THE PRISONERS’ DILEMMA

19 January 2007

The first time I read about “The Prisoners’ Dilemma” was in a course I was doing on biomedical ethics.  It was in a set book called “Applied Ethics” (edited by Peter Singer), in a chapter by the great Nicholas Measor, entitled, “Games Theory and the Nuclear Arms Race”.

In the comments to my post called “Decisions” back in March 2006, I promised I would do a post on “The Prisoners’ Dilemma” because it is something I like, something that struck me at the time as insightful and interesting — and therefore something I would naturally want to share (which is what this blog is all about).

OK, so let’s get to it.

“The Prisoners’ Dilemma” is a grid or matrix and the following anecdote.

ANECDOTE

Two prisoners (You and Frank) have been incarcerated in separate cells unable to communicate with one another.  Both are suspected of a serious crime for which the penalty is 15 years in jail.  In order to obtain a confession the authorities resort to guile; each prisoner is addressed by his interrogator as follows:

“If you confess AND  Frank confesses, then you will both be given a nominal sentence for a minor offence which we would be able to get you convicted of — 2 years in jail would be the total you would serve.

“If neither of you confesses, then you will both be released without charge.

But (and this is a big but) if one of you confesses and the other does not, then the confessor will be awarded a FREE HOLIDAY in the Bahamas, but the other prisoner will be sent to jail for the full term of 15 years!”

This anecdote is then translated into a matrix as follows:

You
Confession No Confession
Frank Confession -2, -2 +15, -15
No Confession -15, +15 0, 0

In this matrix, +15 represents the value of the holiday in the Bahamas, -15 that of fifteen years in jail, 0 release scot-free, and -2 nominal sentence.

OK so far?

  • Now, the question is  — By what process of reasoning should you decide on your course of action?

I was AMAZED to find that MOST people do the WRONG thing.

They reason it out like this: Either Frank will confess or he won’t confess.  Let’s first suppose that he does, then if you confess you will receive a nominal jail term.  But if you don’t, then you will be facing the max — 15 years in jail. So you would be better off confessing.

On the other hand, suppose that Frank keeps quiet.  Then if you confess, you’ll earn for yourself a fabulous holiday of a lifetime, but if you clam up, you’ll simply be allowed to return home.

So whatever Frank does, you’ll be better advised to confess.

This is exactly what happens in real-life; both prisoner will reason in this fashion (and they will believe that they have free will to make the decision). Both will confess and will always end up in the top left-hand box.

But this is absurd!

It is the result of collective irrationality.  Think about it; if you and Frank simply kept your traps shut tight and NOT CONFESSED, you would both be in the bottom right-hand box, and both would be better off!

Now isn’t that fascinating?

Here’s an extra rub — suppose you let the prisoners communicate together before giving their final decisions, would you think this would make the outcome different?

Well, nope.  People may well agree to not confess together — but it is not a binding agreement, and people have (a) self-interest, and (b) distrust.  Both of these are influenced by the holiday bribe.  What happens is that instead of making the decision again (or giving the decision agreed), each prisoner now must make a new decision — the decision to break the agreement or not (which generates a new matrix).

So that’s the famous PD.  It is common enough in the day-to-day real world — from TV game shows to sport.

Because of the way PD works, legal plea-bargaining is forbidden in many countries — think about it, even if each is innocent of the alleged crime, it is in the interest of both suspects to confess and testify against the other! And, worse still, imagine the scene when one party is guilty — here, the innocent one is unlikely to confess, while the guilty one is likely to confess and testify against the innocent!

A derivative of the PD is the Stag Hunt: consider two competing companies deciding how much money to spend on advertising.

The effectiveness of one company’s advertising is partially determined by the advertising conducted by the competition.

If both companies advertise at the same time, then opposing advertising just cancels out, because profits remain the same as before — the only winner is the advertising executives; expenses increase due to the cost of advertising.

So both firms would clearly benefit from a reduction in advertising. But what a risk — should one company choose not to advertise, the competitor could benefit greatly by advertising at that point in time.  This is why (for example) cigarette companies got together and welcomed the ban on advertising! Weird huh?

A version of the Prisoners’ dilemma is the Diners’ Dilemma:

A group of pals go for a meal in a restaurant on the understanding that they will just divide up the bill equally among themselves.

Each individual must now choose whether to order the expensive or inexpensive dish.

Everyone reckons the expensive dish is better than the cheaper dishes (but not better enough to warrant paying the difference if you were eating alone).

As a result, everyone reasons it out like this:  the added expense  added to the overall bill by ordering the more expensive item is very small as it is divided among the group.

However, exactly because every individual reasons this way and they all end up paying for the cost of the more expensive meal, which is worse for everyone than ordering and paying for the cheaper meal! Classic PD irrational thinking.

There are all sorts of varieties of the PD (such as the Travellers’ Dilemma), all are great fun, and all share in common:

  • people THINK they have a free choice in a rigged game;
  • people THINK they act reasonably and rationally;
  • people are selfish, and assume other people to be selfish, so they distrust other people.

As a result, most people make poor decisions, democratic decisions are usually the worst, and people are easy to manipulate.

PD is about “divide and conquer”, it’s about co-operating with the authorities, rather than for the greater good.  When I saw the PD for the first time I was stunned at how easily we can be made to build up nuclear arms, buy advertising, and confess to crimes for which we are innocent! Learning to recognise the PD is a valuable tool for life.

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One Response to “THE PRISONERS’ DILEMMA”

  1. Timelord Says:

    This well written post blew me away completely. WOW. Genius.


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