Monday, July 25, 2005

Prisoner's dilemma is one of the most popular examples of game theory..

Get to know about 'The prisoner's dilemma'

If you are not upto going to some other website, here I have reformatted it to look good in plain text.

The classical prisoner's dilemma

Two suspects are arrested by the police. The police have insufficient evidence for a conviction, and having separated both prisoners, visit each of them and offer the same deal: if one turns Kings Evidence against the other and the other remains
silent, the silent accomplice receives the full 10-year sentence and the betrayer goes free. If both stay silent, the police can only give both prisoners 6 months for a minor charge. If both betray each other, they receive a 2-year sentence each.

It can be summarised thus:


A Denies

A Betrays

B Denies

Both serve six months

B serves 10 years, A goes free

B Betrays

A serves 10 years, B goes free

Both serve 2 years

Assume both prisoners are completely selfish and their only goal is to minimise their own jail terms. Each prisoner has two options: to cooperate with his accomplice and stay quiet, or to betray his accomplice and give evidence. The outcome of each choice depends on the choice of the accomplice. However, neither prisoner knows the choice of his accomplice. Even if they were able to talk to each other, neither could
be sure that they could trust the other. Now, let's assume our protagonist prisoner is rationally working out his best move. If his partner stays quiet, his best move is to betray as he then walks free instead of receiving the minor sentence.
If his partner betrays, his best move is still to betray, as by doing it he receives a relatively lesser sentence than staying silent. At the same time, the other prisoner thinking rationally would also have arrived at the same conclusion and therefore will betray. Thus, in a game of PD played only once by two rational players both will betray each other and the world will become a place for monsters. Betrayal is their only rational choice. However, if only they could arrive at a conspiracy,
if only they could be sure that the other player would not betray, they would both have stayed silent and achieved a better result. However, such a conspiracy cannot exist, as it is vulnerable to the treachery of selfish individuals, which we assumed our prisoners to be. That is where the true beauty and the maddening paradoxicalness of the game lie.

If only they could both cooperate, they would both be better off; however, from a game theorist's point of view, their best play is not to cooperate but to betray. This treacherous quality of the deceptively simple game has inspired libraries full of books, made it one of the most popular examples of game theory and made some people appeal for banning studies on the game.

If reasoned from the perspective of the optimal interest of the group (of two prisoners), the correct outcome would be for both prisoners to cooperate with each other, as this would reduce the total jail time served by the group to one year total. Any other decision would be worse for the two prisoners considered together. However by each following their selfish interests, the two prisoners each receive a
lengthy sentence.

In our day-to-day lives, we are the prisoners who betray, as it serves our selfish interests. Some situations where people betray(don't cooperate) are..

  • loudly wafting your music through the entire neighborhood on a fine summer's day;

  • not worrying about speeding through a four-way stop sign, figuring that the people going in the crosswise direction will stop anyway;

  • not being concerned about driving a car everywhere, figuring that there's no point in making a sacrifice when other people will continue to guzzle gas anyway;

  • not worrying about conserving water in a drought, figuring "Everyone else will";

  • not voting in a crucial election and excusing yourself by saying "One vote can't make any difference";

  • not worrying about having ten children in a period of population explosion, leaving it to other people to curb their reproduction;

  • not devoting any time or energy to pressing gloabal issues such as the arms race, famine, pollution, diminishing resources, and so on, saying "Oh, of course I'm very concerned- but there's nothing one person can do"

When there are large number of people involved, people don't realize that their own seemingly highly idiosyncratic decisions are likely to be quite typical and are likely to be recreated many times over, on a grand scale; thus, what each couple feels to be their own isolated and private decision(conscious or unconscious) about how many children to have turns into a population explosion. Similarly, "individual"
decisions about the futility of working actively toward the good of humanity amount to a giant trend of apathy, and this multiplied apathy trtanslates into insanity at the group level. In a word, apathy at the individual level translates into insanity at the mass level.

(Written by Douglas Hofstadter for 'SCIENTIFIC AMERICAN', can be found in Metamagical Themas' chapter 31).