Suppose players 1 and 2 will play the following prisoners' dilemma.

Prior to interacting in the prisoners' dilemma, simultaneously each player announces a binding penalty pi that this player commits to pay the other player j in the event that player defects and player j cooperates. Assume that these commitments are binding. Thus, after the announcements, the players effectively play the following induced game

(a) What values of p1 and p2 are needed to make (C, C) a Nash equilibrium of the induced game?

(b) What values of p1 and p2 will induce play of (C, C) and would arise in a subgame perfect equilibrium of the entire game (penalty announcements followed by the prisoners' dilemma)? Explain.

(c) Compare the unilateral commitments described here with contracts.