Political Analysis: The Prisoner’s Dilemma

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.

PD-canonical

In this game, there are two features which make it a “prisoner’s dilemma.”

First, each player has a strictly dominant strategy—no matter what you think the other player will do, it’s better to defect.

The second feature is that both players could be better off if they both cooperated, so the result is suboptimal for both players.

A generic form of the prisoner’s dilemma could be this:

PD-TRPS

PD-TripsSo for this to be a prisoner’s dilemma, the hierarchy has to be this: T > R > P > S. You can remember that as TaRPS or TRaPS, or, my favorite, T. RiPS!

You can just put any numbers in those slots, and as long as they follow the hierarchy, it’s a prisoner’s dilemma.

Some of the misconceptions about the prisoner’s dilemma are that it’s best to cooperate (wrong—if you think the other person will cooperate you should defect and get that sweet T pay-off instead of that second-rate R crap), or that real people would cooperate (wtf does this even mean?), or that it’s a problem of self-interest (although “cooperate” and “defect” are just flavor, you could replace “cooperate” with “no gift” and “defect” with “gift,” and you’d have “The Gift of the Magi“—were those people really self-interested?).

What hope for the world, then, if there are situations where both players will inevitably end up with a suboptimal outcome?

Never fear—the centralized solution is here!

Thomas Hobbes was an old Englishman who lived from 1588 to 1679, so he lived through the English Civil War, a big, bloody conflict for the Brits. Naturally, Hobbes wanted to know how such a horrible thing could happen.

He started by looking at nature—what is the state of nature? Basically, anarchy, with everyone acting in self-interest. This is a world that is “solitary, poor, nasty, brutish and short.” Hobbes’s solution to this was to bring in an outside actor—a “leviathan,” which overawes everyone and institutes order (in his time, some kind of monarch, though you can also think of the Overlords in Childhood’s End.)

So with the prisoner’s dilemma, the leviathan would change the payoffs, like so:

PD-changedpayoffs

These are called selective incentives—rewards for choosing specific strategies.

The leviathan could also penalize defection, which might look like this:

PD-penalize

This is forcing people to internalize the cost of defection.

A third resolution is to eliminate the strategy of defection altogether. That would look like this:

PD-eliminate

I guess I didn’t really need to draw that out.

Anyway, this resolution seems like a bit of a cop-out—obviously eliminating the ability to defect would be great, but how the hell do you do that? One idea is propaganda—make people believe that defection is impossible, unthinkable. Another idea is technology—making defection so inefficient and costly that no one does it (like how we’re slowly moving away from the defection strategy of burning coal as technology makes greener solutions more viable.)

That’s the centralized solution. Alternately, we have the decentralized solution—a defense of anarchy!—which we’ll talk about next post.

“I know you’re bored and you wish there was a reason to live, but this is my reason to live.”
-Professor Dion

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