Thursday, 14 May 2015

After tragic death, John Nash's game theory lives on

John Forbes Nash Jr, the Princeton University mathematician who shared a Nobel Prize in 1994, was killed with his wife in a car crash on Saturday.

Mr Nash, 86, and Alicia Nash, 82, were in a taxi when the incident occurred, according to New Jersey police reports. The vehicle lost control trying to pass another car. The couple was pronounced dead at the scene.

The fiercely intelligent Mr Nash, who inspired the movie “A Beautiful Mind” was widely regarded as one of the greatest economics and mathematics minds of the 20th Century.

His pioneering equations created during the Cold War was integral to keeping the United States and the Soviet Union from war, as well as a foundation for a wider socio-political theory of human society which would impact the modern world in revolutionary ways.

The film, which stared Russell Crowe, was highly regarded by movie critics and yet also considered “historical revisionism” by those who knew Mr Nash and by independent historians. A Beautiful Mind focused on Mr Nash’s apparent paranoid schizophrenia while paralleling his Nobel Prize-winning economics achievements.

Perhaps the most important insight to come from his long career was his formalisation of the concept known today as game theory – the mathematics of decision-making.

While working for the RAND Corporation, Mr Nash developed ideas based on a vision of humans as driven by only self-interest and as being continually distrustful of others. Left to their own devices, humans could be expected to pursue their own ends – an insight with potentially terrible consequences for the two great Cold War belligerents.

The theory of games
Mr Nash thought he could stabilise this self-interest not just in the geopolitical arena but also in human society. The mathematician worked on a series of experimental games called “FUCK YOU BUDDY” in which the only way to win was to calculatedly and brutally betray one’s partner.

In order for game theory to work, Mr Nash had to presume regular humans behaved in exactly the same way as the policy-makers and military leaders involved in the intercontinental nuclear standoff. Hs ideas assumed that humans constantly monitor each other in a life-long tussle to achieve their own selfish ends.

Employing the equations which eventually won him the Nobel Prize, Mr Nash showed that a system driven by suspicion and self-interest did not have to lead to chaos. His games proved there was an equilibrium point at which everyone’s self-interest was balanced against everyone else’s.

Mr Nash was recorded as saying normal people “seek optimisation like poker players”. The key was that all players must behave selfishly for the balancing to work. Despite what more optimistic social scientists believed at the time, the theory suggested that cooperation would mean the games became predictable and dangerous.

This game was officially called the “Prisoner’s Dilemma”, and many versions were invented after the first experimental iterations. Perhaps the most famous was the game show called “Golden Balls

The Library of Economics and Liberty describe the Prisoner’s Dilemma as the “best-known game of strategy in social science”.

“In the traditional version of the game, the police have arrested two suspects and are interrogating them in separate rooms. Each can either confess, thereby implicating the other, or keep silent. No matter what the other suspect does, each can improve his own position by confessing.

“If the other confesses, then one had better do the same to avoid the especially harsh sentence that awaits a recalcitrant holdout. If the other keeps silent, then one can obtain the favourable treatment accorded a state’s witness by confessing. Thus, confession is the dominant strategy for each. But when both confess, the outcome is worse for both than when both keep silent.”

How game theory grew
In the Cold War, his equations intriguingly helped show that any hope of both the Russians and the Americans mutually giving up their nuclear weapons, so long as the other side followed suit, could never happen. Unfortunately for world peace, neither was able to trust the other not to cheat.

Yet while the predictions for nuclear conflict might have appeared more pessimistic, there was a strange logic in Mr Nash’s theories which kept the Cold War frozen. No nuclear exchange occurred during the decades of standoff, although it is still unclear whether game theory was integral to this outcome.

Nevertheless, social scientists used Mr Nash’s theory to explain how the rest of human society operated. Politicians also loved his ideas because it showed that society could exist based on individual freedom and that it wouldn’t devolve into chaos as some had suspected.

One consequence meant this reinvigorated idea of freedom encouraged citizens to be suspicious and distrustful of everyone else if the system of political organisation was going to work.

Before Mr Nash’s theories entered public consciousness, most politicians were worried a society fundamentally based on self-interest would lead to chaos. But these new game theory equations proved the fear might be misguided.

In the real world however, the Prisoner’s Dilemma doesn’t quite operate to the extent Mr Nash hypothesised. Rather than betray each other, as the equations suggest participants will, human players tend to trust each other and generally end the game by choosing cooperation.

Despite the conflicting trials with human subjects – and the eventual recognition that the mathematician suffered from paranoid schizophrenia by which he was intensely distrustful of people – Mr Nash’s ideas quickly percolated through Cold War politics in the United States.

New society of order
His game theory equations helped set up a new ordering of society in the mid-20th century based on the foundational concept of individual freedom. Those ideas were not from Mr Nash, rather they emerged from the thinking of Austrian-born Friedrich von Hayek in the 1940s and 1950s.

Mr Nash’s ideas have been influential beyond the mathematical sphere and many who attended Princeton University and studied under the Nobel Prize winner remember him as an inspiring person. Others who interacted with Mr Nash recall him as prickly and difficult to work with.

Mr Nash’s schizophrenia symptoms eventually faded in the late 1970s as his condition slowly improved. He also helped activists organise new legislation for mental health in the United States by being open about his illness and from his position as a mathematics celebrity.

He is survived by his two sons, John David Stier and John Charles Martin Nash, and a sister, Martha Nash Legg.

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