A Beautiful Mind

A Beautiful Mind


Sylvia Nasar

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The Nash Equilibrium Symbol Analysis

The Nash Equilibrium Symbol Icon

In A Beautiful Mind, mathematical ideas—especially the “Nash equilibrium,” Nash’s most important contribution to game theory—come to represent Nash’s own independent identity, his competitive and often vindictive spirit, and his self-interested approach to life. Nash becomes famous for his advances in game theory, a field dedicated to decision-making, interactions, and strategies among rational actors in competitive scenarios. Game theory applies the idea of “games” broadly, studying negotiations in various situations in which individuals are attempting to win, make a profit, or otherwise gain something. In his own life, Nash is intensely competitive, often challenging other mathematicians to “games.” He also develops rivalries with his colleagues and strategizes about how best to one-up his opponents or exploit others for his own benefit. Additionally, Nash often uses the language of mathematics to explain himself and his own relationships. In a letter, he describes himself as a “singularity,” a special point around which “variables,” other people, are arranged—a comparison that speaks powerfully to his own narcissism. Indeed, as a younger man, Nash’s relationships were unbalanced. He views himself as superior to his romantic interests, considering his own needs, or “payoffs,” before theirs. Alicia, Nash’s wife, sacrifices her own life for him, sparing no cost to help him recover from the devastating effects of schizophrenia; he rarely acknowledges her efforts.

Yet for all of his arrogance, Nash also longs for human connection. He wishes to love and be loved, in spite of his flaws, and the Nash equilibrium might be seen as a symbol for the kind of life he eventually learns to lead. In a Nash equilibrium between two players in a game, neither player can improve their strategies; they have both made the best decisions possible to them, and they share the payoff. As Nash slowly begins to return to society after years of suffering from schizophrenic delusions that severed his connection to reality, he realizes the error of his ways, and he attempts to make amends with those he has wronged, including Alicia. Nash acknowledges the importance of caring for those who have cared for him, and he comes to value love over rivalry and competition. By the end of A Beautiful Mind, Alicia and Nash are living together in a kind of harmony, an “equilibrium”: they take care of each other and their son, Johnny, sharing the “payoff” of this life—happiness.

The Nash Equilibrium Quotes in A Beautiful Mind

The A Beautiful Mind quotes below all refer to the symbol of The Nash Equilibrium. For each quote, you can also see the other characters and themes related to it (each theme is indicated by its own dot and icon, like this one:
Mental Illness, Recovery, and the Quest for Knowledge Theme Icon
). Note: all page numbers and citation info for the quotes below refer to the Simon & Schuster edition of A Beautiful Mind published in 1998.
Chapter 10 Quotes

Today, Nash’s concept of equilibrium from strategic games is one of the basic paradigms in social sciences and biology. […] Like many great scientific ideas, from Newton’s theory of gravitation to Darwin’s theory of natural selection, Nash’s idea seemed initially too simple to be truly interesting, too narrow to be widely applicable, and, later on, so obvious that its discovery by someone was deemed all but inevitable. […] Its significance was not immediately recognized, not even by the brash twenty-one-year-old author himself.

Related Characters: Sylvia Nasar (speaker), John Forbes Nash Jr.
Related Symbols: The Nash Equilibrium
Page Number: 98
Explanation and Analysis:
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The Nash Equilibrium Symbol Timeline in A Beautiful Mind

The timeline below shows where the symbol The Nash Equilibrium appears in A Beautiful Mind. The colored dots and icons indicate which themes are associated with that appearance.
Genius, Morality, and Relationships Theme Icon
...professor whom she was interviewing: this “crazy mathematician” was John Nash, of the famous “Nash equilibrium.” In 1994, Nash won a Nobel prize in economics, and Nasar pitched a story about... (full context)
Genius, Morality, and Relationships Theme Icon
...best response to the other players’ best strategies. This is the basis of the Nash equilibrium, which forever changed the guiding principles of economics. (full context)
Mental Illness, Recovery, and the Quest for Knowledge Theme Icon
...the field of economics; many mathematicians and economists assumed that the “Nash” of the “Nash equilibrium” was dead. Yet Nash was also beginning to show signs of recovery. He interacted with... (full context)
Chapter 13 – Game Theory at RAND
Mental Illness, Recovery, and the Quest for Knowledge Theme Icon
Genius, Morality, and Relationships Theme Icon
Shortly after Nash formulates his famous equilibrium, Albert Tucker formulates a similar theorem, the “Prisoner’s Dilemma,” to describe a situation in which... (full context)
Chapter 49 – The Greatest Auction Ever
Genius, Morality, and Relationships Theme Icon
...dependent on what other licenses the users are able to purchase. Game theory—including the Nash equilibrium—helped the government to ensure that licenses could be purchased by corporations that could use them... (full context)