Blog: Dr. Nash’s Legacy: Nash Equilibrium


Dr. Nash’s Legacy: Nash Equilibrium

Best result comes when one does what is best for oneself and for the group.
Dr. Nash’s Legacy: Nash Equilibrium

Mathematician Dr. John Nash, who inspired the Oscar-winning film A Beautiful Mind, died in a car accident with his wife earlier this week. Recipient of the Nobel Prize for Economics in 1994, the mathematician was renowned for his work in game theory.

In one of the scenes of A Beautiful Mind, Russell Crowe who plays Dr. Nash, explains and expands game theory while sitting at the bar with 3 friends and takes a beautiful blond woman with her 4 brunette friends as the analogy. In this scene, Dr. Nash argues that all men will try to go for the blond, but nobody will eventually succeed; and then when they want to go for the brunettes, they would be rejected once again (as nobody wants to be someone’s second option). However, instead, if the men ignore the blond, and go for the brunettes, each one of them will get a chance to dance with a girl that evening. Dr. Nash (Russel Crowe) states that “Adam Smith said that best result comes from each one in the group doing what is best for themselves. Because the best result happens when everyone in the room does what is best for himself and for the group.”

Thus, the famous Nash Equilibrium, which is a “solution concept of a non-cooperative game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy.”

A fascinating life of a man that brought several breakthroughs in math’s and economics while he fought schizophrenia for most of it. Dr. Nash married Alicia Larde in 1957, they divorced in 1962 and remarried in 2001.

Game theory was invented by John von Neumann in the first half of the 20th century, Dr. Nash contributions to this field have been his extension of the analysis beyond ‘zero-sum’, ‘I-win-you-lose’ scenarios, to more complex situations in which all of players could gain if they were to look for the most stable situation that benefits both themselves and the group. Here is an interesting explanation by Khan Academy.

Dr. Nash brought the ability to analyze situations of conflict and of co-operation and bring predictability about how will different parties behave. His equilibrium theory is a significant contribution to economics that has found applications to several fields including corruption, and financial crises.

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Topics: Culture, Watercooler

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