Friday, 15 April 2011

The Iterated Prisoner's Dilemma

Critical to fully understanding the evolution of behavioural traits is understanding some basic game theory, such as the iterated prisoner's dilemma.

The basic prisoner's dilemma is as follows: two criminals are taken to the police station and interviewed separately. They went on a crime spree together and there is enough evidence to convict them of some of the minor offences. Imagine you are one of the prisoners and you are given a choice, which you assume your partner in crime has also been given: confess to everything and thereby grass up your partner for the major charges [defect]; or keep your mouth shut [cooperate]. If you talk and your partner doesn't, then you get a reduced sentence of 2 years in prison because of helping to convict your partner; and he gets 10 years. If he talks and you don't then obviously the reverse happens. If you both give a full confession then you both get 8 years, and if neither of you talk you both get 4 years. What do you do?

Now imagine that you and your partner can both live forever, and any time either of you are not in prison you go on another crime spree together and each time you get caught and face the same decision. You know your partner's previous responses, so this will obviously affect whether you cooperate or defect in the latest interview with the police. This situation is the iterated prisoner's dilemma, and occurs (in other forms!) every day in societal life (the social contract).

The various consequences to the options can be formalised into a pay-off matrix, and different weightings given to the possible outcomes. So long as all the options are sensible, for example the benefit to you for defecting when your partner cooperates should always be more than the benefit to you for cooperating when your partner cooperates, then it is possible to make some firm conclusions about the worth of different strategies.

Axelrod created a tournament in which different programs played against each other (200 iterations for one game) and then each program's total score was added up. Some of these programs had very sophisticated algorithms to predict whether the opponent would cooperate or defect, however the overall winner was a program called tit-for-tat which simply started out cooperating and then did whatever the opponent had done the previous move. In the second tournament the winner was called tit-for-2-tats, I don't think I need to explain that one's tactics!

It is important to note that in a population it isn't as simple as there being an optimum strategy that everyone should abide by. One of the founders of modern game theory, John Nash (of “A Beautiful Mind”), showed that strategies of cooperation and defection settle to a balance (the Nash equilibrium) – so long as the frequency of defection is low, then on average the cooperators gain by continuing to cooperate and the small number of defectors can take advantage.

23 comments:

CandleintheDark said...

This is so deep. I love this stuff

Living cheap said...

Wouw good post. can you give examples how this happens in our daily life?

ResCogitans said...

lol a bit deeper than my usual posts, but it's an critical concept that feeds into the rationale behind many other opinions of mine so i thought it important to have it posted at some point.

it is difficult to come up with a 'pure' example of the IPD in real life where the temptation (defection) reward, and cooperation reward are the same for both parties. the core concept is really that mutual cooperation is an evolutionarily fit strategy in societies. we see mutual cooperation all around us in societies, for example it would be pretty easy to not pay for a meal out or for petrol/gas [defect] but if this became common then measures would be put in place to prevent it and the cost would be passed on to the consumer, so that although in the short term you got a free dinner, in the next iteration there would be a cost to you.

the study of criminology uses game theory in the guise of 'rational choice theory'. the police have finite resources, so if a burglar operates in an area with a low police presence they are less likely to serve time. the police will move to have a larger presence in areas with high crime, so pushing the criminals into a different area. the burglars also want to operate in areas with richer pickings, which tend to be less densely populated - so do the police spread their resources to minimise the worth of stolen items or to minimise the number of crimes? in reality not only game theory is taken into account when allocating police resources, but also politics...

Kelly said...

This is way over my head. Wish I could comment.

Anonymous said...

i thought sociopaths were intellectually shallow?

ResCogitans said...

kelly - i think you just did! the crux of it is that most people are cooperators but it is entirely natural for a minority of people to feel rules don't apply to them and that it is ok to take advantage of sheep.

anon - where have i ever said i was a sociopath?

I love tn said...

There are two contestants at the end of a reality show. There is a prize money. Both the contestants are taken to separate places and asked if they want to take all the money or share it with the other contestant, they are told that if they both choose to share it the money will be split equally, if one of them chooses share and the other take all, the one who said take all will get all the money, if they both choose take all, neither of them will get any money. (That, I've heard was the end of a series of 'Big Brother') They both chose to share it.

Anon - Emotionally, not intellectually. Though some are certainly more than a little intellectually deficient...

ResCogitans said...

yeah i knew about the big brother example, but it wasn't iterated and the contestents also had a vested interest in being publicly seen to be cooperators. their money ticket comes from their public image after the show, not the BB prize money.

Anonymous said...

"anon - where have i ever said i was a sociopath?"


On SociopathWorld many times.

Anonymous said...

"Anon - Emotionally, not intellectually. Though some are certainly more than a little intellectually deficient..."


True they are emotionally shallow but also intellectually shallow, they can act like experts because they are so glib but it's a facade, psychopaths generally have no idea what their talking about.

I love tn said...

"a vested interest in being publicly seen to be cooperators" Ha. I never thought of that, I was under the impression they all looked like selfish bastards already, just from being on the programme. But I never watched it.

I beg to differ anon. Whist I can seem knowledgeable about many things I know little about I also know a lot about a lot of things. But then, I do love to read.
As they say, knowledge is power, and I really like power. But I wouldn't just want to seem smarter than most of the other people in the room, I want to actually be smarter than them.

G said...

I love game theory it's so relavent to a lot of how people operate in the world...cool post!

Anonymous said...

"I beg to differ anon. Whist I can seem knowledgeable about many things I know little about I also know a lot about a lot of things. But then, I do love to read.
As they say, knowledge is power, and I really like power. But I wouldn't just want to seem smarter than most of the other people in the room, I want to actually be smarter than them."

You haven't been diagnosed as a sociopath I assume, unless you have been clinically diagnosed you're oppinion is invalid, sociopaths are shallow in every area but are masters of emotional manipulation. Maybe you're going through a phase?

notme said...

Hi Res. I'm good thanks! Still alive. :)

I love tn said...

"Your opinion is invalid" How exactly, pray tell, is yours any more valid than mine?

Anonymous said...

what?

ResCogitans said...

anon
well, i've never deleted a comment so you should have no problem providing many examples.

notme
you been away? glad you're still about :)

G
yep between evolution and game theory you sure can explain a lot about behaviour.

tn
i like to know a little about a lot of things too, precisely so that i can give a superficial impression to someone of anywhere along the line from stupid to intelligent&cultured. of course, i also do have some depth of knowledge :)

I love tn said...

As do I, Res, my dear, knowing a little about a lot of things is still knowing a lot more than most people. Although I confess, the world of the celebrity and all that kind of stuff, I cannot tolerate, and as such I know almost nothing about it. Also I cannot for the life of me understand why someone would be nervous upon meeting someone famous? Ah the mysteries of life...
(As an excuse for the rambliness of this comment I would just like to point out that I am drunk... Rambliness isn't even a word)

Ana said...

interesting :)

this is also noted in wild animal populations; while certain species with group/cooperative behaviour is less predated (predated?) and have bigger populations overall; the ones with a more individual behavior tend to have more deaths and the overall number of specimens is smaller/some near extinction.

it is true that being in smaller number defectors can take advantage of the cooperation between cooperators. they go along, get carried further.

Ana said...

this is regarding the benefits of long-term cooperation.

Anonymous said...

Keep posting stuff like this i really like it

Lukas said...

well, i've never deleted a comment so you should have no problem providing many examples.

But if you were a sociopath, you wouldn't have any problem lying about whether you had deleted comments.

Anonymous said...

what I was looking for, thanks