The Falsely Restricted Outcomes of the Prisoner’s Dilemma

2019 — This blog is charged with Contributing to the Delinquency of Citizens. Its recent post, “The Government Should Mind Its Own Business” was found, by the ministry of free speech, to be “subversive and disquieting”, offenses punishable by death. Arrests were made.

It was discovered that the blog’s owner did not write the article, a fact which saved his skin. His punishment was a mere six years educational readjustment.

During the course of his routine interrogation to extract information related to the crime, the blog owner, after being forced to listen to Bruce Springsteen’s “Born in the USA” three times in a row, cracked.

Before losing the last of his marbles, the blog owner was able to tell his inquisitors two names: “Mike” and “Ari.” Subsequent IP and weblog analysis revealed unequivocally that these two gentlemen were the only possible authors.

Both were arrested and stored in separate cells, into which a selection of Beatles tunes were looped to soften them up.

These prisoners had a dilemma!

Four outcomes were possible:

  1. Mike rats out Ari, Ari remains loyal; Mike goes free, Ari fries.
  2. Mike and Ari remain loyal; both receive six years reeducation, because the government would never execute where there is ambiguity.
  3. Mike remains loyal, Ari rats out Mike; Ari goes free, Mike fries.
  4. Mike rats out Ari, who rats out Mike; once more there is ambiguity, and both are sentenced to hand copy the “Declaration of the Rights of Man and of the Citizen” for the remainder of their sorry lives.

Both men know these possibilities. Mike sits and stews, wondering if he should rat out Ari, hoping that if he does so, he’ll go free, but Ari will fry. “Of course,” Mike thinks, “Ari knows that if he rats me out and I keep quiet, I fry.”

“But,” he reasons, “that means we both might turn rat. We’d be alive, but life would be hell.”

Meanwhile, Ari similarly muses. “Mike is usually a stand-up guy. He’ll probably keep his mouth shut, which means I should too, since I am so sweet. We’ll both have to endure reeducation, but it’s better than frying. Of course, Mike does have that streak of irascibility…”

The textbooks tell us that the “rational” solution for each man is to rat the other out and win his freedom. Well, this is obvious, right? Each man’s life and freedom is dear to him, after all.

But the textbooks, as they often are, and as you will by now be unsurprised to learn, are wrong. The reason they are wrong is because there are more than four possible outcomes.

There appear to be only four, because of (1) a lack of imagination, and (2) the usual mad rush to quantify the unquantifiable, a malady from which our cultures suffers greatly and to which many statisticians contribute.

Here are more possible outcomes:

  • Mike rats out Ari, Ari remains loyal; Mike goes free, Ari fries. Mike rats because he knows that Ari will be too weak to lead the resistance, and that he must live.
  • Mike remains loyal, Ari rats out Mike; Ari goes free, Mike fries. Ari rats because he and Mike agreed to this beforehand, since Mike is old and decrepit.
  • Mike remains loyal, Ari nervously rats out Mike; Ari goes free, Mike fries. Ari kills himself in shame.
  • Mike and Ari remain loyal; both receive six years reeducation, but upon release they are secreted away to China (as they knew they would be), where they can live a life free of government interference.
  • Mike boasts loudly to a guard that he will rat to save his life, knowing word will reach Ari who will then rat, too. But Mike doesn’t rat because Mike loves Ari; his plan is to sacrifice himself.

Perhaps you don’t find these situations plausible; if so, feel free to imagine your own. You can be sure that Mike and Ari will be thinking of infinite possibilities and not just the four laid out by the warden. In particular, we know, but the quantifiers do not, that not every man assesses the value of his life identically.

Quantification fails even if the punishments are changed from frying and reeducation to monetary fines. Because why? Because nobody thinks wholly in monetary terms (except, possibly, socialists, who are obsessed with money).

Even though the men are warned that only the immediate outcomes in front of them are pertinent—consider no other!—each will defy this directive and think about what happens subsequent to the immediate payout/punishment. Their thoughts on these matters figure inescapably into the calculations of their actions.

These criticisms are known to some extent, especially when considering experimental “iterated” prisoner’s dilemmas. But even then, those involved always think beyond the immediate horizon, about how their actions affect “players” not formally in the game (including how the players will be seen by the experimenters).

The worst of it is not that these figurings are impossible to quantify, but that people think that they are not important because they cannot be quantified.

14 Comments

  1. Mike and Ari both know that several prison guards are sympathetic to the “Movement” and will let the Movement’s unimprisoned leaders know everything that transpires in the hoose-gow.

    Both prisoners understand the Movement’s mentality well enough to realize that if one rats on the other, while the “rattee” remains loyal, then the “rattor” will face not only a horrible death by torture at the hands of movement members once he leaves prison, but also that the rattor’s wife and daughters will be raped and enslaved, while his sons all will be murdered.

    Therefore both prisoners — being 100% rational — stay loyal to one another, undergo six years’ re-education, and are welcomed by the Movement as Mandela-like heroes when they return to the Outside World.

  2. You forgot a couple::

    Mike rats on Ari. Ari remains loyal. Both fry because governments are like that.

    Mike rats on Ari. Ari remains loyal. Mike fries and Ari goes free because bureaucracies are like that.

  3. Mike rats out Ari to save Ari from the 6 years of hell re-education would otherwise face if Mike remained loyal to him, Mike accepts the guilt of this for the rest of his life.

  4. But then, Mike realizes that Ari will be thinking the same way so he re-doubles his effort to roll first to teach the dirty rat a lesson.

  5. Mike, who has watched too much MacGyver, builds a small incendiary device out of oatmeal and rat droppings, burns the bars loose, and escapes into the hills where he leads the life of a romantic guerrilla warrior, complete with a bevy of loose-moral women who are loyal to a fault.

    Ari, who has watched too much Food Channel, whips up a to-die-for casserole from oatmeal and rat droppings, charms the guards with his culinary skills, and becomes head chef at the Ministry.

    Later they meet accidently at a picnic site and share women, wine, and Kobe beef hamburgers served by Matt, who lost his marbles but is still marginally functional as a servant/waiter.

  6. Mike and Ari both rat each other out. Both go to the re-education camps, and both are severly beaten, because the other campers can’t stand a rat.

    Ari coordinates with Mike so that Ari will get maximum punishment because he believes his writings will rise in popularity if he is a political prisoner.

  7. Well done, Briggs. This is a very welcome little essay which I hope will help to corrupt the minds of philosophy students. Back in the Cretacious when I was taking undergraduate philosophy courses, I annoyed both the professors and the philosophy majors mightily by complaining that much of their material was based on straw-man arguments and oversimplification. Their response was to frog-march me over to Prof. Gerald Massey, a logician and a kindred soul whose students were mostly math majors.

  8. It turns out the re-education camps are based on Berkeley High/LSU curricula. Ari takes Marxist cookery and Mike takes statistics for math illiterates. Both make the mistake of actually doing the reading, and lift the grading curve. They are severely beaten. JJD majors in frog marching and is named valedictorian.

  9. Mike and Ari talk over this scenario beforehand and both rat out the “devil who made them do it”, in the form of Matt, who is located lounging on the beach with loose women at a remote Bermuda hide-a-way, and is subsequently rendered by the Brits back to Rikers Island – where he fries.

  10. Another endless supply of ambiguous results could be achieved if Mike and Ari both took vows of silence and/or went on hunger strikes.

    The “martyr” aspect might be fascinating to the regime. Maybe Mike and Ari would be studied like lab rats. Rats. Ha.

    One thing is certain, in my opinion–there could be no truly happy ending in the year 2019.

  11. I agree that the one shot prisonner’s dilemma is just a toy model for situations with highly different outcomes .
    However when the rules are well defined and the choices are iterative we are much closer to a RL simulation even if still idealized .
    What I have always found interesting were experiments where the outcomes were varied by making them more and more different .
    It’s interesting to see that people tend to behave logical and nice when the differences in the outcome are not very big but there are thresholds where they stop doing so .

    Yet , it is precisely in these highly non similar outcome situations that the number of non easily quantified scenarios tends to increase too what makes interpretations difficult .

  12. Tom,

    Of course, the standard axioms of rational choice can lead to reasonable models sometimes. I don’t think anybody questions that. But that do not always do so; and when they fail, the do so spectacularly. Meaning, it appears, that expected utility theory captures the average well enough, but fails on the tails (if you like).

    And that means of course that the theory is wrong, or incomplete. And probably wrong: take, for example, the transitivity axiom, a state of affairs common, but not strictly true always.

  13. Rational choice assumes too much and leads down a road that shouldn’t be traveled.

    Rational choice is based on my view of your action. If you choose that which I do not agree with, you choose irrationally.

    Let’s aggregate that. We (those in power) decide that your choice is irrational, so we rule against your choice.

    That is the end result of game theory: there exists a rational choice that is not selected (due to coordination failures, etc), therefore we — acting through government — need to be the altruist hand guiding the actors toward the rational (as we defined it) choice.

    But we have seen the end result of the so-called altruistic hand, time and again. Yet we still choose government as the solution.

    So, if government leads to evil, why is government (or any power/entity that assumes omniscience) still considered the rational choice?

  14. “And that means of course that the theory is wrong, or incomplete. And probably wrong: take, for example, the transitivity axiom, a state of affairs common, but not strictly true always.”
    .
    Yes I completely agree with the first sentence .
    I see it as a kind of useful (e.g allowing interesting insights) semi quantitative model that has little predictive skills for the real world .
    Does that ring a bell ? 🙂
    However when we allow it to get more statistical by f.ex taking the iterating variant or when we make parameters vary , then it gives a serious and real information .
    Like the existence of psychological thresholds etc .
    .
    For anecdote . When I was around 20 , I have won 3 years in a row the Championship of strategical and diplomatic games .
    I have based my strategies on the iterative variant of the prisonner’s dilemma (with some refinements and adaptations) .
    Well I can tell you that within a sample of a couple of thousands competitors , the model is rather relevant and , as I experimentally demonstrated , successful too .
    Of course I didn’t tell them 🙂

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