A loser doesn’t know what he’ll do if he loses, but talks about what he’ll do if he wins, and a winner doesn’t talk about what he’ll do if he wins, but knows what he’ll do if he loses – Eric Berne
John Nash Jr., 1994 Noble Prize winner in economics for his contribution to game theory died last week in a car crash in USA. Hollywood movie “A Beautiful Mind” is based upon his life played by Russell Crowe. As tribute to his genius, below is an amateurish journey through the wonderful world of Game Theory.
As people we interact, act, negotiate, win and lose. As we playing out our part in the interactions we are always considering alternatives, weighing their effectiveness and assuming the response of the other party. Decision making by humans has been a subject of interest to many psychologists. Eric Berne’s Game People Play is a classic book on the same. His student Thomas A Harris wrote the blockbuster “I’m OK, You are Ok”.
Psychology is an interpretative science. Few mathematicians and economists tried to give it a more structured feel – method and maths to be precise. John von Neumann was the pioneer of what is now called the Game Theory.
Game Theory is a mathematical study of conflict and cooperation between rational decision makers. Simply defined it is interactive decision making theory. Game Theory is interpreted through games and by studying the outcome of the games. A simple and famous game is “Prisoners Dilemma”.
Suppose A & B have been caught in a financial scandal which they operated together. Both are lodged in different cells and being interrogated without knowing what the other is saying (confessing or denying). Herein lies the dilemma as both want lesser prison sentence. There are 4 game outcomes with legal implications:
- If A pleads not guilty and B confesses, B will get 1 year sentence and A will get full 5 years
- If both plead not guilty and implicate the other, both will get 2 years sentence.
- If both plead guilty and also implicate their partner, both will get 3 years sentence.
- If B pleads not guilty and A confesses, A will get 1 year sentence and B will get full 5 years
Each of course want reduced prison time but are not sure what the other is up to. What is the solution?
Nash Equilibrium: Nash introduced the equilibrium concept to resolve the above and similar game situations (which are more complex, with more players and different payoffs). In the above the Outcome 2 is the equilibrium point. It is not similar to Aristotle’s Golden Mean where in we arrive at a mid-point to close out the interaction (typical negotiation in Indian bargain shop – na mera 30, na aap ka 50, chalo 40 par close karte!)
As per Nash, equilibrium is arrived at for every scenario when all the players know their own and their opponent’s strengths and no side will benefit by changing course. For example, India and Pakistan know their strengths, weakness and loss expected on conventional war and hence do not indulge in it. Similar was the situation between US and Soviet Union during Cold War.
RBI faces a highly complex game with interest rates. Increase in rates may reduce inflation but will increase cost of doing business which can lead to further erosion in economic activity but will receive higher hot money. Reduction in rates will increase inflation but will reduce cost of funds but may not increase economic activity (due to other factors) but will reduce the savings rate of common man. Damn you raise the rates, damn you lower the rates!
Nash Equilibrium helps all the participants to plan and execute strategies in a better and efficient way thus building an efficient society and environment.
Game Theory is today being used in economics, biology and many other spheres of life.
Game Theory in real life: We do not need a Ph.D in economics to use or understand game theory in day to day life. By applying game theory principles you can do better in financial markets, while buying a car, while buying a house, negotiating a salary hike or playing poker.
Books on Game Theory: there is lot of good books out there on game theory. Of the few I’ve read these 2 stand out. Thinking Strategically by Avinash Dixit and Barry Nalebuff explains the theory with good examples. Other is The Game Tehory by Uri Bram which is simple and well written (you will know through game theory why women wear yoga pants!)
A tribute to John Nash: “This guy is a genius” was the recommendation with which he came to Princeton as Ph.D student. He lived up and went beyond that description. He is the only one to win both Abel Prize (for mathematics) and Nobel Prize(economics) – highest honour in both the fields. Both his award winning works came in the first 30 months of his graduate study. His Nobel winning work is just a 23 page document! At a very young age he was diagnosed with schizophrenia and had to undergo treatment after which he returned to active work after 21 years.
His life and struggle with schizophrenia is the basis of the film “A Beautiful Mind”. He died in a car crash while returning home after receiving Abel Prize. Reportedly he was not wearing a seat belt and might have missed the equilibrium that the belt would have provided and thus saved his life! Such is the game of life!
RIP John F. Nash Jr.