Skip to main content
Macmillan Childrens Publishing Group

The Game Theorist's Guide to Parenting

How the Science of Strategic Thinking Can Help You Deal with the Toughest Negotiators You Know--Your Kids

Paul Raeburn and Kevin Zollman

Scientific American / Farrar, Straus and Giroux



In 2005, Takashi Hashiyama, the president of the Maspro Denkoh Corporation, a Japanese electronics company, laid out the terms for what might be the oddest and most expensive children’s game ever played.

He wanted to auction off the company’s $20 million art collection, which included works by Cézanne, Picasso, and van Gogh. But he couldn’t decide which auction house would do the best job—Christie’s or Sotheby’s. After some thought, Hashiyama announced that he had devised a rather unconventional way to settle the matter: The companies would play Rock, Paper, Scissors. And the winner would sell the art.

Two representatives from each of the companies were called to a Maspro conference room and asked to sit down at a long table facing one another. Each team was given a piece of paper and asked to write one thing: the Japanese word for rock, paper, or scissors. Christie’s picked scissors. It was the winner, beating Sotheby’s paper.

Most of us would assume that was fair. It was a game of chance; Christie’s got lucky. But it wasn’t simply luck. Christie’s had a strategy. Before the showdown, a Christie’s executive consulted two experts on the subtleties of the game: his eleven-year-old twins. “Everybody knows you always start with scissors,” they told him. “Rock is way too obvious, and scissors beats paper.” After the contest, Sotheby’s acknowledged that it had not devised a strategy. It lost several million dollars in commissions as a result.

Rock, Paper, Scissors is a classic example in the study of game theory. Originally developed as a part of mathematics, game theory is the study of how people play games, interact, and negotiate. It deals with strategic thinking in situations where one person’s choice of action will affect what the other does in response. Solitaire has nothing to do with game theory: it’s just you and the deck of cards. Chess is quite different. Opening with pawn to e4 immediately affects the strategy of your opponent, whose move will, in turn, affect your next move. Those are the kinds of situations that fascinate game theorists.

Game theory was devised by economists and mathematicians, but researchers quickly realized that it had applications far beyond economics. It has become the foundation for industrial-strength negotiations, and it is used by presidents and prime ministers, celebrities and CEOs.

* * *

The roots of game theory extend deep into the past, long before its establishment as a science in the mid–twentieth century. One famous example of a game-theory strategy concerns the military figure Kong Ming (also known as Zhuge Liang), who was forced to defend himself against overwhelming odds in a battle in Yangping, China in 149 B.C. It’s a twist on the familiar story of the Trojan horse. Both stories involve deception—but in different ways. In the tale of the Trojan horse, the soldiers came out of hiding. In the case of Kong Ming’s defense, the soldiers went into hiding.

Authorities disagree over whether this is a historical fact or part of Chinese military lore, but the story is too good for us to leave out. Kong Ming was engaged with an enemy, Suma-I, whose forces vastly outnumbered his. Furthermore, Suma-I’s warriors had blocked all potential avenues of retreat. Considering the odds, Kong Ming faced certain defeat. He was out of options. Retreating was impossible. Staying to fight was suicide.

At this point, Kong Ming had a brilliant idea. As Suma-I crept forward with his forces, preparing to attack, he stopped. He couldn’t believe what he was seeing. Kong Ming had opened the gates to the city of Yangping—and there were no soldiers in sight. (Kong Ming had directed all the guards to hide.) Suma-I saw before him an unguarded city. A solitary figure sat in a tower playing a lute. Suma-I could not understand why Kong Ming would leave the city vulnerable like this. He concluded that it must be a trap, and quickly retreated. Kong Ming had won the battle without throwing a punch. It was a triumph.

The point of this story is that Kong Ming and Suma-I each had to anticipate what the other would think. If Suma-I hadn’t stopped to think about why Kong Ming opened the gates, he would have overrun the defenseless city. Kong Ming’s actions would have been recorded as a military blunder, and we wouldn’t be talking about him now. But Suma-I did stop to think. And Kong Ming knew that he would. He knew exactly what Suma-I would think, and he was right. This is why Kong Ming emerges from this story as a military genius.

Game theory did not become a true sensation, however, until 1944, when its principles were spelled out in detail by the brilliant economist, physicist, mathematician, and computer scientist John von Neumann and his colleague Oskar Morgenstern. That was the year they published their groundbreaking book Theory of Games and Economic Behavior, which launched game theory as a new science—the science of strategic thinking. Some authorities think von Neumann, an acknowledged genius, was mainly responsible for the breakthrough, and that Morgenstern’s role was to goad von Neumann into applying himself to this new field. In any case, their names are now linked as the co-developers of the theory.

One of the most important developments since then came in the early 1950s with the work of John Nash, another brilliant Princeton mathematician whose work on game theory inspired the book and film A Beautiful Mind. He published several scientific papers that took von Neumann’s and Morgenstern’s work much further, and he doubtless would have published many more had he not been diagnosed with schizophrenia a few years later. For a time he left the field, but he ultimately received treatment for his illness and was able to resume his career in the 1990s. In 1994, he was awarded the Nobel Memorial Prize in economics for his work on what are now called Nash equilibria, work that explains a lot about human behavior, including how people acting in their own best interest don’t always arrive at the best solution. That makes him one of at least eleven game theorists who have won Nobels for their work. Unfortunately, tragedy struck Nash a second time in 2015. He and his wife were killed in a car accident on the New Jersey Turnpike while we were working on this book.

In the years since von Neumann and Nash, game theory has been applied to political science, public health, psychology, and even studies in animal behavior. (Spiders and fish, it turns out, can be excellent game theorists, although they can’t be said to think at all. Evolution has equipped them with wonderful strategies that they pursue without knowing why.)

Only recently, however, have game theorists turned their attention to one of the most challenging strategic problems of all—raising children. It’s now clear we can put game theory to work in our families. Game theory can help us persuade kids to do their homework, brush their teeth, get out of bed in the morning, and crawl back into it at night. And if we explain the rules clearly to our kids, we can help them get along better with us and with each other—and we can do it without administering any punishment.

Kevin is a philosopher and game theorist at Carnegie Mellon University who studies the evolution of language and the mathematics of social behavior. Paul, a writer, has written two books and numerous articles on parenting, and has five children. We quickly realized, when we got together to talk about this, that game theory has a lot to teach parents. An understanding of game theory and its application to kids and families can help parents avoid arguments, reduce sibling conflicts, and encourage a sense of fairness.

Let’s face it—we’re up against tough odds. As parents quickly discover, children can be very crafty. Even before they can talk, kids devise strategies to use with their parents. They learn that pointing to a bag of cookies on the shelf or reaching for a toy is a good strategic move—because it usually gets them the cookie or the toy. They engage in the classic maneuver of raising both arms to signify that they want to be picked up. And what parent doesn’t comply? Now ask yourself: Who has the upper hand here? Parents need help!

And children are clever, developing strategies that might challenge even some Nobel Prize–winning parents. We should be smarter than our children, right? We’ve been around a lot longer. But so often they seem to outmaneuver us. When children stay up later than they should, they’ve outwitted us. When they insist on spaghetti every night for dinner—and they almost always get it—they’ve defeated us. When they collapse in tears while doing their homework, we’ve all failed. Nobody’s strategy has worked.

In The Game Theorist’s Guide to Parenting, we will look at how parents and children devise their strategies, where those strategies go wrong, and how we, as parents, can use those strategies to help raise happy, healthy, intelligent children. We’re talking about kids who can subconsciously use game-theory strategies to their advantage, but do it with kindness and generosity. The idea is not to set up games in which we are winners and our children are losers. On the contrary, game theory offers us much more than that—the opportunity to help us craft the behavior of our children using games in which we all come out ahead. While game theory can get complicated, in most situations you need to know only three things: the players, their preferences, and what they can do.

You are already using improvised strategies with your kids. That makes you amateur game theorists, whether you’re aware of it or not. We will explain how these strategies work, and how you can use them more effectively to encourage your kids to behave in ways that will be good for them—and good for you.

One of the most famous examples of applying game theory to kids is what’s known as the Rotten Kid Theorem. It comes from the influential work of the late Nobel Prize–winning economist Gary Becker of the University of Chicago. It’s fascinating, partly because it seems to defy common sense. And it’s controversial—some economists say the theory doesn’t quite fit the facts in real families. But here’s how it goes:

You might think that kids who don’t care at all about the good fortunes of their family—because they are “rotten”—would not make much of a contribution to their parents and siblings. But if the parents show that they care about the welfare of their rotten kid—despite his behavior—he will soon learn that it serves his selfish interest to treat his parents better—because they will then treat him better. According to the theorem, even rotten kids, in the right circumstances, might be maneuvered into becoming little angels. Or if not angels, then at least less rotten!

As we talk about playing “games” with our children, it’s important to remember that we are talking about scientifically based strategies. We’re not talking about playing games in the derogatory sense that might prompt one of us to say, “Don’t play games with me. I know you didn’t do your homework—your teacher sent me a note!” Game theory is not about deception. It’s about being smart in dealings with other people—understanding how people are likely to behave, and devising a strategy that will produce the outcome we’re looking for. That’s true whether we’re talking about global political negotiations or about what to have for dinner.

We can use game theory every time we want to divide a scarce resource fairly among our kids, whether it’s Twizzlers, LEGO bricks, or time on the iPad. Think of the classic cake-cutting problem: How do we divide a cake fairly when kids have different interests?

The technique for dividing a cake also applies to dividing up time with favorite toys, establishing how much a child’s allowance should be, or deciding how to spend a vacation. Game theorists have built careers on the problem of dividing things fairly. Parents who learn how to do that can help to forestall the familiar wail “But that’s not fair!” And remember, these little negotiators are clever. A boy who calls a division unfair might mean that he thinks it’s unfair. It can also mean that he’s setting himself up to have the advantage the next time this comes up: “I didn’t get as much candy before! It’s my turn now!”

As we started working on this book, we saw that the game theory problem known as the Prisoner’s Dilemma has direct implications for the family. So does the theory of rewards. And what about the Ultimatum Game—which deals with the issue of credible and non-credible threats? That one does, too. How many times have we told our kids that we will cancel a trip to the beach if they don’t eat their breakfast? They know we’re faking, because we want to go to the beach, too—and they know we won’t jeopardize our own vacation over a bowl of Froot Loops.

As Ralphie finds out when he asks for a BB gun in the movie A Christmas Story, the classic parental admonition—“You’ll shoot your eye out!”—can’t be beaten. “That deadly phrase honored many times by hundreds of mothers was not surmountable by any means known to kid-dom,” he laments. But he gets the Red Ryder carbine-action two-hundred-shot range-model air rifle he coveted, because his strategy plays on his father’s sympathies—which trump his mother’s fears. Well played, Ralphie! (We wonder whether he’d been reading von Neumann’s book…)

It’s not unusual for children to emerge victorious, as Ralphie did. Too often, we, as parents, feel we’re outmatched by people half our size in a strategic game of wits. That’s where game theory can help.

We have teamed up to give you the tools you can use to match wits with your kids, to make fair decisions, to stop the squabbling. We know you don’t want to fight with your children—and you don’t have to.

All it takes is a little thought, a little economics, a little psychology—and a little practice. We’re talking about evidence-based parenting. Not fads, not guesses, not tricks. In the best of circumstances, you will create a win-win situation. Not only will you reduce conflict and encourage your children to do what they should, you will also be teaching them strategies for solving problems they will face long after leaving the family and starting out on their own. Game theory works. And everybody wins.

Copyright © 2016 by Paul Raeburn and Kevin Zollman