Economics brief: six big ideas.
Game theory: Prison breakthrough
The fifth of our series on seminal economic ideas looks at the Nash equilibrium.
JOHN NASH arrived at Princeton University in 1948 to start his PhD with a one-sentence recommendation: “He is a mathematical genius”.He did not disappoint.Aged 19 and with just one undergraduate economics course to his name, in his first 14 months as a graduate he produced the work that would end up, in 1994, winning him a Nobel prize in economics for his contribution to game theory.On November 16th 1949, Nash sent a note barely longer than a page to the Proceedings of the National Academy of Sciences, in which he laid out the concept that has since become known as the “Nash equilibrium”.
This concept describes a stable outcome that results from people or institutions making rational choices based on what they think others will do.In a Nash equilibrium, no one is able to improve their own situation by changing strategy: each person is doing as well as they possibly can, even if that does not mean the optimal outcome for society.With a flourish of elegant mathematics, Nash showed that every “game” with a finite number of players, each with a finite number of options to choose from, would have at least one such equilibrium.His insights expanded the scope of economics.In perfectly competitive markets, where there are no barriers to entry and everyone's products are identical, no individual buyer or seller can influence the market: none need pay close attention to what the others are up to.
But most markets are not like this: the decisions of rivals and customers matter.From auctions to labour markets, the Nash equilibrium gave the dismal science a way to make real-world predictions based on information about each person's incentives.One example in particular has come to symbolise the equilibrium: the prisoner's dilemma.Nash used algebra and numbers to set out this situation in an expanded paper published in 1951, but the version familiar to economics students is altogether more gripping.(Nash's thesis adviser, Albert Tucker, came up with it for a talk he gave to a group of psychologists. )It involves two mobsters sweating in separate prison cells, each contemplating the same deal offered by the district attorney.
If they both confess to a bloody murder, they each face ten years in jail.If one stays quiet while the other snitches, then the snitch will get a reward, while the other will face a lifetime in jail.And if both hold their tongue, then they each face a minor charge, and only a year in the clink.There is only one Nash-equilibrium solution to the prisoner's dilemma: both confess.Each is a best response to the other's strategy; since the other might have spilled the beans, snitching avoids a lifetime in jail.The tragedy is that if only they could work out some way of co-ordinating, they could both make themselves better off.The example illustrates that crowds can be foolish as well as wise; what is best for the individual can be disastrous for the group.
This tragic outcome is all too common in the real world.Left freely to plunder the sea, individuals will fish more than is best for the group, depleting fish stocks.Employees competing to impress their boss by staying longest in the office will encourage workforce exhaustion.Banks have an incentive to lend more rather than sit things out when house prices shoot up.The Nash equilibrium helped economists to understand how self-improving individuals could lead to self-harming crowds.Better still, it helped them to tackle the problem: they just had to make sure that every individual faced the best incentives possible.If things still went wrong—parents failing to vaccinate their children against measles, say—then it must be because people were not acting in their own self-interest.In such cases, the public-policy challenge would be one of information.
Nash's idea had antecedents.In 1838 August Cournot, a French economist, theorised that in a market with only two competing companies, each would see the disadvantages of pursuing market share by boosting output, in the form of lower prices and thinner profit margins.Unwittingly, Cournot had stumbled across an example of a Nash equilibrium.It made sense for each firm to set production levels based on the strategy of its competitor; consumers, however, would end up with less stuff and higher prices than if full-blooded competition had prevailed.Another pioneer was John von Neumann, a Hungarian mathematician.In 1928, the year Nash was born, von Neumann outlined a first formal theory of games, showing that in two-person, zero-sum games, there would always be an equilibrium.When Nash shared his finding with von Neumann, by then an intellectual demigod, the latter dismissed the result as “trivial”, seeing it as little more than an extension of his own, earlier proof.In fact, von Neumann's focus on two-person, zero-sum games left only a very narrow set of applications for his theory.
Most of these settings were military in nature.One such was the idea of mutually assured destruction, in which equilibrium is reached by arming adversaries with nuclear weapons (some have suggested that the film character of Dr Strangelove was based on von Neumann) .None of this was particularly useful for thinking about situations—including most types of market—in which one party's victory does not automatically imply the other's defeat.Even so, the economics profession initially shared von Neumann's assessment, and largely overlooked Nash's discovery.He threw himself into other mathematical pursuits, but his huge promise was undermined when in 1959 he started suffering from delusions and paranoia.His wife had him hospitalised; upon his release, he became a familiar figure around the Princeton campus, talking to himself and scribbling on blackboards.