Nash Equilibrium

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Suppose a bunch of people are each making a choice, and how well each person does depends not only on their own choice but on what everyone else chooses too. Experts call this kind of situation a "game," even when it is not a game you would play for fun. A traffic jam is a game. A price war between two stores is a game. Even where you decide to sit in the lunchroom can be a game.

A Nash equilibrium is a special, settled moment in a game like that. It is a set of choices where nobody can do any better by changing their own choice alone, as long as everyone else keeps doing what they are doing. Because no single person has a reason to switch, everyone stays put. It is a kind of balance point.

A simple example: which side of the road?

Think about cars driving on a road. In the United States, everyone drives on the right side. Now imagine you are one of those drivers and everyone around you is on the right. Would you switch to the left? Of course not, you would crash. So staying on the right is your best choice, and it is everyone else's best choice too. Nobody wants to change. That is a Nash equilibrium.

Here is the interesting twist: everyone driving on the left side would work just as well, which is exactly what they do in countries like the United Kingdom. So "everyone drives right" and "everyone drives left" are both Nash equilibria. What matters is that everybody makes the same choice, so no one has a reason to be the odd one out.

The balance point is not always the best one

A Nash equilibrium is where people settle, but that does not mean it is the happiest ending for everyone.

Picture a crowd at a concert, all sitting down and able to see the stage just fine. Now one person stands up to see a little better. The people behind them cannot see anymore, so they stand up too. Soon the whole crowd is standing. Everyone can see about as well as they did before, but now everybody's legs are tired. Nobody wants to be the only one to sit back down, because then they would see nothing at all. So the whole crowd stays standing.

"Everyone stands" is a Nash equilibrium, even though "everyone sits" would be more comfortable for all of them. This is a famous lesson from Nash equilibria: when everyone only looks out for themselves, the whole group can get stuck in a spot that is worse for everybody. The same idea shows up in a classic puzzle called the Prisoner's Dilemma.

Who was Nash?

The idea is named after John Nash, an American mathematician who came up with it around 1950, when he was still a young student. He proved that almost any game of this kind has at least one of these balance points, which turned out to be a very big deal. Today his idea, part of a field called Game Theory, is used to understand economics, business deals, elections, wars, and even how animals share food and territory. In 1994, Nash won the Nobel Prize in economics for it.

Fun facts

• John Nash's life story was turned into a famous movie called "A Beautiful Mind," which won the Academy Award for Best Picture.
• The same game can have more than one Nash equilibrium, like driving on the left or on the right, and sometimes it has many.
• Experts hunt for the Nash equilibrium in a situation to predict what people, companies, or even whole countries are likely to do, because a balance point is where things tend to settle.