# Optimal Solution Concept

Do you remember Adam Smith? He is considered the father of modern economics. His theories were used for more than 150 years by governments, industries, banks etc. One of his famous laws states that people act in their own self-interest. He postulated that in a free market, you will have to compete to survive. He explained how rational self-interest and competition can lead to economic prosperity. Is this always true? Can you think of a case where this theory might not lead us to the most optimal solution? This is not a philosophical discussion, so I actually want you take a minute and think. If people are competing against each other, then what strategy would lead to the most optimal overall result.

Prisoner’s dilemma

Let’s consider the following situation. Two men are arrested, but the police do not possess enough information to convict them. The two men are kept in separate rooms and the police offer both of them a similar deal — if one testifies against his partner, and the other remains silent, the betrayer goes free and the one that remains silent receives the full one-year imprisonment. If both remain silent, both are sentenced to only one month in jail for a minor charge. If both of them testify against each other, each receives a three-month imprisonment. They don’t receive a full one-year imprisonment in this case because both of them cooperated. Their sentence is not just one month (like earlier) because both of them are found to be guilty.

Now each person must choose either to betray or remain silent. The decision of each person is kept as a secret from the other prisoner. What should they do? According to Adam Smith, people act in their own-interest. In this situation, each person is concerned with lessening his own time in jail. So if we follow his law, then each prisoner will betray the other prisoner to minimize his prison time. But the prison time would have been lesser if they had cooperated with each other. What went wrong here? Is Adam Smith wrong? Did the world follow the sub-optimal law for more than 150 years?

Nash Equilibrium

A young mathematician named John Nash was working on a similar problem back in the late 1940s for his PhD thesis at Princeton University. If everybody acts in their own self-interest, we will not get to the optimal point. In a situation where we are competing with other people, the best solution is obtained if you think of your own interest and everyone else’s interest. So in our prisoner example, each prisoner’s best interest would be to betray the other person. If each prisoner thinks about the other prisoner, he will keep quiet. This will help both of them get the minimum imprisonment of all the possible situations. This is called Nash Equilibrium. John Nash was just 22 years old when he wrote his famous PhD thesis which shook the very foundation of game theory and modern economics. This theory is used in market economies, computing, artificial intelligence, politics, military and many more fields. John Nash was awarded the 1994 Nobel Prize in Economics for formulating this theory. He got a Nobel Prize for something he did when he was just 22 years old!

Why is it relevant?

When we consider economic problems on a global scale, the penalties become huge. It’s not just one-month vs three-months vs one-year kind of penalties. It often involves billions of dollars and if you don’t plan carefully, a huge amount of resources will be wasted. In the field of artificial intelligence, this becomes even more relevant. We have to teach the machine to make the best possible decisions considering the surroundings. Imagine two robots exploring another planet. It’s absolutely vital for us that the two robots survive the whole trip. So we definitely need some kind of coordination between them while they make decisions. If you have some time, take a look at the mathematical formulation of Nash Equilibrium. You will realize how beautiful mathematics can be!

There’s actually a movie based on the life of John Nash. Remember ‘A Beautiful Mind’? Russell Crowe starred in this movie and brilliantly portrayed John Nash. Watch it if you get a chance, it’s a really good movie! In that movie, they have taken a different example to explain Nash Equilibrium and it’s not entirely accurate. You can read about it here (thanks to Aravind for the link) and dig further to understand why that’s the case.

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## 3 thoughts on “Optimal Solution Concept”

• Thanks for the link Aravind. I will put it in the post. I remember him mentioning this in class … That’s why the Prisoner’s dilemma is the best way to understand Nash equilibrium 🙂