What is Nash equilibrium and why is it important?

This week, “The Economist Explains” is devoted to the economy. For each of the six days through Saturday, this blog will post a brief explainer on a basic idea.

ECONOMISTS can usually explain the past and sometimes predict the future, but not without help. One of the most important tools at their disposal is the Nash Balance, named after John Nash, who won a Nobel Prize in 1994 for his discovery. This simple concept helps economists determine how competing firms set their prices, how governments should design auctions to get the most out of bidders, and how to explain the sometimes self-defeating decisions groups make. What is Nash equilibrium and why is it important?

One of the best-known illustrations is the prisoner’s dilemma: two criminals placed in separate cells face the same offer from the prosecutor. If they both confess to a bloody murder, they each risk ten years in prison. If one remains silent while the other confesses, then the Snitch will be released, while the other will face a life in prison. And if the two hold their tongues, they each face a minor load, and only a year into the tinkle. Collectively, it would be better if the two were silent. But given the setup, an economist armed with Nash’s concept of equilibrium would predict the opposite: the only stable outcome is for the two to confess.

In a Nash equilibrium, each person in a group makes the best decision for themselves, based on what they think the others will do. And no one can do better by changing their strategy: each member of the group is doing as well as they can. In the case of the prisoners’ dilemma, keeping quiet is never a good idea, no matter what the other gangster chooses. Since one suspect may have spilled the beans, the snitch saves the other a life in prison. And if the other is silent, then the confession sets him free. Applied to the real world, economists use the Nash equilibrium to predict how companies will react to the prices of their competitors. Two large companies that establish pricing strategies to compete with each other are likely to squeeze customers harder than they could if they each faced thousands of competitors.

Nash’s equilibrium helps economists understand how decisions that are good for the individual can be terrible for the group. This tragedy of the commons explains why we overfish the seas and why we emit too much carbon into the atmosphere. Everyone would be better off if we could agree to show restraint. But given what everyone else does, fishing or gas mileage has individual meaning. In addition to explaining gloom and gloom, it also helps decision-makers find solutions to tricky problems. Armed with the Nash Balance, economic geeks claim to have raised billions for public money. In 2000, the UK government used its help to design a special auction that sold its 3G mobile phone operating licenses for £ 22.5 billion ($ 35.4 billion). Their trick was to treat the auction like a game and change the rules so that the best strategy for bidders was to bid bullish (winning bidders weren’t happy with the outcome). Today, Nash’s equilibrium underpins modern microeconomics (but with some refinements). Given that it promises economists the power to pick winners and losers, it’s easy to see why.

Previously in this series
Monday: Akerlof lemon market
Tuesday: The Stolper-Samuelson Theorem