turangawaewae wrote:Except for this one, there is a definitive answer.
Most people will respond as you have, but you still need to think in terms of the other persons response.
If prisoner 2 confesses, you have two options. Confess, and get 8 years, don't confess, and get 10 years jail time (because prisoner 2 will turn star witness). So if prisoner 2 confesses, your optimal outcome is to confess.
If prisoner 2 doesn't confess, you have two options. Don't confess, and you get 1 year, confess and you get no jail time as you turn star witness. If prisoner 2 doesn't confess, your optimal strategy is to confess.
So no matter what prisoner 2 does, your optimal strategy is to confess!!
You're right, prisoner 2 faces the same chioces. So if both players play their optimal outcome, both confess, and they both do 8 years. Police actually use this technique in real life. Of course, you would both have been better off if you had both not confessed. You could both collude, and make a pact to not confess. But if the other prisoner is not confessing, you have an incentive to confess and do no time, rather than serving a year in prison. Thats why pacts or cartel are inherently unstable.
Of course, this is set up where jail time is the only cost. That is when I bring in the sopranos during lecture. I explain what I have just explained above, then say how would the outcomes differ if you were prisoner one and Tony Soprano was prisoner 2. Unless you want to end up under a concrete slab somewhere, you don't confess. That is because Tony is what we call a credible threat. If you make a deal to collude and both not confess, you know that you are dead if you do confess, which make not confessing and doing one year more attractive than confessing and doing no time. Of course, once Tony knows you are not confessing, he could confess, do no time, and you do 10 years!! So even with the credible threat of Tony, it may still be optimal to confess.
All of this assumes that Prisoner 2 makes a decision or confesses first. That information was not supplied. Or was it?