IN THE film A Beautiful Mind, John Nash and his buddies, all of them graduate students in mathematics at Princeton University, are sitting in a smoky bar when a group of women walk in. As the men tease each other about their chances, Nash is struck with inspiration. Is there a logical, mathematical way of working out the best strategy for each man getting a date? Next thing you know he’s shambling out of the bar, and spends the night furiously scribbling unfathomable-looking equations.
It sounds a little crass, and the episode probably never happened in reality. But in a ham-fisted, Hollywood sort of way, it does hint at how game theory, the branch of mathematics Nash helped to make famous, can apply to our everyday lives.
In fact, we use it all the time without even realising. “Every time you think about what you should do in terms of what someone else will do in response, you’re doing rudimentary game theory,” says of Carnegie Mellon University in Pittsburgh, Pennsylvania.
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The trouble is, we are novices. When we need to think through situations several steps ahead or when they involve more than just a few people, we start to make mistakes. But delve into the theory just a little – there’s no need to be a maths whizz – and you can harness some of the insights to make smarter moves in your own life.
Lesson one is that there are different sorts of games. Broadly speaking, there are zero-sum games, in which one player gains what the other loses, and variable-sum games, in which players have both common and opposed interests.
An example of a zero-sum game would be chess or poker. When you win, your opponent automatically loses and vice-versa. These sorts of situations don’t crop up much in everyday life. Variable-sum games are more common and more complex. They are exemplified by what’s known as the prisoner’s dilemma, a scenario in which the punishment you receive for a crime depends on both your plea and that of an accomplice. You don’t know how your accomplice will behave, but game theory organises the possible outcomes into a pay-off matrix that allows you to think through the various possible outcomes (see “Decisions in the frame”).
It turns out, perhaps counter-intuitively, that your best option for both you and your accomplice is to confess. This decision is what’s known as a Nash equilibrium because neither party can benefit from making a different choice while the other party’s choice stays the same.
Nash died in May, but his contribution to game theory, including the equilibrium idea, helped him win a share of the 1994 Nobel prize in economics. Lessons from the discipline have been applied all over the place, from politics and diplomacy to economics and business. It helped the US formulate its nuclear deterent strategy during the cold war, for instance. Today, broadcasters use it to jostle for the rights to air top-level sports fixtures.
But individuals can harness insights from game theory, too. One example is understanding the power of “credible commitment”, says , an economist at the University of Pennsylvania in Philadelphia. This concept is best described by a game of chicken. Think of two cars accelerating towards each other; the loser is the one who swerves. Here, the Nash equilibria are the two situations in which one player swerves and not the other.
“There is another way to win at chicken: throw the steering wheel out of the window”
But a game theory analysis shows there is another possible way out. One of the drivers can force an outcome by changing the rules of the game – for example by removing the steering wheel and throwing it out of the window. Then the other driver must swerve to avoid destruction. “You’re making your opponent recognise that you have no choice but to take a particular action, which then forces them to do what you want them to do,” says Vohra. “Paradoxically, limiting your options can sometimes make you better off.”
The same principle can be applied to buying rather than crashing a car. Do your research on prices and make a take-it-or-leave-it offer. “By committing yourself, you force the seller to make a choice: either sell at that price or make no sale at all,” says Vohra. This reasoning applies to any situation in which two competing parties have to negotiate a price, including agreeing a salary for a new job, for instance.
Be warned, however: even the greatest game theorists won’t always get it right. The problem is that game theory assumes we act rationally all the time – and we don’t (see “Cognitive bias“). Even the experts will sometimes be thrown off by the quirks of human behaviour.
Like this? Read: “Get smarter: 9 ideas to make your life better“
This article appeared in print under the headline “Need to know: Game theory”
Article amended on 21 December 2015
Correction: The graphic in this article has been updated to better reflect the standard prisoner’s dilemma.
