For decades, psychologists have used mathematical theories to understand tense social interactions from business negotiations to divorce settlements to peace treaties.
Now, a local academic is applying classic game theory to that most primal and divisive of human conflicts – sibling rivalry.
Kevin Zollman, a game theorist and associate professor of philosophy at Carnegie Mellon University, recently wrote “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” with co-author Paul Raeburn.
The book promises to give harried parents a home-field advantage by divulging how to divide household valuables such as shared bedrooms, time with parents and favorite toys.
Example 1: The Minimax Principle
Simon and his sister Ava have one piece of cake left to share. One of the original game-theory principles suggests that by letting Simon cut the cake and giving Ava first choice of the two pieces, Simon is motivated to cut the cake as evenly as possible.
Beyond sibling spats, game theory can apply to other relationship divides, like deciding which friend gets to use the cool sleeping bag at a slumber party or which parent is on duty with the sick child for the night. Game theory even explains self-enforcing contracts through the lens of childhood:
Example 2: Nash equilibrium
Named after mathematician John Nash of A Beautiful Mind fame, a trade between kids best illustrates this example. Imagine that Henry and Allie agree to a plan: Henry will give Allie his lacrosse stick in exchange for Allie’s Divergent series box set. If Henry wants Allie’s books more than his own lacrosse stick, he’s eager to make the trade. And if Allie wants Henry’s stick more than her books, she’s happy to make the trade too.
For more abstract treasures and decisions – like who gets to name the family pet and where to go on the next family vacation – Zollman suggests using the theory of auction to resolve disputes.
Example 3: The sealed-bid, second-price auction
A sealed-bid, second-price auction works for household treasures that can’t be divided. Imagine Grace, Jack and Chloe all want to control the TV remote. Mom asks them each to bid secretly. Grace writes down $12, Jack writes down $10 and Chloe writes down $5. Grace wins the bid because she had the highest bid, but she only has to pay Mom $11 – Jack’s bid plus a dollar. Feel guilty about taking money from your kids? Use chores as currency instead.
Game theory developed in the 1940s, when scientists discovered that the mathematical theories that work for economic interactions could apply to social interactions between humans. In the 1970s, the science of game theory expanded to understand animal behavior, such as how a bird decides where to look for food or why one buck chooses to fight another. Applying game theory to children is a new trend, Zollman says, adding that children are undergoing the same experiments now that psychologists conducted on adults 10 years ago.
Example 4: The Rotten Kid Theorem
This fascinating, famous game-theory example is somewhat controversial and seems to defy common sense. Human behavior would tell us that rotten kids – the ones who don’t care at all about the fortunes of their parents and sibling – wouldn’t make much of a contribution to their family. But if parents show that they care about the well-being of their rotten kid, despite his behavior, he’ll learn that it serves his selfish interest to treat his parents better – because they will then treat him better. Even rotten kids, in the right circumstances, can be manipulated into acceptable behavior, according to this theorem.
“The strategies the kids will learn are strategies they will use at work, when they start dating and get married,” Zollman says, explaining that game theory helps people find agreements that are mutually beneficial. “We’ve taken strategies developed for corporations or animals to solve different problems and applied them to childhood.”
Example 4: Moral hazard
You’ve set a deal with your daughter Maggie that she uses her own money to pay for treats at the movies. But at the last family trip to the cinema, Maggie’s already spent her weekly allowance and desperately wants popcorn. She begs you to buy her popcorn, and you’re tempted to treat her, knowing how much she’ll enjoy it. If you withhold, she may sulk all the way through the movie. But give in, and you’ve made a serious blunder: You’ve given her an incentive that encourages reckless or undesirable behavior, aka a moral hazard.
The book’s strategies are especially relevant to families with kids older than 5 who are able to see the consequences of their actions, Zollman says.
“Instead of just reacting to the world, they’re capable of forethought and planning,” Zollman says. “That’s when kids get this notion of fairness and what does it mean to be treated fairly.”
Example 5: Pareto optimality
Let’s go back to the cake. Suppose it’s half chocolate and half vanilla, and you have a chocolate-loving daughter and a vanilla-loving son. Rather than cutting two half-vanilla, half-chocolate identical pieces, cut it into a chocolate piece and a vanilla piece, to make the division as fair as can be.
In “The Game Theorist’s Guide to Parenting,” Zollman and Raeburn write:
“Psychologists have found that how children approach negotiations—and whether they share or turn spiteful—depends in large part on notions of fair play. And game theorists have devised various ways to approach any negotiation—some of which are more likely to result in fair outcomes than others.”
The key to successful negotiation, Zollman says, is thinking about problems from another person’s perspective.
“You can’t just think about ‘what do I want,’” Zollman says. “Both people can be made happy because you can think of trades. That skill is really fundamental to finding your way through the world.”