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Nash, John (1928-2015)

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Noted mathematician John Nash, Jr. (1928-2015) received his Ph.D. from Princeton University in 1950. The impact of his 27 page dissertation on the fields of mathematics and economics was tremendous. In 1951 he joined the faculty of the Massachusetts Institute of Technology in Cambridge. His battle with schizophrenia began around 1958, and the struggle with this illness would continue for much of his life. Nash eventually returned to the community of Princeton. He was awarded the Nobel Prize in Economics in 1994. The 2001 film A Beautiful Mind , staring Russell Crowe, was loosely based on the life of Nash.

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John Nash's Dissertation

Non-cooperative Games, May 1950, is available in PDF format  Non-Cooperative_Games_Nash.pdf . The dissertation is provided for research use only. 

[Note: Chapter 6 of  The Essential John Nash,  edited by Harold W. Kuhn and Sylvia Nasar (Princeton, New Jersey: Princeton University Press, 2001) contains a facsimile of Nash's 1950 Ph.D. dissertation on non-cooperative games.]

In the movie  A Beautiful Mind  there is a scene in which faculty members present their pens to Nash. What is the origin of the pen ceremony? When did it start?

The scene in the movie,  A Beautiful Mind,  in which mathematics professors ritualistically present pens to Nash was completely fabricated in Hollywood. No such custom exists. What it symbolizes is that Nash was accepted and recognized in the mathematics community for his accomplishments. While some movies are based on books, the film A Beautiful Mind states that it was  inspired  by the life of John Nash. There are many discrepancies between the book and the film.

May I see Nash’s graduate school records?

John F. Nash, Jr's records have been digitzed and are available to view here:  Graduate Alumni Records

May I see Nash’s faculty file personnel records?

Personnel files transferred to the archives after 2003 : Files are closed until 100 years after the person's year of birth or 5 years after the person's year of death, whichever is longer. Therefore, John F. Nash's personell files are closed until, June 13, 2028.

May I have a copy of Nash’s 1994 Nobel Prize acceptance speech?

At the Nobel Prize Award ceremony, His Majesty the King of Sweden hands each Laureate a diploma, a medal, and a document confirming the Prize amount. The Laureates do not give acceptance speeches . The scene in the movie A Beautiful Mind in which Nash thanks his wife Alicia for her continued support during his illness is fictional.

Laureates are each invited to give an hour-long lecture; however, the Nobel committee did not ask Nash to do so, due to concerns over his mental health.

Additional Resources

Princetoniana Committee Oral History Project Records , Interview with Harold Kuhn, Part 1, pp. 31-40.  In this part of the interview, Prof. Kuhn discusses his behind the scenes work for John Nash’s Nobel Prize.

Historical Subject Files Collection, 1746-2005 : A Beautiful Mind.

Article:  John Nash automobile accident May 23, 2015, in Monroe Township, New Jersey.

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• Published: 24 June 2015

John Forbes Nash (1928–2015)

• Martin A. Nowak 1  

Nature volume  522 ,  page 420 ( 2015 ) Cite this article

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• Mathematics and computing

Master of games and equations.

John Forbes Nash, an exalted mathematician whose life took dramatic turns between genius, mental illness and celebrity status, made major contributions to game theory, geometry and the field of partial differential equations.

Nash, who died on 23 May, was born in Bluefield, West Virginia, in 1928. His father was an electrical engineer and his mother a schoolteacher. In 1945, after excelling in mathematics at high school, he attended the Carnegie Institute of Technology (now Carnegie Mellon University) in Pittsburgh, Pennsylvania. At first he studied chemical engineering, but soon after enrolling he switched to chemistry and then to maths.

In Nash's final year, one of his professors wrote a recommendation letter for the 19-year-old supporting his application to graduate school. It simply stated: “He is a mathematical genius.” In 1948, Nash was accepted by Harvard University in Cambridge, Massachusetts, and by Princeton University in New Jersey. He chose Princeton.

As a PhD student, Nash proved the existence of the equilibrium that now carries his name. His 1950 paper 'Equilibrium points in n -person games', contains about 330 words, two references and not one equation (J. F. Nash Jr Proc. Natl Acad. Sci. USA 36 , 48–49; 1950). One of the citations is the 1944 book Theory of Games and Economic Behavior — in which mathematician John von Neumann and economist Oskar Morgenstern introduce game theory, a mathematical approach for studying strategic and economic decisions.

The Nash equilibrium is a position in a game from which none of the players can change their strategy to improve their pay-off. Imagine a game with two players (yourself and another person) and two strategies, A and B. If you both choose A, your pay-off is 2. If you choose A and your opponent chooses B, you score 0. If you choose B and the other player chooses A, your pay-off is 3. If you both choose B, you score 1. The same applies to your opponent.

In this example, the Nash equilibrium occurs when both players choose B. If both players choose B, their pay-off is 1; if either player switches to A, their pay-off falls to 0. In other words, neither player can independently switch their strategy and improve their pay-off. Observe that if both players select A, there is no Nash equilibrium because you could improve your pay-off by switching to B.

Calculating the Nash equilibrium can be a formidable task in a complex game. There is also the uncertainty over whether the person you are playing against is sufficiently rational to play the equilibrium strategy. If both players are rational and their rationality is common knowledge, they would play it. But experiments often reveal that people are not rational. Regardless of whether people actually play the Nash equilibrium in social or economic interactions, working out what it is (or what the Nash equilibria are) is the first step to analysing any game.

Although dismissed at the time by von Neumann as a triviality, the Nash equilibrium has been used to analyse all sorts of competitive situations. As well as being key to decision-making in economics and politics, the idea is important in biology. Here, the nearly equivalent concept, formulated by evolutionary biologist John Maynard Smith in the 1970s is called an evolutionarily stable strategy (ESS). If all members of a population adopt an ESS, then natural selection prevents a rare mutant from spreading.

On completing his PhD, Nash joined the Massachusetts Institute of Technology (MIT) in Cambridge in 1951. He worked — first as an instructor and later as a professor — in the mathematics faculty until he resigned in 1959. It was while he was at MIT that Nash met and married Alicia Lopez-Harrison de Lardé, a physics student there.

Among mathematicians, Nash is best known for his work in real algebraic geometry and nonlinear partial differential equations. He was not afraid to tackle the hardest problems in the field, and he succeeded. In 1957, he — in parallel with Italian mathematician Ennio de Giorgi — solved Hilbert's nineteenth problem involving partial differential equations.

It was during a talk in 1959 on what is seen to be one of the hardest problems in maths — the Riemann hypothesis — that the audience realized that there was something wrong with Nash. His talk was incomprehensible.

He was diagnosed with paranoid schizophrenia that year. Over the next two decades, Nash was in and out of hospitals. He underwent therapy, and for a while left the United States and sought asylum in Switzerland in an attempt to escape his imagined tormentors. For many years he wandered around the Princeton campus. Throughout this period, Alicia, who divorced Nash in 1963, oversaw much of his care.

In the late 1980s, Nash reappeared in academic circles, and in 1994 he was awarded the Nobel Memorial Prize in Economic Sciences for his work on game theory. The Nobel and the 2001 film A Beautiful Mind , based on journalist Sylvia Nasar's book of the same name, which recounted Nash's struggles, propelled him into the limelight.

In May this year, Nash received the Abel prize from the Norwegian Academy of Science and Letters for his work on partial differential equations. On the way back from the celebration in Norway, John and Alicia (who had remarried in 2001) were killed in a car accident in a taxi on the New Jersey turnpike. John was 86.

I met John in 1998 at the Institute for Advanced Study in Princeton. Over the years, I gave several talks there that he attended. One summer's day, when the usual sitting arrangements for lunch were disrupted by the closure of the main kitchen, I noticed John, the physicist Edward Witten and Andrew Wiles, the British mathematician who proved Fermat's last theorem, sitting down together at a small table. I wondered which of them would start the conversation. None of them did. I seem to remember that they ate their meal in silence.

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Martin A. Nowak is professor of mathematics and biology, and director of the Program for Evolutionary Dynamics at Harvard University in Cambridge, Massachusetts, USA.,

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John Nash: The Genius Who Shaped Game Theory and Economics

• Publication date January 18, 2024

John Nash’s profound impact on economics and mathematics is a story of intellectual brilliance, personal struggle, and enduring legacy. His journey from a precocious student to a Nobel laureate illuminates the intersection of pure mathematics and economic theory.

Early Life and Education

Born in 1928 in Bluefield, West Virginia, Nash showed early signs of extraordinary intellectual ability. His parents, recognizing his talent, nurtured his academic interests. Nash’s advanced understanding of mathematics led him to take college-level courses while still in high school.

Academic Prodigy at Carnegie and Princeton

Nash’s academic prowess continued to flourish at the Carnegie Institute of Technology, where he completed both a bachelor’s and a master’s degree in mathematics by the age of 19. His remarkable abilities were encapsulated in the succinct recommendation from his adviser, attesting to his “mathematical genius.”

Groundbreaking Work at Princeton

Nash’s time at Princeton University was pivotal. His doctoral dissertation, “Non-Cooperative Games,” was a mere 28 pages but laid the groundwork for modern game theory. The Nash equilibrium, a concept introduced in this work, transformed the understanding of decision-making processes in economics, where multiple actors with conflicting interests are involved.

Professional Life and Mental Health Struggles

Nash’s professional tenure at the Massachusetts Institute of Technology and his work as a codebreaker for the U.S. government were marked by his developing symptoms of mental illness. Diagnosed with paranoid schizophrenia, Nash’s life took a turn as he faced immense personal challenges. Despite these struggles, his intellectual contributions continued, and he resumed his academic career at Princeton.

Nobel Prize and Recognition

In 1994, Nash’s groundbreaking work was recognized with the Nobel Prize in Economics. This accolade brought his contributions to a wider audience, bridging the gap between abstract mathematical theories and practical economic applications.

Cultural Impact and “A Beautiful Mind”

Nash’s life story, marked by both triumph and adversity, was vividly captured in Sylvia Nasar’s biography “A Beautiful Mind” and the subsequent Academy Award-winning film. These works brought Nash’s story and the complexity of his theories to a global audience, making Nash a household name.

A Tragic End and Enduring Legacy

John Nash’s life tragically ended in a taxi crash in 2015, soon after receiving the Abel Prize, one of the highest honors in mathematics. His death marked the loss of one of the most brilliant minds of the 20th century.

Nash’s work continues to influence a wide range of fields, from economics and mathematics to biology and political science. His legacy lives on through the Nash equilibrium, a concept that has become a fundamental tool in understanding complex systems where strategic interactions occur. John Nash remains a symbol of how intellectual prowess can overcome personal challenges and contribute to the broader understanding of our world.

Politics and Elections

Incredible story of john nash and his short phd thesis.

This is a story about John Nash, the famed mathematician who inspired the movie 'A Beautiful Mind,' and his 27-page-long PhD thesis. He altered our understanding of the world in a mere 27 pages and shaped a life that, while cut short, was long in its reach and profound in its influence.

The year is 1950. John Nash, a young graduate student at Princeton, submits his PhD dissertation. It’s not a voluminous work stretching into hundreds of pages, as one might expect from groundbreaking research. Instead, it consists of a mere 27 pages. Titled “ Non-Cooperative Games ,” this unassuming document would go on to revolutionize the field of economics and game theory. As such it eventually earned Nash the Nobel Prize in Economic Sciences in 1994.

A minimalist approach where less is more

Nash’s thesis was unique not just in its length, but also in its reliance on citations. Only two sources were cited in the entire document. The first was the 1944 seminal work “ Theory of Games and Economic Behavior ” by John von Neumann and Oskar Morgenstern, the book that essentially laid the foundation for game theory.

The second was an article titled “ Equilibrium Points in n-Person Games ” — authored by none other than John Nash himself. This deliberate selection hinted at Nash’s confidence in his original ideas and his audacity to let them stand almost solely on their own merit.

In academic circles, the importance of a thesis is sometimes measured by its length and the number of citations it carries. Nash defied this unwritten rule in a spectacular manner. It was as if he was saying, “ Here are my ideas; they stand on their own .”

The essence of Nash’s brilliance

What made Nash’s dissertation extraordinary was its concept of equilibrium in “ non-cooperative ” games. A significant departure from traditional theories that primarily focused on “ cooperative ” games where participants can make binding agreements.

His work argued that in any game involving two or more players, each with their set of strategies, there exists an equilibrium where each player’s strategy is optimal given the strategies chosen by everyone else.

This would come to be known as the “ Nash Equilibrium. ”

Nash’s theories extended well beyond economics. They found applications in various domains, including biology, political science, and even philosophy. They provided a robust analytical framework to understand how individual decisions in complex systems could ultimately result in a stable, balanced outcome.

Nash’s impact was far-reaching and profound

The magnitude of the impact of Nash’s work can be best understood by the accolades it received. In 1994, nearly five decades after he wrote his thesis, Nash was awarded the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel – Nobel prize for Economics . This prestigious recognition signified the immense influence and lasting relevance of his work.

While the 26 pages may have seemed trivial at the time, the depth and breadth of the ideas contained within were far from it. Many researchers and scholars have since built upon Nash’s principles, and his equilibrium concepts have become a standard teaching module in economics courses worldwide.

Paving the way for modern game theory

Before Nash, game theory was an interesting but limited field. His dissertation blew open the doors to various new interpretations and applications. For instance, Nash’s ideas are now routinely applied in everything from market economics to election strategies. You can find them in negotiations, and even evolutionary biology.

His theories are applied in fields as varied as artificial intelligence, where algorithms often use Nash equilibrium concepts for decision-making. They are visible to international politics, where countries apply non-cooperative game theories in diplomatic negotiations and strategy planning. His work even finds applications in evolutionary biology, as mentioned earlier, explaining survival strategies among different species.

A life fraught with challenges — genius, vulnerability and the enigma of recovery

John Nash’s mental health battles are commonly thought to have been a lifelong struggle. However, the truth, as explained by his biographer Sylvia Nasar, paints a more nuanced picture .

Nash experienced the onset of schizophrenia at age 30 and underwent treatment only up to age 40. After that point, he had what he described as “ aging out of it. ” Nash speculated that hormonal changes played a role in his recovery, a hypothesis that aligns with the principles of cognitive and behavioral therapies that help patients manage delusions rather than will them away.

Nash’s case was exceptional even among those with chronic schizophrenia. He was among the small fraction who experience spontaneous recoveries. Generally, only 8 to 10% of patience experience such recovery.

While his intellectual brilliance was undoubted, another underappreciated aspect of his life was the role his wife Alicia played in his recovery. As Nasar notes, Nash had a stable home and family to return to, providing a sanctuary of sorts that undoubtedly played a role in his well-being.

Hopes and recognition and the Nobel as a crowning achievement and a final cure

The Nobel Prize in 1994 wasn’t just a triumph of intellectual prowess; it served a dual role.

For Nash, the award was a recognition not just from the academic community but also a form of reintegration into a society, The same society that had perhaps distanced itself from him due to his mental illness.

According to Nasar, the Nobel “completed the cure” in the sense that Nash could re-enter a community that, despite years of estrangement, still held significance for him and to which he could contribute anew.

This external validation, while late in coming, offered a sense of closure and belonging. And that cannot be underestimated in understanding Nash’s multifaceted life journey.

The unshakable support of his family and the acknowledgment from a community that had once shunned him combined to provide a form of holistic recovery that is as awe-inspiring as it is rare. Nash’s story isn’t merely one of intellectual triumph but is equally a narrative about the resilience of the human spirit, underscored by the roles of love, belonging, and recognition.

A tale of two narratives — Hollywood vs. Reality

Nash’s life was depicted in the 2001 film “A Beautiful Mind,” inspired by Nash’s life. While the movie captured the essence of Nash’s genius and his battle with schizophrenia, it took several creative liberties.

One such discrepancy is the film’s portrayal of visual hallucinations, which Nash himself did not experience. Moreover, the movie chose to focus on the more dramatic aspects of his condition. At the same time it omitted significant elements of his personal life. For example, his divorce and eventual remarriage to Alicia.

What the film did accurately convey, however, was Nash’s resilience and the unwavering support he received from Alicia. It managed to humanize a man often perceived merely as a towering intellectual figure. It brought to light the everyday battles he fought against his own mind.

A final chapter

The story of John Nash and his wife Alicia took a heartbreaking turn on May 23, 2015. Just shortly after Nash had received the Abel Prize for his contributions to mathematics , the couple died in a car crash while returning home from the airport. It was a shocking and sudden end. Not just to a life marked by incredible highs and lows, but also to a love story that had withstood the test of time, illness, and even separation.

The news of their deaths reverberated across academic circles and beyond, offering a grim reminder of the unpredictability of life. At the time of his passing, Nash was still active in his work, never one to rest on his laurels. His death, therefore, served as a stark full stop to a career that had recently received another accolade, and a life journey that had been marked by extraordinary resilience.

The couple’s sudden departure was an unfortunate punctuation to an enduring narrative of love, perseverance, and intellectual curiosity. As much as Nash’s theories revolutionized economics and mathematics, his life story with Alicia provided a real-world testament to the power of human endurance and connection.

Though they left the world abruptly, the indelible marks both John and Alicia Nash made—on science, on perceptions of mental health, and on each other’s lives—endure as a testament to their shared journey. They may have departed, but their story continues to resonate, serving as a complex but ultimately inspiring legacy.

A lifetime of legacy in 27 pages and a life that stretched its bounds

In the grand arc of John Nash’s life, which was full and long, living to the age of 86, one can see echoes of the succinct but powerful document that made him famous.

His 27-page PhD thesis, “Non Cooperative Games,” was remarkable for distilling complex theories into an understandable, transformative format. Similarly, Nash’s long life was dense with accomplishments and challenges that transcended the years he lived.

While his life did stretch over eight decades, each chapter was marked by a density of experience. From the highs of academic achievements to the lows of mental health struggles, from the love and support of his family to the ultimate, tragic conclusion — each period of his life was as impactful as those concise 27 pages that first put him on the map.

The abrupt ending to Nash’s life was a cruel stroke of fate. However, in no way it diminishes the longevity or significance of his journey. If his thesis taught us that profound ideas don’t need a lot of space to make an impact, his life demonstrated that the impact of human existence isn’t solely measured by its length, but by its depth and the ripples it creates in the world around it.

John Nash did just that. Altered our understanding of the world in a mere 27 pages and shaped a life that, while cut short, was long in its reach and profound in its influence.

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John F. Nash

J ohn Nash, john harsanyi , and reinhard selten shared the 1994 Nobel Prize in economics “for their pioneering analysis of equilibria in the theory of non-cooperative games.” In other words, Nash received the Nobel prize for his work in game theory .

Except for one course in economics that he took at Carnegie Institute of Technology (now Carnegie Mellon) as an undergraduate in the late 1940s, Nash has no formal training in economics. He earned his Ph.D. in mathematics at Princeton University in 1950. The Nobel Prize he received forty-four years later was mainly for the contributions he made to game theory in his 1950 Ph.D. dissertation.

In this work, Nash introduced the distinction between cooperative and noncooperative games. In cooperative games, players can make enforceable agreements with other players. In noncooperative games, enforceable agreements are impossible; any cooperation that occurs is self-enforced. That is, for cooperation to occur, it must be in each player’s interest to cooperate.

Nash’s major contribution is the concept of equilibrium for noncooperative games, which later came to be called a Nash equilibrium. A Nash equilibrium is a situation in which no player, taking the other players’ strategies as given, can improve his position by choosing an alternative strategy. Nash proved that, for a very broad class of games of any number of players, at least one equilibrium exists as long as mixed strategies are allowed. A mixed strategy is one in which the player does not take one action with certainty but, instead, has a range of actions he might take, each with a positive probability.

A simple example of a Nash equilibrium is the prisoners’ dilemma . Another example is the location problem. Imagine that Budweiser and Miller are trying to decide where to place their beer stands on a beach that is perfectly straight. Assume also that sunbathers are located an equal distance from each other and that they want to minimize the distance they walk to get a beer. Where, then, should Bud locate if Miller has not yet chosen its location? If Bud locates one-quarter of the way along the beach, then Miller can locate next to Bud and have three-quarters of the market. Bud knows this and thus concludes that the best location is right in the middle of the beach. Miller locates just slightly to one side or the other. Neither Bud nor Miller can improve its position by choosing an alternate location. This is a Nash equilibrium.

Nash’s other major contribution is his reasoning about “the bargaining problem.” Before Nash, economists thought that the share of the gains each of two parties to a bargain received was always indeterminate. But Nash got further by asking a different question. Instead of defining a solution directly, Nash asked what conditions the division of gains would have to satisfy. He suggested four conditions and showed mathematically that if these conditions held, a unique solution existed that maximized the product of the participants’ utilities. The bottom line is that how gains are divided depends on how much the deal is worth to each participant and what alternatives each participant has.

As readers of Sylvia Nasar’s biography of Nash, A Beautiful Mind, know, Nash contended with schizophrenia from the late 1950s to the mid-1980s. As Nash put it in his Nobel autobiography, “I later spent time of the order of five to eight months in hospitals in New Jersey, always on an involuntary basis and always attempting a legal argument for release.” His productivity suffered accordingly. But he emerged from his mental illness in the late 1980s. In his Nobel lecture, Nash noted his own progress out of mental illness:

Then gradually I began to intellectually reject some of the delusionally influenced lines of thinking which had been characteristic of my orientation. This began, most recognizably, with the rejection of politically-oriented thinking as essentially a hopeless waste of intellectual effort. 1

About the Author

David R. Henderson is the editor of  The Concise Encyclopedia of Economics . He is also an emeritus professor of economics with the Naval Postgraduate School and a research fellow with the Hoover Institution at Stanford University. He earned his Ph.D. in economics at UCLA.

Selected Works

Related links.

Vernon Smith on Markets and Experimental Economics , an EconTalk podcast, May 21, 2007.

Ariel Rubenstein on Game Theory and Behavioral Economics , an EconTalk podcast, April 25, 2011.

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Read John Nash’s Super Short PhD Thesis with 26 Pages & 2 Citations: The Beauty of Inventing a Field

in Math | June 1st, 2015 1 Comment

Last week  John Nash , the Nobel Prize-win­ning math­e­mati­cian, and sub­ject of the block­buster film A Beau­ti­ful Mind , passed away at the age of 86. He died in a taxi cab acci­dent in New Jer­sey.

Days lat­er, Cliff Pick­over high­light­ed a curi­ous fac­toid: When Nash wrote his Ph.D. the­sis in 1950, “Non Coop­er­a­tive Games” at Prince­ton Uni­ver­si­ty, the dis­ser­ta­tion (you can read it online  here) was brief. It ran only 26 pages. And more par­tic­u­lar­ly, it was light on cita­tions. Nash’s diss cit­ed two texts: One was writ­ten by John von Neu­mann & Oskar Mor­gen­stern, whose book,  The­o­ry of Games and Eco­nom­ic Behav­ior   (1944), essen­tial­ly cre­at­ed game the­o­ry and rev­o­lu­tion­ized the field of eco­nom­ics; the oth­er cit­ed text, “Equi­lib­ri­um Points in n‑Person Games,”  was an arti­cle writ­ten by Nash him­self. And it laid the foun­da­tion for his dis­ser­ta­tion, anoth­er sem­i­nal work in the devel­op­ment of game the­o­ry, for which Nash won the Nobel Prize in Eco­nom­ic Sci­ences in 1994 .

The reward of invent­ing a new field, I guess, is hav­ing a slim bib­li­og­ra­phy.

Relat­ed Con­tent:

A Brilliant Madness — 2002 Film on the Nobel Prize Winning Mathematician" href="http://www.openculture.com/2012/06/john_nash_ia_brilliant_madnessi.html" rel="bookmark">John Nash: A Bril­liant Mad­ness — 2002 Film on the Nobel Prize Win­ning Math­e­mati­cian

The Short­est-Known Paper Pub­lished in a Seri­ous Math Jour­nal: Two Suc­cinct Sen­tences

The World Record for the Short­est Math Arti­cle: 2 Words

Free Online Math Cours­es

by OC | Permalink | Comments (1) |

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Comments (1), 1 comment so far.

This was shock­ing to know about the demise of John Nash. I had a chance to view the film “a beau­ti­ful mind” with a close friend, Steve Land­fried in Wis­con­sin-Chica­go where John Nash was a sub­ject of this film. I am glad that Steve made this choice for me since I could see and feel all, that this mag­ni­fi­cient sci­en­tist had gone through.This is still my favorite film because of its sub­ject

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Year 91 – 1951: “Non-cooperative Games” by John Nash, in: Annals of Mathematics 54 (2)

Posted on April 7, 2011 in All years , Uncategorized

Over the past 60 years, game theory has been one of the most influential theories in the social sciences, pervasive in economics, political science, business administration, and military strategy – the disciplines most consulted by the powers-that-be for “real-world,” high-stakes decisions. But just as there would be no semiconductors or (God forbid) laser pointers if not for the abstruse mathematics of quantum theory, game theory can be traced back to theoretical work by academic mathematicians. In a set of papers in the 1950s, mathematician John Forbes Nash set forth breakthrough ideas that helped transform game theory from an ivory tower abstraction into an indispensable analytical tool used by strategists from Wall Street to the Pentagon.

The foundational game theory work of mathematician John von Neumann and economist Oskar Morgenstern, published in 1944, provided a framework for solutions to zero-sum games, where one player’s win was the other’s loss. Nash, in his dissertation research at Princeton (published in this and three other papers), extended game theory to n -person games in which more than one party can gain, a better reflection of practical situations. Nash demonstrated that “a finite non-cooperative game always has at least one equilibrium point” or stable solution. This result came to be called the “Nash equilibrium,” a situation where no one player can get a better payoff by changing strategies, so long as other players also keep their strategies. Using Nash’s framework, predictions can be made about the outcomes of strategic interactions.

Based on Nash’s advances, game theory developed into one of the pre-eminent tools of economics in the second half of the 20th century. In recognition of his breakthrough work, Nash was joint recipient of the Nobel Prize for Economics in 1994 for “pioneering analysis of equilibria in the theory of non-cooperative games.”

If visions of Russell Crowe have danced in your head while you’ve been reading this post, that’s probably because you remember that Crowe played John Forbes Nash in the 2001 film A Beautiful Mind (at least we hope that’s why). Part of the movie takes place at MIT, portraying Nash’s years as an instructor in mathematics at the Institute, where he worked from 1951 to 1959, until mental illness curtailed his mathematical career.

Find it in the library

John F Nash PhD

Project Details

In this page you can find Nash’s PhD thesis:

• Original document
• Transcribed into tex/pdf *

*: Thanks to Rebeca Duarte Miguel for this, and to Jeek Midford for spotting some spelling mistakes.

Others form category

List of Experimental Economic Labs of the world

Game Theory Online Tools

Game Theory Society

Experiments on SciOn

Game Theory Nobelists

Software for Experiments

Online courses about Game Theory

GT in the media

Top 10 Game Theorists on Google Scholar

ETH Controversies Workshops

Modellbildung: Game theory and strategic interaction

Game Theory Movie

SciTech Tuesday: John Nash and the Legacy of WWII

One of the hallmarks of the war effort during WWII was the use of intellectual capital. The Manhattan Project and other efforts brought together the best minds to solve big problems. With the end of the war, there was fear that the military and intelligence communities would lose all that intellectual capital.

Think-tanks like RAND (started by Douglas Aircraft Corporation) aimed to continue big science after the war. Tension with the USSR and the Soviet development of weapons so close to the war’s end fueled the fear.

John Nash was born in 1928, and so passed his teenage years in wartime West Virginia. He was a gifted student, who attended Carnegie Institute of Technology (now Carnegie Mellon University) on a merit scholarship. Nash graduated at the age of 20 with both Bachelors’ and Masters’ degrees, and headed to Princeton with this succinct recommendation from his advisor: “This man is a genius.”

Besides inventing a game that swept Princeton math’s common room, and later became Parker Brothers’ Hex, Nash wrote a dissertation called ‘Non-Cooperative Games’ in which he framed negotiation in a context that allowed prediction of benefits to parties and thus outcomes. Nash provided a way to analyze outcomes that did not require zero-sum calculations. The Nash Equilibrium, formally stated in that dissertation, won John Nash the Nobel Prize for Economics in 1994.

This advance in concept and mathematics revolutionized economics, and provided a theory for branches of evolutionary biology and other fields, where it is still influential today.

After taking only 2 years to complete his doctorate from Princeton, Nash was recruited to work for RAND. RAND was very interested in analyzing outcomes of competitive situations–for obvious reasons. His restless mind and desire for collaboration led him to stay at RAND only briefly. He accepted a position at the Massachusetts Institute of Technology in 1951, and worked at RAND as a consultant until 1954.

Nash had always been odd–persistently whistling the same bars from Bach, and leaving equations on the boards in empty classrooms–but a year after he received tenure from MIT, it was clear he was suffering from schizophrenia. His paranoid delusions were filled with spycraft and details from his time at RAND. They were influenced also by the cryptography work he had done over the first years of his time at MIT. Alicia Nash, an MIT physics graduate who had married John Nash in 1957, admitted him to a psychiatric hospital, in 1959, and gave birth to his son a few weeks later.

Nash was seriously ill with schizophrenia until 1970, living under delusions of voices of persons involving espionage and secrecy. He began to recover when he left those visions behind. Decades later his reputation as a mathematician was rehabilitated, and his relationship with his wife was tool. They had divorced in 1963, but she had supported him in the 1970s as he worked to recover. In 2001 they remarried.

Sadly, the couple died last week, on May 23rd. They had landed at Newark on a return flight from Norway, where John Nash had received the Abel Prize. The taxi in which they were riding on the New Jersey Turnpike struck the guardrail, and they were ejected from the car. John was 86 and Alicia was 82.

Post by Rob Wallace, STEM Education Coordinator

The beginning of John Nash’s dissertation.

• Posted : Tuesday, June 2nd, 2015 @ 8:45 am
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