Two persons, A and B, play the Prisoner’s Dilemma above three times (say, at t = 1, 2, 3). The difference with Problem 5.3 is that CKR is relaxed. To be precise, B begins the game with some doubt in...

Two persons, A and B, play the Prisoner’s Dilemma above three times (say, at t = 1, 2, 3). The difference with Problem 5.3 is that CKR is relaxed. To be precise, B begins the game with some doubt in his mind about A’s instrumental rationality; that is, she thinks that there is a probability p (>0) that A co-operates blindly as long as B does so too. In contrast, A is perfectly certain that B is fully instrumentally rational (a case of one-sided asymmetrical information). Draw the extensive form of this finitely repeated Prisoner’s Dilemma and, by means of Nash backward induction, compute the game’s sequential equilibrium (see Sections 3.3.3 and 3.5.3 of Chapter 3)