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Nash Equilibrium: A theory of choosing the best response

The greatest contribution of professor John Nash, the renowned mathematician who died in a car crash on Sunday, was in the expansion of Game Theory — a theory that’s widely applied across fields from foreign affairs to economics, from politics to biology.

world Updated: May 26, 2015 01:17 IST
Harikrishnan Nair
John-Nash-was-killed-in-a-car-crash-along-with-his-wife-Alicia-REUTERS
John-Nash-was-killed-in-a-car-crash-along-with-his-wife-Alicia-REUTERS

The greatest contribution of professor John Nash, the renowned mathematician who died in a car crash on Sunday, was in the expansion of Game Theory — a theory that’s widely applied across fields from foreign affairs to economics, from politics to biology.



Game Theory was originally developed by mathematician John von Neumann and Oskar Morgenstern in their book, “Theory of Games and Economic Behaviour”, published in 1944.



The duo described ‘games’ in its simplest form – when one man’s gain is another man’s loss.



Nash, however, questioned the proposition and asked what would be the best response in case one player had no idea about what the player might do.



An analysis of this question led to what is now called the Nash Equilibrium.



The Nash Equilibrium reckons that the best scenario possible would be to do something that would maximise the person’s benefit while assuming that the other person would do the same based purely on self interest- a concept known as mutual gain.



For example, if you were sharing your room with another person, you would be well-served if your room mate were to pay for everything, whereas the opposite would be true for your room mate.



If both of you were to choose to ‘not pay’, then you have reached a state of Nash Equilibrium – both are benefited economically through a game of non-cooperation.



Of course, the better option would be to shift to a strategy where both pays – a game of ‘cooperation’.



This would mean that both would have to suffer a ‘shift’ in strategy. And who would be ready for that unless the other person is sure that his roommate would offer to contribute to the cause?



In that case, the person to first shift his strategy would lose out and this would create a conflict.



Besides, both would prefer to be on the side of least loss.



This 'game' has been played by countries, corporations and even personalities throughout generations. Imagine the two roommates to be India and Pakistan and you may get an idea of the importance of Nash Equilibrium.



Experts say that Nash’s brilliance was in the fact that his conclusions were remarkably simple.



“It was a natural discovery,” Dr. Harold W. Kuhn, a mathematics professor at Princeton told the New York Times.



“A variety of people could have come to the same results at the same time, but John did it and he did it on his own.”



The theory did have its short comings, though.



The Nash Equilibrium assumed that the players would not know anything about the other person’s strategy and completely undercut human emotions such as sacrifice and compassion.



This opened up new possibilities in Game Theory and was later taken up by mathematicians John Harsanyi and Reinhard Selten.



The trio of Nash, Harsanyi and Selten were later simultaneously awarded the Nobel Prize in Economics in 1994.