AI Teaser Topic: The Prisoners' Dilemma

Two men are arrested, but the police do not possess enough information for a conviction. Following the separation of the two men, the police offer both a similar deal—if one testifies against his partner (defects/betrays), and the other remains silent (cooperates/assists), the betrayer goes free and the cooperator receives the full one-year sentence. If both remain silent, both are sentenced to only one month in jail for a minor charge. If each 'rats out' the other, each receives a three-month sentence. Each prisoner must choose either to betray or remain silent; the decision of each is kept quiet. What should they do?

The aforementioned problem, known as the Prisoners' Dilemma is a classic example of a game. Game theory is an important part of AI, with its applications ranging from Economics to Politics, from Biology to Psychology. You probably know about one notable game theorist: John Nash (Remember "A Beautiful Mind"?)

Think about the problem presented above. Put yourself in the position of one of the prisoners. And try to find out what will be the intelligent/rational decision? What will be the optimal decision for both players?

Suppose I am a prisoner. Now I can get four type pf results - 1 month of sentence, 3 month of sentence, I year of sentence or none. Now Let me see what I can ensure- If I betray then at most I will have a sentence for 3 month or rather may not even get a sentence. And if I remain silent then there is a scope of getting 1 month of sentence or getting 1 year of sentence. So in first case there may be two results - 3 month or 0 and in second case - 1 month or 1 year. And as i don't know the probability of each of those cases, I guess I should betray .

N.B. Though from ethical point of view I should remain silent

From an ethical point of view, you shouldn't have committed the crime in the first place

But you're right. It seems that the logical decision would be to betray (assuming that the only thing you are concerned about is minimum jail time). But what will be the optimal solution for both?

I agree with Alim's explanation. But I hesitated to give it here because it was - well.. unethical :S

The optimal one should be to rat out his partner. As it is said, an optimal solution is not a perfect solution. Rather, it is a solution which is made in accordance with reality. By ratting out, the result is either 3 months or nothing at all for the prisoner - which ignores the other combinations to achieve the possibility of having no punishment at all for thyself. However, when one chose to remain silent, he also creates the possibility of having an one year long punishment. So the sets are

1. One month or One year
2. Free or three months

From the above sets, having just three months punishment at max - looks lucrative.

Then again, it depends on how well acquainted the prisoners are with each other. If they have gone through similar situations before - they will certainly choose remaining silent. There are many unknown factors we are unaware of. Depending on those exceptional cases, the results may vary.

The rational decision would be to defect, for both of them (Interestingly, We'll have a Nash Equilibrium in that case, 'cause none of them will be able to improve their position solely by changing their decisions).

IMHO, the global optimal decision for both is to remain loyal. But it's not rational.

Excellent! So the optimal solution (called the Pareto optimal, btw) here is different from the rational solution. Thats precisely why its a dilemma

Can anyone point out some practical examples of the Prisoners' Dilemma?

I think Cold War is an interesting example. Both U. S. and Soviet Union can upgrade their nuclear arsenal, or both of them can reach a mutual agreement to dispose them. In this case, if both of them chose to upgrade, we'll have an equilibrium. But the global optimal solution is to dispose them because in that case both of them get to save humanity from extinction, and thus save themselves.

Interestingly, both of them disposed most of their nuclear arsenal in the end, which theoretically wasn't rational. Well, i guess humans are strange creatures that way.

Excellent example Agent Shakkhor Similar examples can be drawn from two companies competing for the market of similar products, two political parties campaigning for votes etc.

Kabir-IIT wrote:Agent Shakkhor

I feel like I've started working for FBI or someting

Kabir sir wrote wrote:Similar examples can be drawn from two companies competing for the market of similar products, two political parties campaigning for votes etc.

Ahemm... sorry to bother you all. An example came to my mind which was illustrated by Mushtaq sir in our Business Studies course.

Coca-cola and Pepsi are two market leaders in beverage. Instinctively,both wants to make max revenue from their product sale. Campaigning is a typical way of product promotion which leads to increase in sale. Some years back,both Coca-cola and Pepsi used to campaign for their product almost at a same time.

After doing this for successive years,they found out that campaigning both at once is not helping their cause.Their objective of campaigning was to attract the consumers of their counterpart. But consumers are likely to stick to their beverage as both companies came up with their full force during campaign. It stood like they were busy grabbing attraction of their own consumers. So neither of them were able to make a full use of it. This was much like a game with no winner.

Soon this is realized, Coca-cola and Pepsi came to an informal(or non-announced you can say) agreement to play the GAME. That is, when one company campaigns, the other just keeps it quite and vice-versa. This lets both of them catch the attention of new consumers for at least a period of time which earns them optimal revenue.

Thanks Agent Iftekhar ... A terrific example of a prisoners' dilemma (and thanks to Mushtaq sir)