Question

Q2. The Prisoners' Dilemma: Bob Confess Remain Silent Bob: 20 years Bob: 8 years Jill: 8 years Jill Confess Jill: Free Bob: 1 year Jill: 1 year Bob: Free Jill: 20 years Remain Silent 2A: Find Nash equilibrium? 2B. Is the Nash equilibrium best outcome for them? 2C. If your answer of Q2 is 'No', then why they choose an outcome which is not best for them.

Answer 1

2A. Let's draw a payoff matrix where the payoffs are years in prison.

Jill/Bob	Confess	Remain Silent
Confess	8,8	20,0
Remain Silent	0,20	1,1

Both players want to minimize their "payoffs".

If Bob confesses, Jill's best response is to confess too and both face a prison time of 8 years. Similarly, if Bob remains silent, Jill's best response is to confess and face no prison time. Similarly, from Bob's point of view, if Jill confesses, Bob's best response is to confess and f Jill remains silent, Bob's best response is to confess and be free.

Therefore, the Nash Equilibrium of this game is that both players will confess and face a prison time of 8 years.

2B. No, the best outcome for Bob would be when Jill remains silent and Bob confesses and faces no prison time. The best outcome for Jill would be when Bob remains silent and Jill confesses and faces no prison time.

2C. The "best" outcome is almost never an outcome of a game because of non cooperation. In order to get the best outcome, if Bob confesses, Jill would confess too to minimize her sentence and similarly, if Jill confesses to get her best outcome, Bob will confess too to minimize his sentence.