Friday, April 25, 2008

Prisoner's dilemma , iterations and analogies



The basic Prisoner's dilemma model:

Two prisoner's are lodged in different cells.They can't communicate with each other. They were partners in some crime. The police interrogates. The situation is like this....

IF both say they aren't guilty, both will get 3 years imprisonment due to non-cooperation.

If one says he is not guilty, but if the other accepts that he is guilty then the second person will get a lighter sentence due to cooperation with the police and the first person who pleaded not guilty would get a longer sentence.

So the thinking process of any prisoner will be that if i say i am not guilty but the other prisoner doesn't support then i will get a heavier sentence. And the other person will definitely not say guilty for fear of the first pleading guilty."Trust" is not trustworthy. So ultimately it boils down to the fact that both will say that they are guilty and both will get a longer term than had they both pleaded that they aren't guilty.


This might be child's play for everyone to understand.....but this can be made more exciting.

Say for instance that there are several iterations where in both the people are allowed to remember each other's responses. Then how will the game proceed. Say for instance, in the above example both Dave and Henry have pleaded guilty according to our explained thought process. It was too early for them to trust each other in the first round itself.


In the second or some later round, say Dave starts thinking. He thinks that we both know that pleading not guilty together is best for us. Is there any chance of cooperation from the other prisoner? I am a logical person and so is he. Both want our terms to be reduced. So if i plead not guilty, will he say not guilty too. Lemme take the chance since it seems we are starting to understand each other.

But all human beings are different. Trusting someone might be easier for someone and not so easy for others. So say DAVE says not guilty. Henry has still not gained so much trust of Dave. He pleads guilty. Dave is the loser in this case

In the next round, both again start thinking. Dave is smarting from the non-cooperation. Henry feels a bit guilty for letting down his partner in crime. He wishes that he had shown more faith. Henry pleads not guilty. Dave has two options. He might plead not guilty and both achieve the best outcome. This is very much possible since people think in many ways. For our case let's say he doesn't trust Henry so much now. He is unsure. He says guilty. So now Henry is the loser.


In the next round Henry thinks that Ok .. Dave didnt support me. Maybe it is my own fault. I had let him down. So he was not sure whether to trust me. Also he knows that now i have had a change of heart. So there is a possibility that he too pleads not guilty. So Henry says "not guilty". Dave thinks so too...that there is a change of heart of Henry and there is a possibility of a best outcome. So he will say "not guilty"

And the best outcome is achieved.

We can see that at some point in time, trust starts building. And in the long run, both achieve the best outcome due to cooperation with each other.


This is what happens in real life too. Consider our formative years. Children are referred to as gifts of GOD. Maybe it is true....but definitely not in the sense of virtues. Truth is that they are the most selfish of all human beings. Just look into ur childhood. Most of us will have so many images which we know shouldn't have been so. In a multiple environment, we see and observe...and learn to trust more people than our near ones. We start cooperating. And we start growing literally and figuratively. In the long run, the selfishness may remain in some part of our heart...but the awareness of need for behaving in a particular way in situations to benefit the society is cemented in our minds. Some sort of balance is reached. And the society functions in harmony.

This is not to say that selfishness is bad. Selfishness has its own virtues. Take a family for example. The mother is said to be the bonding locus of control. She is the one who binds the whole family together and makes it a proper home. She has a natural nurturing nature. She thinks these are my children. And this feeling is so strong that she wants to protect them from all possible harm. Think a bit earlier. She is part of a new family. Her husband is the most important for her in that family. She has left her home of years to come and stay with this person. Everything is strange and new. Her husband is the main comforting factor. Secondly, her old house is no longer her house. This is her house for ever now.

These feelings ..... my husband....my house....my children....all these "my's" contribute to the selfishness. Care is a natural corollary. This selfishness creates the happy home we are talking about. Here selfishness is not bad because we are not trying to gain anything by snatching from others. Life is not a zero sum game.

Adam Smith had said that the best result will come when everyone in the group thinks what is best for himself and acts so. He says that individual efforts contributes to the growth of the whole. Might be so in the short term. But in the long run, best result will come only when all individuals think what is best for themselves and for the group.