Last week I wrote about the prisoner’s dilemma, and a centralized, Hobbesian solution to that—essentially, to get people to cooperate you have to bring in an outside authority, like a monarch. This is the decentralized solution.
The decentralized solution to the prisoner’s dilemma has three elements:
- The game is repeated an unknown number of times
- The strategy is reciprocity—if A cooperates, B does too. If A defects, B does too.
- The shadow of the future is sufficiently long.
That “unknown” bit is important. If people know the game’s gonna end, and they know when, there’s no reason to develop trust with the other person. “Unknown” can mean infinite iterations, or just a percentage chance each time that the game will be replayed.
So if you’re going to play forever (or potentially forever), two basics strategies are always defecting (“All-D”), or always cooperating (“All-C.”) These strategies are useful for reference points, but they aren’t actually practical, because they aren’t reciprocal strategy—they’re not based on what the other person is doing. And in a normal-form game, what the other person does, combined with what you do, determines your payoff.
One reciprocal strategy is “Tit-for-Tat”—whatever the player did last turn, do that this turn.
We’re going to focus on the “Grim Trigger” strategy. God, that sounds badass. With Grim Trigger, you start out by always cooperating, but if the other player ever defects, you switch to All-D.Read More »
Now for a classic of political analysis—the prisoner’s dilemma.
“Rational individuals select actions to achieve their most preferred outcomes. If two rational individuals can do better by acting collectively, then they will do so, because they are rational.”
Annnnh! Wrong! That is the rock pile method, and it’s false, and we can see this with the prisoner’s dilemma.
A lot of people teach the Prisoner’s Dilemma, and a lot of them get it wrong. “If you’ve heard of it or had a class that covered it, get a lobotomy to eliminate that part of the brain,” says Professor Dion.
I’ll get to some misconceptions in a moment, but first, here’s the story of the prisoner’s dilemma: two accomplices in a crime are taken in for questioning. The police have enough to convict the two on a small charge, but they want to get them on this bigger crime. The two criminals are separated, and each is offered a deal—rat on the other guy (“defect”) and you’ll get to walk free, and the other guy will get a really harsh sentence. They’re also told that this deal is being presented to both of them. What ends up happening? They both defect, of course. If they expect the other person to say nothing (to “cooperate”), it’s best to defect, because then they’ll walk free. And if they expect the other person to rat on them, it’s also best to defect, because while they’ll still get a harsh sentence, it won’t be as harsh, because it’s split between them.
So, here’s the Canonical prisoner’s dilemma, shown as a normal-form game.
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