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As every parent knows, kids are surprisingly clever negotiators. But how can we avoid those all-too-familiar wails, "That's not fair!" and "You can't make me!"? In The Game Theorist's Guide to Parenting, the journalist Paul Raeburn and the game theorist Kevin Zollman pair up to highlight tactics from the worlds of economics and business that can help parents break the endless cycle of quarrels and ineffective solutions. They show that some of the same strategies successfully applied to big business deals and politics--such as the Prisoner's Dilemma and the Ultimatum Game--can be used to solve such titanic, age-old parenting problems as dividing up toys, putting down those screens, and sticking to a bedtime.
Raeburn and Zollman open each chapter with a common parenting dilemma, such as determining who started a fight or who gets a bedtime story first. Then they show how carefully concocted schemes involving bargains and fair incentives can save the day. Through smart case studies of game theory in action, Raeburn and Zollman reveal how parents and children devise strategies, where those strategies go wrong, and what we can do to help raise happy and savvy kids while keeping the rest of the family happy too.
Delightfully witty, refreshingly irreverent, and just a bit Machiavellian, The Game Theorist's Guide to Parenting looks past the fads to offer advice you can put into action today.
|Publisher:||Farrar, Straus and Giroux|
|Product dimensions:||5.60(w) x 8.40(h) x 0.90(d)|
About the Author
Paul Raeburn is the award-winning author of four books, including Do Fathers Matter?, a National Parenting Publications Gold Medal Winner. His articles have appeared in Discover, The Huffington Post, The New York Times Magazine, Scientific American, and Psychology Today, among many others. You can find him on Twitter at @praeburn and on his website at www.paulraeburn.com. Kevin Zollman is a game theorist and an associate professor of philosophy at Carnegie Mellon University. His work has been covered in The Wall Street Journal, The New Yorker, Scientific American, and elsewhere. Visit his website at www.andrew.cmu.edu/user/kzollman.
Read an Excerpt
The Game Theorist's Guide to Parenting
How the Science of Strategic Thinking Can Help You Deal with the Toughest Negotiators You Know â" Your Kids
By Paul Raeburn, Kevin Zollman
Scientific American / Farrar, Straus and GirouxCopyright © 2016 Paul Raeburn and Kevin Zollman
All rights reserved.
I Cut, You Pick
When Paul was a child, he and his younger sister made brilliant use of game theory without knowing they were doing it — and without using a lick of mathematics. They stumbled on what seemed like the perfect way to divide a piece of cake or a candy bar: one would cut, and the other would pick. Perfectly fair, right? Maybe not. Paul quickly discovered, as older siblings often do, that there was a way to maintain an advantage, even while seeming to be scrupulously fair: he insisted that his little sister always cut the cake. She could never divide it perfectly — one piece was always a bit bigger than the other. So by the unassailable logic of I Cut, You Pick, he always got the bigger piece — at least until his sister figured out what was going on.
Cake-cutting is of great interest to kids everywhere, especially those celebrating birthdays. It's also one of the classic problems in game theory. The theory that explains cake cutting is more than two thousand years old, and it's found in ancient texts from all over the world. One of the earliest references appears in the poem Theogony, by Hesiod, which dates to 750–600 B.C. In Hesiod's telling, Prometheus — the trickster who stole fire from the gods — aimed to settle a dispute with Zeus by cutting up a great ox into two equal portions. It was a version of cake cutting: Prometheus would cut, and Zeus would pick. "Zeus, most glorious and greatest of the eternal gods, take whichever of these portions your heart within you bids," Prometheus said. That should have led to two fair shares of the cake, ending the dispute.
Prometheus should have been smart enough to know that you don't mess around with a god that can hurl lightning bolts. Instead, he tried to deceive Zeus. One of the portions he prepared was all meat. The other was nothing but bones covered with glistening fat. This second one looked like the bigger and better portion, but it wasn't. The ever-wise Zeus saw through the trick, and refused the bones and fat. Out of vengeance, he withheld fire from mortals. (Prometheus later stole fire in a hollow fennel stalk, Hesiod reports.) Zeus, in addition to knowing how to control lightning, apparently had a little subconscious understanding of game theory. He understood the principle involved — that the person doing the cutting should divide the spoils into two equal portions. Prometheus didn't do that, and Zeus knew something was up. He enjoyed a sweet victory over the scheming Prometheus.
A similar story shows up in the book of Genesis, when Abraham and Lot had more livestock than they could manage, and disputes broke out between their herdsmen. Abraham pressed Lot to end the strife by dividing the land between them. "Separate thyself, I pray thee, from me," Abraham said. "If thou wilt take the left hand, then I will go to the right, or if thou depart to the right hand, then I will go to the left." Lot chose the plain of Jordan, so Abraham took the land of Canaan. And their dispute ended. Abraham offered Lot either of the two portions, and Lot picked.
The same idea arose yet again in the desperate circumstances during World War II inside Auschwitz, as the writer Primo Levi recalled in Moments of Reprieve. "Grigo pulled out a ration of bread and handed it to me together with the knife," he wrote. "It was the custom, indeed the unwritten law, that in all payments based on bread one of the contracting partners must cut the bread and the other choose, because in this way the person who cuts is induced to make the portions as equal as possible."
These are simple cake-cutting problems: Two players. One cuts, and one picks. But cake-cutting can quickly become more complicated if additional players are involved, or if the situation is more complex, as it was in Auschwitz. Most cakes, for example, have different parts. One part might be chocolate, another vanilla. One part might have delicious frosting, while another is covered with hard, tasteless candy flowers. And the outside pieces have a lot more frosting than the inside ones. While we're talking about cutting cake, remember that the principles here apply to many goods and privileges that kids might want to divide fairly, such as time on the computer or television picks.
To explain how the principles of cake-cutting work, game theorists are likely to answer our cake-cutting questions with more questions: What precisely do we mean when we say we want to cut the cake fairly? What does "fair" mean in this context?
They have a point. A fair division could mean that the cake is divided into two pieces exactly the same size, with the same amount of frosting. We might feel good about that; it certainly seems fair. But cutting the cake like this doesn't take into account all of the circumstances. The chocolate-loving birthday boy won't feel he's been fairly treated if he gets stuck with the vanilla piece of cake, and neither will his vanilla-craving sister if she's left with the chocolate. Each envies the other's piece, and both are unhappy. Swap the pieces between them, giving each the flavor he or she likes, and the envy disappears, with both kids feeling they've been treated fairly. This is another kind of fairness — a solution that is said to be envy free.
Game theorists have been able to prove that even with cakes as complicated as the one we've imagined here, I Cut, You Pick is guaranteed to produce an envy-free division of the cake. For this to be true, of course, the child dividing the cake has to have the motor skills to actually cut it exactly the way he wants to, as Paul's sister eventually learned. This doesn't mean each child gets exactly what he or she wants. It means that each believes his or her piece is as good as the other's. So neither envies the other's piece of cake.
Among the most famous game theorists who have studied this problem are Steven J. Brams of New York University and Alan D. Taylor of Union College, in Schenectady, New York, who describe their work in the book The Win-Win Solution: Guaranteeing Fair Shares to Everybody.
Brams and Taylor point out that the notion of cutting a cake can be extended to many other situations. Some years ago, for example, British and Egyptian archaeologists decided it was time to divide certain archaeological remains between them. The objects were all different, so it was impossible to simply give half of the objects to the Egyptians and the other half to the British. How did they solve it? With I Cut, You Pick, of course.
The British divided all of the objects between two rooms in the Cairo museum. Then the Egyptians were allowed to pick one room or the other. The idea, as with cutting a cake, is that the British would have incentive to make the two collections as comparable as possible, because they knew the Egyptians would pick first.
This strategy doesn't just work for antiquities: parents can use it to divide the labor of raising kids. Suppose that you and your partner have a week of shuttling the kids to band practice, play dates, and doctors' appointments. I Cut, You Pick can work to help divide the labor fairly between the two of you. Mom can separate all of the weekly obligations into two piles that she thinks are equal. She will then be satisfied with either pile. The piles will not be identical; one might represent more yard work and less dishwashing than the other, let's say. If Mom has done her best, they will, however, be equal — in her eyes — in terms of the amount of work required.
When Dad chooses, he picks the pile that he thinks represents the least work for him, or the work he's most willing to do. Maybe he prefers kitchen work to yard work, so he chooses the set of chores that's heavy on washing dishes. Mom cuts, Dad picks.
This kind of inter-parental game theory worked well for Kevin's friends Mark and Tia. One was a night owl, the other a morning person. Mark proposed the following split: One of us should get up with our child in the morning. The other should put her to bed. Tia, the night owl, happily chose to manage bedtime, while Mark, the early riser, was pleased to be handling wake-up. It was a win-win — much better for each of them than, say, alternating bedtime and morning parenting.
Kids can use this trick, too. Suppose your children decide they want to divide a shared box of LEGO bricks, toy cars, or stuffed animals. One child divides the objects into two groups, and the other picks one group.
If this naive use of game theory often happens naturally with kids and adults — as it did, for example, with Paul and his sister — what's the big deal? Why do game theorists find cake-cutting so interesting?
The answer is that this is about more than cake, frosting, and the proper division thereof. Understanding how to divide cake means understanding the difference between an equitable division (the two pieces are the same size) and one that is envy free (neither child thinks the other got a better deal). As we've said, the principle here can help with all kinds of situations in which kids need to divide something equally. This can be a useful tool for parents. (And useful for solving problems in government policy and geopolitics, which can seem almost as challenging as raising children.)
Suppose you find yourself, as Paul did recently, standing in the middle of a crowded Toys"R"Us, where an eager store employee is demonstrating a new kind of erasable tablet that you know will never work as well for your kids as it does for him. Your son is interested in the tablet, and he's also trying to raise his voice over the din to ask for a pack of Pokemon cards. Your daughter, meanwhile, wants more Hexbugs to run in the track that already fills up half of her bedroom.
What is a fair division of your resources? How do you cut the cake this time, when the "cake" consists of the tablet, Pokemon cards, and Hexbugs?
Do you spend the same amount of money on each child? You could try that, but what if one Hexbug is more expensive than a whole pack of Pokemon cards? What if the tablet is more expensive than the other two put together? Spending the same on each child won't work. Suppose you ignore the cost and buy each child one toy — one Hexbug for your daughter, and one pack of cards or the tablet for your son. If your son thinks the Hexbug is more valuable than his pack of cards, he might demand another pack of cards — or a Hexbug of his own. If the daughter realizes the tablet is the most expensive gift of all, she might throw the Hexbug on the floor in disgust.
Dividing the resources in your wallet is not the same as cutting a piece of cake — because you are not dividing all of the cake — that is, all of the money in your wallet. You are not spending everything you have on Pokemon cards and Hexbugs (we hope). After you've divided some of your money between your children, you still have some left over. If you are dividing a cake into two parts, when it's gone, it's gone.
There is an important distinction to make between cake cutting and toy buying, as we've described them. Dividing a piece of cake is what's called a zero-sum game. If one person gets more, the other gets less — by exactly the same amount.
Baseball is a zero-sum game. One team wins (giving it a +1 in game theory terms) and the other loses (-1). Add them together and you get zero. Buying toys is not a zero-sum game. Both kids can win. (The only loser is you — because you supply the money to fuel this game!) And there is no physical limit on what you can spend. You know — and your children know — that there is more in your wallet than the money you give them to buy Pokemon cards, tablets, and Hexbugs. And it doesn't take long for kids to learn that credit and debit cards might be, in their eyes, a limitless source of free money.
First, let's look at the zero-sum games a little more closely. Zero-sum games (John von Neumann, the father of game theory, invented that term) were the first situations that game theorists tried to explain. And one of the first examples they looked at was chess. One player wins — you could score that as +1 — and the other loses (-1). Their scores add up to zero. (If they reach a draw, each scores zero — neither winning nor losing — and the total still adds up to zero.) Von Neumann was also interested in poker, which is another zero-sum game, because the total winnings and the total losses are the same. Every dollar von Neumann lost went into the pocket of somebody else at the table — and vice versa: every dollar he won came from somebody else. Subtract the losses from the winnings, and you get zero every time.
One of the first game-theory principles that von Neumann and his colleague Oskar Morgenstern came up with is what's called the minimax principle. They proved that for zero-sum games, minimax play always leads to outcomes in which neither player could improve by switching strategies. Not only that, minimax strategies are "safe." You can ensure that no matter how much smarter the other players are, they can't take advantage of you. The idea is to think about the most you can lose, and devise a strategy to reduce that worst-case scenario. You want to minimize the maximum you can lose. Hence, minimax! If you begin a poker game with $100 on the table and carry nothing else with you, $100 is the most you can lose. And you can lower the maximum you can lose if you bring only $50 the next time. That's the minimax principle at work — you can't lose any more than what you put on the table. But if you have another hundred dollars in your pocket and you reach for it, you've abandoned your strategy, and the most you can lose now begins to rise.
Cake cutting is a good example of the minimax principle. Suppose Paul's sister is cutting the cake. If she cuts the cake into unequal pieces, she stands to lose more than half of the cake. If she cuts it into two equal pieces, the most she can lose is half of the cake. She has minimized her maximum loss. That's minimax reasoning at its best.
The same reasoning helps us understand what's going on when people make decisions about their health insurance, for example. Some healthy young adults might choose to buy minimal insurance plans, figuring that they are unlikely to get sick, and so unlikely to face high medical costs. That could leave them responsible for thousands of dollars in deductibles and other costs if they do get sick. So why should they buy a better, lower-deductible plan? Because it helps to minimize their maximum loss. If they get sick, they pay lower deductibles and get more comprehensive coverage. Their maximum losses are minimized.
This works only if all of the players are more or less rational. As Ken Binmore, a game theorist at University College London, points out, "game theory can't predict the behavior of lovesick teenagers like Romeo and Juliet, or madmen like Hitler or Stalin." For us as parents, that's not a problem — if we behave rationally, and our kids do, too.
Now, let's be honest about this. Our kids are not always rational. They blurt out things they don't mean. They hurt their own cause by continuing to complain after we give in. And let's be even more honest: We're not always rational either. We blurt out things we don't mean. We're influenced by our emotions as well as our common sense.
Most of the time, however, parents and children behave rationally. We try to act in the best interests of ourselves and the family and try to be even-handed in solving family problems. And given the right encouragement and our intelligent use of game theory, our children will behave in their own best interests most of the time. They might continue to throw temper tantrums now and then, but even temper tantrums, as irrational as they can seem at the time, can sometimes be part of a good strategy for kids. And kids usually know it.
Indeed, children might be more strictly rational than adults when it comes to dividing a cake. In his book Rock, Paper, Scissors, the scientist and author Len Fisher describes an experiment he tried at a party where a plate of cake slices was served. When only two were left, he offered them to another guest, who took the smaller of the two pieces. Was this a violation of game theory, which suggests players will maximize their benefits?
He asked the guest why she had taken the smaller piece. "She said that she would have felt bad if she had taken the larger piece," he writes. "The benefit she would have gotten from taking the larger piece (in terms of satisfying her own hunger or greed) would have been more than offset by the bad feeling she would have had about herself for being seen to be so greedy." As it turns out, the game theory prediction was correct. She had not taken the larger slice, which allowed her to have her cake and feel good, too. This is where adults differ from children. Paul can say confidently that his two young boys would always take the larger slice in similar circumstances and feel perfectly fine about themselves. While that makes them good game theorists, he fears it reveals a failure in their moral upbringing — and in his parenting. (This isn't the first time this has crossed his mind.)
Excerpted from The Game Theorist's Guide to Parenting by Paul Raeburn, Kevin Zollman. Copyright © 2016 Paul Raeburn and Kevin Zollman. Excerpted by permission of Scientific American / Farrar, Straus and Giroux.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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Table of Contents
1 I Cut, You Pick 13
2 Don't Cut Barbie in Half! 32
3 He Got a LEGO Set? That's Not Fair! 47
4 You Can't Be Serious! 70
5 The Dog Ate My Homework 89
6 He Started It! 109
7 Why Can't You Pay for This? 127
8 Are You Saying You Don't Believe Me? 144
9 You Can't Tell Me What to Do! 167
Epilogue: Leaving the Nest 185