Magazine / From Game Theory to Gossip: How Common Knowledge Shapes Our World

From Game Theory to Gossip: How Common Knowledge Shapes Our World

Book Bites Politics & Economics Psychology

Below, Steven Pinker shares five key insights from his new book, When Everyone Knows That Everyone Knows . . .: Common Knowledge and the Mysteries of Money, Power, and Everyday Life.

Steven is a cognitive scientist and a professor of psychology at Harvard University. He has won many prizes for his teaching, research, and his twelve books. He is an elected member of the National Academy of Sciences, a two-time Pulitzer Prize-finalist, and one of Time’s “100 Most Influential People in the World Today.”

What’s the big idea?

How do people think about what other people think they think? Understanding the logic of common knowledge and coordination is important in understanding politics, money, and everyday life.

Listen to the audio version of this Book Bite—read by Steven himself—below, or in the Next Big Idea App.

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1. Common knowledge allows for coordination.

Hans Christian Andersen’s immortal story, “The Emperor’s New Clothes,” draws on a momentous logical distinction. When the little boy said the emperor was naked, he wasn’t telling anyone anything they didn’t already know, but he added to their knowledge, nonetheless. By blurting out what every onlooker could see, he ensured that everyone within earshot knew that everyone else knew what they knew, and everyone knew that, and so on. That changed their relationship with the emperor from obsequious deference to ridicule and scorn.

With private knowledge, I know something and you know it. With common knowledge, I know something and you know it—but in addition, I know that you know it, and you know that I know it. On top of that, I know that you know that I know it, and you know that I know that you know it, and so on, ad infinitum.

This matters because common knowledge is necessary for coordination. In a classic example from game theorist Thomas Schelling, a couple gets separated in New York City—incommunicado—but need to somehow find each other. He knows that she likes to hang out in a bookstore, so he heads there, but then realizes that she’ll predict that he will go to a camera store, so he changes course and heads to the camera store until he realizes that she will anticipate that he will guess that she will opt for the bookstore, so he does another about-face. But then he can’t let go of the fact that she’s aware that he likes to haunt the camera store, so he pirouettes once again. Meanwhile, she is whipsawed by the same futile empathy. Nothing short of common knowledge can guarantee they’ll end up at the same place at the same time.

2. Capturing common knowledge.

People can’t literally think an infinite chain of “I know that she knows” thoughts—what cognitive psychologists call recursive mentalizing. Our heads start to spin three or four layers in, let alone an infinite number. In a well-known episode of Friends, Phoebe says, “They don’t know that we know that they know we know Joey. You can’t say anything.” And Joey replies, “I couldn’t even if I wanted to.”

Instead, common knowledge can be captured in a simple mental state. The intuition that something is self-evident or public can be conveyed through direct speech. In the case of the couple separated in New York, a phone call would solve their dilemma quickly. Indeed, solving coordination dilemmas is probably the reason our species evolved language in the first place.

“Our heads start to spin three or four layers in, let alone an infinite number.”

The next best thing is a focal point or common salience. Schelling suggests that the separated couple might go to the big clock at Grand Central Station, even if it wasn’t close to where they’d been separated, simply because each knew it was likely to pop into the mind of the other.

A third solution is a convention, or a tacit agreement among people to do things in a certain way for no other reason than that they agree to do it that way. The couple might agree that if they’re ever separated again, they’ll adopt the convention of chivalry and meet at the bookstore; or patriarchy and meet at the camera store; or whimsy and meet at a department store Lost and Found.

3. Not all examples are obvious.

On a larger scale, focal points and conventions drive financial and legal coordination. An obvious example is driving on the right or left side of the road. It doesn’t matter, so long as everyone agrees on the same side. Another obvious example is currency, where I accept a piece of paper in exchange for an old couch because I know my grocer will accept the paper in exchange for food, because he knows that his suppliers will accept it, and so on.

However, not all examples are obvious. Why are autocrats terrified of public protests? The basic reason was explained by Gandhi in the eponymous movie: “100,000 Englishmen cannot control 350 million Indians if the Indians refuse to cooperate.” But all those citizens can refuse to cooperate if each one fears that no one else will join him.

In a public demonstration, each protestor can not only see the others, but also see that the others are seeing the others. This common knowledge can allow them to coordinate their resistance, whether by literally storming the palace or by bringing state machinery to a halt through work stoppages and boycotts. This is the basis for a joke from the old Soviet Union about a man standing in the Moscow train station handing out leaflets to passersby. Soon enough, the KGB arrest him only to discover that the leaflets are blank sheets of paper. “What is the meaning of this?” they demand. The man replies, “What’s there to write? It’s so obvious.” The point of the joke is that the man was generating subversive common knowledge. In a case of life imitating a joke, in 2022, Russian police arrested a woman for holding a blank sign.

Another less obvious example comes from finance. Economist John Maynard Keynes compared professional investment to a newspaper beauty contest: The goal is not to choose the prettiest face, but the face that other competitors are most likely to choose, each anticipating what others will anticipate. In the same way, speculative investors buy securities not because of their underlying value, but in the hope of unloading them on other investors—the so-called “greater fool.” This dynamic means that exuberant cycles of recursive mentalizing can be set off by a conspicuous focal point, like a Super Bowl ad. Everyone knows that the Super Bowl attracts mass attention—and everyone knows that everyone knows it. In 2022, cryptocurrency exchanges ran high-concept ads that tried to stir up a shared expectation of rising prices, not by touting any advantages of crypto, but by warning: “Don’t be like Larry. Don’t miss out.”

“Everyone knows that the Super Bowl attracts mass attention—and everyone knows that everyone knows it.”

Of course, it’s only so long that an asset can levitate in mid-air, suspended by nothing but common expectation. Bubbles pop when a market starts running out of the greater fools who don’t want to miss out on the next big thing, or when a reason for doubt becomes common knowledge. That can send investors running for the exits, each desperate to sell their assets out of fear that others are selling them out of fear. The result can be a bank run, hyperinflation, or a depression.

When Franklin Delano Roosevelt said, “The only thing we have to fear is fear itself,” he was not offering a mere feel-good slogan, but capturing a principle of common knowledge. With investors always on the lookout for focal points, economic leaders must be careful wordsmiths. As former Chair of the U.S. Federal Reserve Alan Greenspan once quipped, “Since I’ve become a central banker, I’ve learned to mumble with great incoherence. If I seem unduly clear to you, you must have misunderstood what I said.” When Jimmy Carter’s inflation czar Alfred Kahn was told by his boss never to use the self-fulfilling word “depression,” he said, “We’re in danger of having the worst banana in 45 years.”

4. Common knowledge in everyday life.

Social relationships are coordination games. Two people are friends, lovers, allies, dominant and subordinate, or transactional partners because each knows that the other knows they are. These understandings are cemented by common knowledge generators, such as:

  • Eye contact, where you’re looking at the part of the person who’s looking at the part of you that’s looking at that part of them.
  • Blushing, when you feel the heat of your face reddening from the inside, knowing others are seeing it from the outside.
  • Laughter, where a conspicuous noise exposes the common assumptions held by everyone who gets the joke.

Conversely, when we don’t want to upend a relationship, we take steps to avoid common knowledge that would threaten it. We avoid looking someone in the eye, ignore the elephant in the room, or mumble with great incoherence. This explains why people don’t often blurt out what they mean, but instead veil their intentions in euphemism and innuendo. There’s the classic sexual come-on: “Would you like to come up and see my etchings?” By the 1930s, this phrase was familiar enough that humorist James Thurber drew a cartoon in which a hapless man says to his date, “You wait here, and I’ll bring the etchings down.” Nowadays, etchings has become Netflix and chill. People also veil their bribes, as in, “Gee, Officer, is there some way we can settle the ticket here?” Or there are threats, as in, “Nice story you got there. Real shame if something happened to it.”

“These euphemisms don’t pass the giggle test, but they provide plausible deniability of common knowledge.”

The point of an innuendo is not exactly to provide plausible deniability. These euphemisms don’t pass the giggle test, but they provide plausible deniability of common knowledge. If Harry says, “Want to come up for Netflix and chill?” and Sally says no, then Sally knows she’s turned down an overture, and Harry knows she’s turned down an overture. But does Sally know that Harry knows? She could think, Maybe Harry thinks I’m naïve. And does Harry know that Sally knows that he knows? He could think, Maybe Sally thinks I’m dense. With no common knowledge, they can maintain the fiction of a platonic friendship, but if Harry had said, “Would you like to come up and have sex?” then Harry knows that Sally knows that Harry knows that Sally knows—and they cannot maintain the fiction of a friendship. That’s what lies behind the feeling that with blurted-out speech, you can’t take it back. It’s out there.

5. Preserving common knowledge—like it or not.

The logic of coordination and common knowledge explains why we deplore all the hypocrisy, white lies, role-playing, and rituals of social life, yet we wouldn’t want to live without them. As dystopian comedies like Liar Liar show, our relationships are cemented by commonly accepted creeds of unstinting loyalty, generosity, and fidelity.

Privately, we know these creeds are fundamentally fictitious, but making that awareness common knowledge would undermine the assumptions that allow us to get along. Many seemingly arbitrary conventions in political, economic, and social life are possible solutions to coordination problems. Games that depend on common knowledge—and many of our rituals and hypocrisies—exist to preserve it.

I’ll leave it to you to ponder how this logic may explain other puzzles:

  • Social media shaming mobs.
  • Kardashian celebrity (when someone is famous for being famous).
  • Strategic ambiguity in politics.
  • The difference between CC and BCC in email etiquette.
  • The classic “gaffe” in Washington (when a politician accidentally says something true).

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