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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Now we come to the final topic from my notes on political analysis—at least from the first half of the class. I’ll probably do another series of posts at the end of this semester, but for now, this is the final word on power.
“How many divisions does the Pope have?”
Thus spake Joseph Stalin in response to Churchill’s concerns about the Vatican’s views.
So far in this discussion of power, we’ve focused on hard power—threats, bargains, consequences—the kind of stuff that Stalin could respect. But what about the Pope? Does he not have power just because his only divisions are brightly dressed swiss pikemen?
It turns out (sorry Stalin) that there is such a thing as soft power, and to talk about soft power we have to talk about expectations, and to talk about expectations, we’re going to talk about John Maynard Keynes and beauty contests.Read More »
This post we’ll be talking about games—contrary to what people often say in dramas, this is a game.
An extensive-form game is a tree of decisions branching out, with actors forming the nodes in the branches, and the branches representing choices that the actors can make. The assumption is always that each actor is making rational choices, trying to get their best outcome, at every point.
To determine the outcome of an extensive-form game, you work from the ends backward to the beginning, using backwards induction. To demonstrate, here’s this game:
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