The Prisoner's Dilemma

[packbat]

Another classic game-theory hypothetical for you all:

Yesterday, you and an accomplice pulled off the bank job of the century - a haul large enough for each of you to retire to your favorite island paradise with no extradition to your home country. The money is all untraceably socked away in secret bank accounts, but, unfortunately, the police caught up to you on your way out of town. After a high-speed chase, you both ended up in separate cells in solitary, where you have been stewing away overnight.

This morning, the state attorney visited you in your cell.

"Okay, listen up," he said. "I know you'll just deny it if we ask, but we know you two did it, even if we can't prove it. So I'm going to offer you a deal. Even if both of you say nothing, we can get a year inside for both of you on a reckless endangerment charge for that wild driving last night. I'm willing to drop that charge and let you go if you'll testify against your partner.

"But before you start thinking about altruism and all that, I'm warning you - my partner's right down the hall, offering the exact same deal to your partner. If you clam up and your partner talks, you'll get twenty-five years and your partner will be let off scot free. If you both testify, I'll give you time off for cooperation - fifteen years apiece.

"That's the deal - your choice. Think it over. I'll be back tonight."

Assume that you do not know and have no loyalty to your accomplice - all you want is a minimum sentence for yourself. (You can make up a scenario to explain it if you like - the key part is that you're strangers, only together for one job.)

[Poll #1207554]

(Edit: Anyone interested in further reading may wish to read the Wikipedia Prisoner's Dilemma article.)

(Edit 2: The crosspost to thequestionclub may be found here.)

Comments

[ceruleanst.livejournal.com]

Most people arrange the grid of assumptions like this:

He squeals. If I squeal, 15 years. If I don't, 25 years.
He doesn't. If I squeal, 0 years. If I don't, 1 year.

Viewed this way, the advantage of squealing appears to be guaranteed. Assuming a 50% probability of the variable I don't control, confessing has an expected return of 5.5 more years of freedom than the expected return of staying mum, and a lower risk.

But instead, it can be arranged this way:

Allowed to think about the same problem, we will come up with the same answer. If I squeal, 15 years. If I don't, 1 year.
Allowed to think about the same problem, we will come up with different answers. If I squeal, 0 years. If I don't, 25 years.

This is an equally valid way to divide the possibilities. The advantage of one choice is no longer guaranteed. If we assume that there's no way of knowing, and that the probability here is 50% as before, the comparative expected return remains the same, but there are compelling arguments not to treat this like a 50% chance. Hofstadter says that you should assume that your partner is probably as smart as you and therefore will come to the same conclusion as you. Most other people are given to assume that they are probably much smarter than anyone they're paired with. I think the details of the situation will point to which is more likely. In your version, we've just pulled off an epic bank heist together, so it stands to reason that we are comparably clever.

[packbat.livejournal.com]

Thanks for the input! (I remember Hofstadter's analysis of this - I've always thought his analysis was clever, although I know of few whom it convinced.)