John Nash's Game Theroy

GAME THEORY

Before Nash, economists studied the market using sophisticated versions of Adam Smith's price theory -basic supply and demand. Smith said as "buyers and sellers pursue their self-interest, the "invisible hand" of the market distributes products efficiently".

But price theory can't explain the abundant real-world examples of market inefficiency. Nash approached this problem by reformulating economics as a game.

To most people, a game is a way to while away a rainy afternoon. But to mathematicians, a game is not just chess or poker but any conflict situation that forces participants to develop a strategy to accomplish a goal. 

To mathematicians, a game is a regimented world where math is king. And a game can be a window to mathematical insight. When I was a student, Princeton math professors collected every afternoon in the third-floor lounge for tea and a round of backgammon. Professor Conway told us that he stumbled upon the discovery of a lifetime while studying Go, an ancient board game played with smooth stones. Nash's central insight, the one for which he won a Nobel Prize in 1994, was to prove that every economic game has an equilibrium point — that is, an approach to play in which no player would choose to change his strategy. If a player were to try to change his Nash equilibrium strategy, he would end up worse off than before.

John Forbes Nash, Jr.

John Forbes Nash,  Jr. is an American mathematician whose works in game theory, differential geometry, and partial differential equations have provided insight into the forces that govern chance and events inside complex systems in daily life.

This article focuses on John Nash, recipient of the Nobel Prize in Economics in 1994, and subject of the Award winning 2001 film A Beautiful Mind, who was diagnosed with paranoid schizophrenia in 1958 at the age of 29. After presenting an account of the emergence, course, and eventual remission of his illness, the article argues for the relevance of his contribution to game theory, known as the Nash equilibrium, for which he received the Nobel Prize, to research studies of the schizophrenic brain and how it deviates from the normal brain. The case is made that the Nash equilibrium is descriptive of the normal brain, whereas the game theory formulated by John van Neumann, which Nash's theory challenges, is descriptive of the schizophrenic brain. The fact that Nash and his colleagues in mathematics did not make the association between his contributions to mathematics and his mental breakdown and that his later recovery exemplified the validity of this contribution are noted and discussed. Religious themes in his delusional system, including his view of himself as a secret messianic figure and the biblical Esau, are interpreted in light of these competing game theories and the dysfunctions of the schizophrenic brain. His recognition that his return to normalcy came at the price of his sense of being in relation to the cosmos is also noted.