John Nash, RIP

John Nash and his wife died yesterday in a car accident.

CNN: Nash, who won the Nobel Prize for Economics in 1994, was known for his work in game theory, and his personal struggle with paranoid schizophrenia. His life story inspired the 2001 Oscar-winning film “A Beautiful Mind” starring Russell Crowe and Jennifer Connelly as the Nashes.

Nash’s 27 page dissertation would eventually win him a Nobel prize in economics. Nash’s dissertation extended von Neumann and Morgenstern’s theory of games from cooperative, bargaining-type solutions to non-cooperative solutions in which each player is assumed to act in their self-interest and in so doing made the theory tremendously more relevant to economics, business, political science, and even theories of animal behavior and evolution.

Here is further background on Nash’s work in game theory. Here is the PBS documentary A Beautiful Madness with lots of links to interviews and further explanations of his work and influence.


I was going to write this in the comments, but I assumed correctly you were preparing an appropriate eulogy.

Nash's seminal paper was indeed worthy of praise, but do you think that this one paper for pioneering analysis on non-cooperative equilibria would have been sufficient today to earn this award?

I don't mean this to demean Nash, but rather to inquire whether, like publications, the bar has been raised. I suspect that there are modern economists who have published more sophisticated models that haven't been seminal and hence not worthy of a Nobel. Was Nash picking low hanging fruit with this paper?

I have never seen a low-hanging fruit argument that wasn't circular.

Please explain?

Do you mean that at any given point in time, the "easiest" stuff is hard?

I used to believe that, but then I read Newton and realized he would have done well in a Math PhD program today. I'm sure Nash would do equally as well, but this first paper isn't sufficient for that.

The sophistication of a theorist isn't that strong an indicator of the intellectual importance of that theorist. If anything, sophistication is anti-correlated with importance.

There were, for instance, incredibly sophisticated Ptolemaic models of epicycles built on epicycles to explain the motions of the stars and planets. But Copernicus had an idea that upended all of that, despite its simplicity and the fact that at the beginning, it was actually less accurate than the sophisticated Ptolemaic models.

The "easy stuff hard" idea is important. Later genrations use analytical tools that were only formless intuitions in the minds previous generations. Sometimes when I read (moderately) old but famous physics papers, they quaintly explain in a paragraph plain English what could be aluded to in half a sentence of modern jargon.

But of course that paragraph goes to show that they understood the problem at hand more deeply than I ever will, precisely because they had to deal with it in on its own terms land not as a special case of something they learned about in school.

A lot of ground breaking work appears obvious once someone has done it. The genius comes in seeing it before someone else has trod the way. It's more an act of creativity to spot the opportunity than raw intellectual horsepower to push ahead.

The point is not the sophistication of the models Nash studied (his only example in the dissertation being a 3-player version of poker), the point is that the concept of Nash equilibrium is used in nearly all papers on game theory. He found just the right idea for what solution concept should be used, and as a bonus managed to prove existence in a large number of cases.

As for whether the fruit was low-hanging, it is worth considering that game theory had been studied for a number of years when Nash wrote his paper and no one had had the idea before him.

von Neumann and Morgenstern did in fact study noncooperative games and their equilibria (to which Nash's name had not yet become attached, of course).

Does anyone have a link to a more legible copy of the dissertation?

Appears a Spanish professor in artificial intelligence, Ulises Cortes, has a pdf on his website.

Is that the shortest PhD dissertation ever? Or do other geniuses beat the 27 page mark?

I drove by the crash scene last night. It was on the inner lanes of the NJ Turnpike. They needed a crane to lift the taxi because it was so mangled.

Wonder what the details were.

Knowing that it was NJ plus a taxi "reckless driving" would not be too bad a guess?

I'd venture to say the driver is a recent immigrant from a nation where aggressive driving is the norm. I'm not dissing immigrants (I am one myself, sort of) but that is all who appears to be driving our taxis nowadays.

Sounds like a reasonable guess. Like whenever a plane crashes it is very likely that the human error was white.

I'd also venture to guess the driver was very tired from long hours behind the wheel.

Correction: Nash won the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, not the Nobel prize in economics. There is no Nobel prize in economics.

Nor is there one for supercilious pedantry... So you'll have to wait for Ikea to create one.

Naw - Ikea's founder was a fascist, so he would be much more likely to fund an average is over type of award, something pioneering.

Maybe it could be the Volkswagen Prize of Nazi Pedantry.

What's pedantic about pointing out a counterfeit?

There is no one on this blog who doesn't know there us no actual Nobel Prize in economics. There is also no one here who doesn't know the prize is just as meaningful as all the genuine ones initiated by the dynamite salesman.


Thanks for the information.

There is no need to be sarcastic.
Just because you know that something is a misconception doesn't mean that it should not be corrected.
This also applies to Jonathan's needlessly insulting comment.

Given that (a) the distinction of prize name has no practical importance and (b) the dude is freshly dead, I think Bernard and Jonathan were remarkably restrained.

At this point the number of idiots pointing this out is getting tiresome. This is usually posted sneeringly by idiots who think that the original Nobels have some sort of holy status and think that economics is an inferior form of study. I say that the quality of a prize and its reputation are proportional to the quality of its selections. By that standard the Econ Memorial Nobel is a top three or four Nobel while the Lit prize is too quirky to be taken seriously and the Peace Prize is a genuine embarrassment -- often violating the Nobel rule still adhered to by the others that no more than three individuals may share the prize.

Certainly I am willing to bet a large sum of money that posterity will treat the average winner of the econ Nobel more seriously than the average winner of either the Peace of Lit prizes which have both looked rather myopic in hindsight -- especially if we start counting up those who were denied the prize.

Pointing out there is no actual Nobel Prize in Economics is similar to the people who tell us the unemployment rate doesn't actually count everyone who is unemployed, and hold up U-6 like they just shat a lump of gold.

If the name has no 'practical importance' then why the fuck do the bloggers here invariably conflate the '1969' Prize with the original?

You [and they] can't have it both ways.

Because the fuck it's a convenient fucking shorthand, fucker. Like talking about the fucking constitution when you also include all these fucking amendments. Clear? Sheeeeit.

You're pedantic but wrong. Now, do something useful.

Of course :-)

I saved that pdf file to my evernotes and it was a unexpectedly hallowing experience writing out every relevant tag so I could search for this later. What a rich mathematical development, almost "overlooked" at the time that spawned or expanded so many relevant fields.

"Game theory and the decision of couples to wear their seat belts"

What an ironic coincidence ! Interesting that there is a such lower probability of bothmaking different decisions on buckling up.

I've never worn a seat belt in a cab. Most people in back seats don't. I'm not sure why the treatment is remarkably different than front seats, but it is.

I think back seat belting is mostly more uncomfy than front.

Nash's game theory paper pales in comparison with his extraordinary work in partial differential equations and differential geometry.
Gromov, one of the leading contemporary geometers, writes "What he has done in geometry is, from my point of view, incomparably greater than what he has done
in economics, by many orders of magnitude." (
Nash proved in particular that every Riemann manifold can be isometrically embedded into Euclidean space, and also that real-analytic manifolds can be analytically embedded into numerical space R^n.
He would probably have received a Fields medal if it weren't for the fact that Thom was to be given one in the same field, differential topology, in 1958.
Fortunatly he received the Abel prize in March 2015, just as Gromov did in 2009 (and the average quality of the recipients of that prize is higher than that of the Fields medal, even if journalists have not yet found out and go on pontificating that the Fields medal is the mathematicians' Nobel prize).

Here is a link to a fine book on Nash, including nine of his most important papers :

Appropriate comment, Attila, and indeed Nash himself denigrated his dissertation result as being relatively trivial mathematics compared to his other work and interests (those that were more or less sane, at least). Obviously it has been the applications by economists of his most important game theory result that has made it the focus of public attention (as well as his visit to Stockholm to shake the hand of the Swedish king, with whom he reportedly shared an interest in racing cars).

A sign of the ongoing decline of the Washington Post is that in its front page story on Nash's death it was claimed that he developed cooperative game theory as well as non-cooperative as an advance over the work of von Neumann and Morgenstern. It is true the VnM and some others dealt with non-coop games (with Borel the really truly underrated and ignored figure here working prior to VnM), but none of them solved or proved the equilibrium found by Nash.


I love the bibliography page of the Ph.D dissertation.

Have you seen this:

Synopsis (from Wikipedia):
In this episode, Curtis examines the rise of game theory used during the Cold War and the way in which its mathematical models of human behavior filtered into economic thought.

The program traces the development of game theory with particular reference to the work of John Nash (famous from "Beautiful Mind"), who believed that all humans were inherently suspicious and selfish creatures that strategized constantly. Using this as his first premise, Nash constructed logically consistent and mathematically verifiable models, for which he won the Nobel Prize in Economics. He invented system games reflecting his beliefs about human behavior, including one called "So Long Sucker---F*ck Your Buddy", in which the only way to win was to betray your playing partner, and it is from this game that the episode's title is taken. These games were internally coherent and worked correctly as long as the players obeyed the ground rules that they should behave selfishly and try to outwit their opponents, but when RAND's analysts tried the games on their own secretaries, they instead chose not to betray each other, but to cooperate every time. This did not, in the eyes of the analysts, discredit the models, but instead proved that the secretaries were unfit subjects.

What was not known at the time was that Nash was suffering from paranoid schizophrenia, and, as a result, was deeply suspicious of everyone around him”including his colleagues”and was convinced that many were involved in conspiracies against him. It was this mistaken belief that led to his view of people as a whole that formed the basis for his theories. Footage of an older and wiser Nash was shown in which he acknowledges that his paranoid views of other people at the time were false.

Curtis examines how game theory was used to create the USA's nuclear strategy during the Cold War. Because no nuclear war occurred, it was believed that game theory had been correct in dictating the creation and maintenance of a massive American nuclear arsenal—because the Soviet Union had not attacked America with its nuclear weapons, the supposed deterrent must have worked and the theories would later be propagated through other segments of society.

I have not listened to the link, but the summarized account here is off in various respects, even if Phil Mirowski likes to say that the Nash equilibrium reflected his paranoid schizophrenia. The hard fact is that his illness came on some years after he stopped working on game theory. It is true, however, that he strongly felt that rational people should not cooperate and should follow the strategy assumed in his equilibrium

Indeed, the more important event at RAND was the initial round of Prisoner's Dilemma experiments by Dresher and Flood there, repeated 100 round games with economist Armen Alchian being the one who held out following the Nash strategy longer than a mathematician who considered him and idiot for doing so. Nevertheless, even Alchian cooperated eventually (with reversion to Nash strategy at the end of the rounds). It was observing these experiments that so upset Nash that he stopped working on game theory and went back to worrying about Riemann and all that. Ironically, a bit later it would be his own major prof, the late W. Albert Tucker, who would coin the term "prisoner's dilemma" when recounting the Dresher-Flood experiments to an audience at a meeting at Stanford of the American Psychological Assocation.

And as for nuclear strategy, the hardest liner of them all was that great exponent of cooperative game theory, John von Neumann, whose view of the Soviets was that if it was a good thing to nuke the Soviets at 5 this afternoon, it was even better to do so at 1 this afternoon., or something like that, in any case, the sooner the better.

Nash's major prof was the late Albert W. Tucker, not "W. Albert Tucker." He indeed was the Tucker of the Kuhn-Tucker theorem.

And as for nuclear strategy, the hardest liner of them all was that great exponent of cooperative game theory, John von Neumann, whose view of the Soviets was that if it was a good thing to nuke the Soviets at 5 this afternoon, it was even better to do so at 1 this afternoon., or something like that, in any case, the sooner the better.

What a great man John von Neumann was. It ought to be obvious to the most naive little waif that RAND secretaries are not General Secretaries of the Soviet Union. So that games played by nice middle class girls who have not murdered millions of people are probably poor predictors of how games might be played by people who have.

You may think you are very amusing or even insightful, SMfS, but Dresher and Flood were very far from being either "RAND secretaries" or "nice middle class girls.." Von Neumann was arguably the most brilliant mathematician of the 20th century, at least for certain parts of math, but he was also in many ways somewhat of an awful, if fascinating, person.

I have no idea what I think. But my comment referred to Patrick's comment:

but when RAND’s analysts tried the games on their own secretaries, they instead chose not to betray each other, but to cooperate every time.

I did not refer to either Dresner or Flood as secretaries.

Most great mathematicians are difficult people. But von Neumann was right about the Soviet Union. If only America had used its nuclear monopoly when it had it to stop the spread of Communism. Millions of people would still be alive. Tens of millions. This is undeniable.

Does anyone know, was it an Uber car or a regulated taxi that he was riding in?

A more curious question may be whether or not his and his wife's failure to attach the seat belts in the vehicle was simply a matter of laziness or irrational discounting of the risks involved or an expression of his apparently pro-libertarian sentiments to protest seat belt laws. Obviously we shall almost certainly never know the answer to that one.

But if there is any good to this sad event, it may well be to highlight to people that they really should fasten their seatbelts in cabs and other vehicles. Just within the last few days I was in a cab with several people with one of them declaring that it was not necessary or important to do so. I disagreed and attached mine, despite getting mildly ridiculed for doing so. And this was in Corsica, where the roads are winding and the drivers are somewhat wild.

Why couldn't it be rational discounting? At 86 maybe it wasn't that great a relative risk.

Comments like these are why I like you so much.

Ought to start blogging for you entertainment. :)

I'm pretty sure taxi passengers are not required to wear seat belts - though maybe children are in some areas.

Perhaps it was simpler than that - perhaps he was trying to force the driver to drive more slowly? He has very little means to make the driver change his behavior so perhaps he decided that he would raise the stakes in the event of an accident by not wearing a seat belt. That should have forced the driver to reconsider his priors and the costs associated with his speed. This rather simple non-co-operative game just didn't work out that well.

But as you say, we shall never know.

Knowing their age demographic I'd say not a Uber car.

I doubt that it is relevant whether this was an Uber car or a regular taxi. Dragging that into this is just silly.

No one is reading anything more into it.

Does anybody wear seat belts on buses (the kind that run from DC to NY)?

I've never seen seat belts on US buses I've traveled on.

Seatbelts are very unlikely to save you from death or injury on a large bus, even assuming you got everyone to wear one. The mass of the bus means that the riders of whatever hits or is hit by the bus had better have one on, though.

Seatbelts may not have mattered for this taxi given the gruesomeness of the crash described by a commenter above.

And given all the various ways of fading out ignominiously, dying suddenly with your loved one in a crash is not the worst way to go.

Perhaps forgoing a seatbelt did not seem so irrational after all. Considering how much time by age 86 one has wasted fastening seat belts unnecessarily combined with the reduced utility of the remaining lifespan.....

They may have also implicitly wanted to die together. John and his wife I mean.

Sudden car crash versus two years in the hospice. I wonder what most 86 year olds would choose.

They may. Or they may not. They married in 1957. Nash was granted tenure in 1958. He resigned in 1959 and his wife had him committed. She divorced him in 1963. He was awarded the "Nobel" prize in 1994. She married him again in 2001.

Rahul, not many hospices will allow you to stay for two years. But we know the answer to this question. Most 86 year olds can manage to arrange an accident. Most die in a hospice or the like. Life is tenacious.

And on a much less well known side of John Nash, .

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