The beautiful mind of John Nash
Equilibrium, as defined by the Merriam-Webster, is a state of adjustment between opposing elements. This applies to the wants of everyone. But this adjustment lacks in it the moral consideration which we all, being an interdependent species, must hold with. The moral of ‘common good’. It does not need to be taken into account when dealing with the equilibrium of, lets say forces on a body in physics or the chemicals in physical chemistry, but particularly when dealing among humans we must consider this ideology of ‘common good’ which refers to good-for-all. The subject economics is very intricately related to the emotional balance of people; a testament to it is the very branch of economics that relates to behavior, that is behavioral economics.
John Forbes Nash Jr. in 1951, introduced his concept of equilibrium called the ‘Nash equilibrium’ in economics. It can be applied to find the best possible strategy in any non-cooperative game, which are of two types:
- Extensive form- “Sequential play games”. Example- Chess.
- Normal form- “Simultaneous play games”. Example- Rock-papers-Scissors.
The optimal strategy here is that option/move taken by both the players in order to induce the maximum profits/gains to both of them or to achieve the maximum possible gains. This virtue of this equilibrium comes from the way in which it is derived; by iterating the choice of other players over a fixed choice of one player and thus finding the place from where no one wants to move and is acceptable to everyone. Hence, the Nash equilibrium intends to talk about the collective good of the rivals/components involved in a trade.
The title of this blog is, indeed, inspired by the movie “A beautiful mind” which itself is based on the life of John Nash. And its more of an attempt to observe and point out how he truly had a beautiful mind. Few excerpts in the movie which more or less indicate towards this:
- The way he proposed his abstraction where he claimed Adam Smith’s theory as wrong seemed to be based upon the very idea of common good or the good-for-all. The thing that Adam Smith could not deliver through his theory as he suggested that everyone should go for gaining what is best for himself and eventually everything will fall in place to be the best for everyone. The idea behind the free markets that stabilize themselves. But it did not actually work well with everyone when the “best” is the same for everyone.
- His equilibrium theory helped various players in the market to deal with the Antitrust issues which is the most prominent issue in a market or industry in oligopoly.
The crux of this theory of equilibrium lies in the common good of everyone, unlike Adam Smith’s. He worked on making this world a better place for everyone by theorizing the Nash Equilibrium. It seems that he had eventually expanded the domain of the definition of equilibrium from mere adjustment to best common adjustment between opposing elements. I believe it was the sheer thought of his beautiful mind to lead everyone to what is the best for them all, that got him the Nobel Prize.
There’s an exception to the Nash equilibrium too. It is called the prisoner’s dilemma. It is the only case where the two players end up giving the worst to each other. Though prima facie it seems to be the failure of Nash equilibrium, but maybe we just need to change our perception of this dilemma. If we really wish for the common good for the society, then what can be better than the prisoners deciding to give the worst to each other, which is the maximum years of imprisonment. So that means, in a way, the Nash equilibrium has not really failed. Our beautiful mind still remains to be beautiful.
Visit this link given below to thoroughly understand the game theory and the application of Nash equilibrium in collusion game theory.
