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<b>Madhav Raghavan:</b> The world needs a new Nash equilibrium

The most famous concept in game theory will live forever. But economics has diversified and the stage is set for the 21st century. We just need a new Nash

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Madhav Raghavan
Last Updated : May 25 2015 | 9:41 PM IST
With the tragic death of John Forbes Nash, Jr, in a New Jersey road accident on May 23, 20th century free-market economics has lost its last heavyweight. Though to be fair to him, Nash never actually entered the ring.

Nash was a once-in-a-generation game-changer. His mathematical work is timeless. But his contribution to economics is best appreciated in its 20th century context.

The Cold War era was a profound time for economics. In America, where combating the Soviet Union was paramount, the battleground was often as not the economic order.

As a result, economists such as Milton Friedman, Paul Samuelson, Gerard Debreu, Kenneth Arrow and Friedrich Hayek made their name by arguing that there was no better economic system than the free market.

But simply claiming that the West is the best was not enough. It had to be backed by an unassailable argument. Nash's mathematical work provided the basis for a lot of it.

The premise of the free market is instantly recognisable - individual freedom, individual rights and the sparing use of the state. It is no coincidence that this is exactly the opposite of the communist way.

But stating a simple and compelling idea, and delivering a full-fledged theory are two very different things. The success of the free-market programme eventually came down to finding solutions to two knotty problems.

The first was how to enshrine individual liberty into the very foundations of the economic order. The second was how to aggregate individual activity into a market system strong enough to crush the scourge of communism.

Take the first. The logical conclusion of individual liberty is that people will be free to do whatever they want, within the law. To build a world order based on this involves first showing that this would not lead to chaos.

That is, it had to be shown that even if everybody were to single-mindedly pursue their own self-interest ('maximise their individual utility', in the jargon), the collective could remain predictable, benign and desirable.

Enter the most famous concept in game theory: the Nash equilibrium.

In his PhD thesis, a 27-page masterpiece, which is the envy of PhD students even today, Nash showed that even if everybody behaved selfishly, the collective would remain tractable. There would always be a unique outcome, the chief characteristic of which was that nobody would gain from altering the strategy that led to it.

Thus, the Nash equilibrium put non-cooperation (selfishness) on a firm footing. Later, economists extended this concept into what they called the Nash programme: namely, the reduction of cooperative situations into their non-cooperative equivalent, which could then be solved via Nash's procedure.

Suddenly, everything became a game - a non-cooperative game to boot - and every game had one solution: the Nash equilibrium (or a close variant). Over the past 50 years, this has provided research livelihoods to many economists, myself included.

It was also a major ideological achievement in the fight against communism. But by itself, it would not be sufficient. For that, the role of the state needed undermining.

That is, it remained to be demonstrated that the state was not needed to provide aggregate coordination or allocation of resources - that the free market could handle everything. This was the second knotty problem.

For nearly 200 years, the free-market answer to coordination was the invisible hand. Adam Smith argued in 1776 that if everybody pursues their own self-interest, the needs of society will automatically be met. "It is not from the benevolence of the butcher, the brewer, or the baker, that we expect our dinner, but from their regard to their own interest."

This argument culminated in the 20th century, with Arrow and Debreu, in the technically masterful (and impossibly abstruse) general equilibrium theory. But they couldn't have done it without the technical methods used by Nash.

In particular, the proofs used the concept of the fixed-point theorem, which is the mathematical equivalent of a vortex of water, in which an object will inexorably be pulled to the unique, static centre. This is the basis of the proof of the Nash equilibrium.

The Nash equilibrium will live forever. But since the collapse of the Soviet Union, economics has diversified. Many of the foundational assumptions of neoclassical economics are no longer taken for granted.

For example, individuals are no longer assumed to be rational all-calculating automatons. The state is no longer assumed to be entirely a bad thing. What's more, the financial crisis has yet again called into question the viability of free (unregulated) markets.

At the same time, the American order is being assailed by the rise of China, which has presented the world with an alternative, state-heavy model of government. This also seems to work quite well.

With both the foundations under question and the edifice under attack, Western economic thought needs a new foundation. So, too, does the model of "socialism with Chinese characteristics", if it is to establish its primacy.

The stage is set for the 21st century. We just need a new Nash.
Madhav Raghavan is a PhD candidate at the Indian Statistical Institute, New Delhi, and specialises in matching theory

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Disclaimer: These are personal views of the writer. They do not necessarily reflect the opinion of www.business-standard.com or the Business Standard newspaper

First Published: May 25 2015 | 9:28 PM IST

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