Wednesday, April 04, 2007

The Prisoner's Dilemma Demystified

We all have at some point in life faced major dilemmas. The ones which can make your life interesting to say the least, when you would suddenly start to understand that Heisenberg with his uncertainty principles was not such a big fool after all or why was the word vacillating added into the English language. But what concerns us on a day to day basis and seems largely inexplicable is not something that cannot be quantized and is very much tangible. It seems that those geeky scientists who seem to be so preoccupied with their great unsolved problems, weird hypothesis, earth shattering researches and ground breaking procedures also seem to look into the dark labyrinth of the human mind and fish out something so funny, interesting and yet life changing that will leave us surprised. It makes us realize that we are living in a vicious circle. First simplify the complex things and then use science to complexify( couldn't think of a word actually !!!) them. Well the purpose of my post is to allow one to have a peek into the classical prisoner’s dilemma problem and yet demystify it and see its applications in day to day life. For the uninitiated, here is the problem.

The Prisoner's dilemma was originally framed by Merrill Flood and Melvin Dresher working at RAND ( the same place John Nash worked for some time) in 1950. Albert W. Tucker formalized the game with prison sentence payoffs and gave it the "Prisoner's Dilemma" name

The classical prisoner's dilemma (PD) is as follows:

Two suspects, A and B, are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal: if one testifies for the prosecution against the other and the other remains silent, the betrayer goes free and the silent accomplice receives the full 10-year sentence. If both stay silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a two-year sentence. Each prisoner must make the choice of whether to betray the other or to remain silent. However, neither prisoner knows for sure what choice the other prisoner will make. So this dilemma poses the question: How should the prisoners act?

The dilemma can be summarized thus:

Prisoner B Stays Silent

Prisoner B Betrays

Prisoner A Stays Silent

Both serve six months

Prisoner A serves ten years
Prisoner B goes free

Prisoner A Betrays

Prisoner A goes free
Prisoner B serves ten years

Both serve two years

The dilemma arises when one assumes that both prisoners only care about minimizing their own jail terms. Each prisoner has two options: to cooperate with his accomplice and stay quiet, or to defect from their implied pact and betray his accomplice in return for a lighter sentence. The outcome of each choice depends on the choice of the accomplice, but each prisoner must choose without knowing what his accomplice has chosen to do.

Applications of Prisoner’s Dilemma in real life

Warning: These ideas move from the very serious to the downright crappy!! , so choose your order of reading, at your own risk

The Jews

If you look at the time line of Jews as a community, ever wondered why they had faced prosecution at the hands of various communities without putting up a fight and actually submitted themselves as slaves. The answer may lie in our analysis of the prisoner’s dilemma

Throughout history, the Jews have lived under the shadow of an immense future, believing in the promise of them being the chosen people, of their belief of a second coming. They lived as scattered communities in areas that were hostile to them or around people who initially saw them as a nuisance. Any sort of action, which was either “non cooperative” or even mildly unfriendly was dealt with severely. So they actually had a better chance surviving without putting up a fight or in PD terms cooperating and not defecting

This strategy worked well for two thousand years until they met the Nazis who seemed to have a mania to purge the world of Jews and carried out their systematic extermination for years to come. The hatred they had faced before had been less deeply rooted, or more inconsistent, or less violent.

That’s why today we see a more violent Israel than they had been in the past as Jewish people. The instinctive action would have been cooperation with the Nazis, which would have resulted in their extinction as race.

The Arms Race

The PD scenario is often used to illustrate the problem of two states engaged in an arms race. Both will reason that they have two options, either to increase military expenditure or to make an agreement to reduce weapons. Neither state can be certain that the other one will keep to such an agreement; therefore, they both incline towards military expansion. The paradox is that both states are acting "rationally", but producing an apparently "irrational" result.

Tour De France

Consider two cyclists halfway in a race, with a large group at great distance behind them. The two cyclists often work together (mutual cooperation) by sharing the tough load of the front position, where there is no shelter from the wind. If neither of the cyclists makes an effort to stay ahead, the group will soon catch up. An often-seen scenario is one cyclist doing the hard work alone (cooperating), keeping the two ahead of the group. In the end, this will likely lead to a victory for the second cyclist (defecting) who has an easy ride in the first cyclist's slipstream.


Consider two companies A and B. If both Firm A and Firm B chose to advertise during a given period the advertising cancels out, sales remain constant, and expenses increase due to the cost of advertising. Both firms would benefit from a reduction in advertising. However, should Firm B choose not to advertise, Firm A could benefit greatly by advertising. Nevertheless, the optimal amount of advertising by one firm depends on how much advertising the other undertakes. As the best strategy is dependent of what the other firm chooses there is no dominant strategy and this is not a prisoner's dilemma. The outcome is though similar in that both firms would be better off were they to advertise less than in the equilibrium.


From my (in)experience about love, the PD is very much applicable. We all have our dirty secrets, the skeletons waiting to tumble out of the closet. What would happen if two people in love want to share some secrets about their past they wouldn’t normally do

The dilemma can be summarized thus: *

Girl remains silent

Girl shares

Boy remains silent

And they live happily ever after

She will go along thinking all her life that all men are some breed of sexual perverts, with sex on their minds all the time ( err…hmm .ooh ) looking only for relationships as a way to show off his machismo and would be very apprehensive next time she commits.

Boy shares

His life is screwed, he will probably go mad for some time, in special cases turn to spirituality, start some sort of secret society which in extreme cases can lead to mass paranoia or run a helpline for relationship advice or look for another girl

If sensibility prevails, they stay together, with lots of guilt off their shoulders.

* Please see end of page. In case you don’t have the patience to read through or have already closed this window, the above observations are purely speculatory in nature

Engineering Vivas

I can already see a smile on your face. This reminds me of the countless vivas I have given to my really fundoo and esteemed Profs and to the moronic; linguistically challenged maniacally mugging machines called Ad- hocs. Here is a not so unfamiliar encounter of a fundoo ( albeit depressed in the end ) Prof and 3 engineers.

If you have been a true engineer, which I need’nt explain, but eventually will, knows nothing about his field of engineering, is always on the brink of getting into the short attendance list, occasionally making it there too, never did a journal on his own, believes that glass was made solely for the purpose of a glass trace and to taste other earthly liquid delights and serves no known scientific or industrial purpose, studied for the exam on the last night, or even better in the morning, doesn’t know where most of his laboratories are located, ends up sitting in the canteen all day ogling at god’s best creation, his fair draft of human beings after creating, man. He is the enlightened one who sincerely believes that the Vivas are places to learn, show off his spontaneous idea guzzling abilities, undo the work all those poor scientists have done by giving out of the world explanations to the most basic of questions. The very fact the you are reading this shows that you have loads of time to kill .Enough, I am already sympathising for the poor Profs. Back to prisoners dilemma and cut to Viva scene

Moi : Good morning Sir

P: good morning all, have a seat

P: it seems you have copied the readings. These do not match with the experiments we did in the lab .

Classic PD …what should the others do, keep shut and let hope float or bring down the house

E 1 : No sir, these are the same readings……..all others nod ( Huraay!! They have cooperated, I knew I could trust you guys )

Suddenly T1 (topper no 1 aka the Ghissoo, insatiable grade earner and GPA hungry, ready to exploit the system to screw his peers…classic PD again )

T 1: no sir, we have copied the readings from the senior’s journal.

All: ( Wtf!! I think we need to talk …and this one is going to be unpleasant. Hostel main mil…. Saari sincerity aur honesty nikaal denge..It seems he had an overdose of morality and ethics . )

P: I thought so. But at least you could have been honest with me. See T 1 had the courage to at least tell the truth. you $^%)%@)(!_&^@%

All : Its all over, CC pakka, now we shall re enroll in the elite 6 pointers club we have been so proud of, a heritage that will die only in our placement and B school interviews, inspired by 300, we decide to fight back )

P: anyways, what is the significance of the Nusselt number (don’t bother, neither did I)

T 1: starts off as if he has very few moments to live on this earth and he feels that he must share his pearls of wisdom with the ignorant, early man-ish, unintelligible, gibberish crowd giving him company at the teachers cabin. He follows his divine duty of enlightening us with ideas even nusslet hadn’t thought of, ensuring that his knowledge has a bearing on the generations to come

Prof is beaming, we are feeling like possessed men with blood shot eyes ready for the kill, only to be killed soon by the prof .

The rest is the question and question session between prof and students (physically available, mentally retarded) which might look very familiar to you, so I am not taking the pains to put you through all that

So basically each time the topper defects and the poor others end up screwing their GPA, their life and never the topper. Classic PD isn’t it?

P.S The prisoner's dilemma can be applied in economics, politics and sociology, as well as to the biological sciences such as ethnology and evolutionary biology. And I sincerely hope that coming this far and after being through 1953 words which make some sense, you don’t expect me to know all the above mentioned stuff.