alter the outcome of the game? Explain.