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Let These Game Theorists Show You A Better Way To Resolve Conflicts

Coin tosses might seem fair at first, but they create envious losers. Here's an alternative that leaves everyone happy.

Let These Game Theorists Show You A Better Way To Resolve Conflicts
[Photo: Flickr user david pacey]

Busy parents know the drill: A friend is having a party, and you can't get a sitter. Who gets to go and who has the pleasure of putting an overtired child to bed after a long day? Little Samantha has soccer practice during Jimmy's first piano recital, and both parents want to make the recital. Who gets the pleasure of the live performance, and who gets left with the jumpy, badly lit iPhone video?

No, solving these domestic conflicts might not seem a like rocket science—one parent usually just takes one for the team and the other returns the favor the next time—but an actual scientific field has developed for understanding disputes like this: game theory. In the 1940s, polymath John von Neumann and economist Oskar Morgenstern started systematically studying conflict and cooperation, and the discipline has grown a whole lot wider and more complex ever since.

Here’s a look at how to solve some of life’s seemingly intractable conflicts—big and small—like a game theorist.

Stop Tossing Coins

The term "game theory" conjures up images of teenagers in the basement arguing about whether to play Halo or Assassin's Creed. But economists use the term "game" to mean much more. For a game theorists, any interaction between two parties counts as a game so long as they each react to what the other does in an attempt to get something they want.

Common games, like chess and poker, count as "games" in the theorists' sense; solitaire—which is just between the player and that stupid deck of cards—doesn’t. And while we'd never colloquially refer to them that way, disputes between kids, parents, businesses, and countries all do count as games in the theoretical sense.

So what can game theory do for parents trying to divide up their duties to their kids, their work, and their social lives—or for that matter, to the overwhelmed manager of a few obstreperous employees? Game theorists would point out that, faced with the soccer-practice-or-recital scenario, two people are fighting over a single "indivisible" resource. The opportunity to go out is a resource, and it can't be split: Mom can't half-go to the party.

To resolve these dilemmas, many of us turn to the old coin toss. This seems fair, after all. You can't split the joy of a recital in half, but you can give each parent an equal chance.

Game theorists don't like this. First, flipping a coin only seems fair to both parties before the coin is flipped. To put it another way, neither parent at that point envies the other—yet. But after you flip the coin, you can be sure what’s to come. One of you gets to go to the party, and the other mumbles about how suspicious it is that their partner seems to win more than their fair share of coin tosses.

The second flaw with tossing a coin bothers game theorists even more: Flipping a coin doesn't give the reward to the person who wants it more. Remember the story of Solomon? He had to adjudicate a dispute between two women each claiming to be a baby's mother. What would’ve happened had Solomon proposed a coin toss? Half of the time, the person who has no right to the child will end up with it.

Start The Bidding

So how do we address these two flaws? Game theorists have a favorite solution: auctions. Here's the idea: If you have one item that can’t be divided, you want to assign it to the person who desires it most. Ask disputing parties to put their money where their mouth is and declare how much they’d be willing to pay for the item in question.

Auctions have been used as a means to sell all sorts of things throughout history. The most common type of auction is an "English" auction (sometimes called an "open cry, first price" auction). This is probably what you think about when you think about auctions.

But game theory textbooks almost always recommend a different type of auction, called a "sealed bid, second price auction." In these, everyone secretly writes down a final bid on a piece of paper and turns it in to the auctioneer—this is the "sealed bid" part. It may not surprise you to learn that the person who bids the most wins the auction. Here’s the surprising part: The auctioneer only charges the winner one dollar more than the bid of the second highest bidder—that’s the "second price" part.

The Nobel Prize–winning economist William Vickrey proved that the best strategy in these auctions is to write down the maximum you're willing to pay. There’s no trickery here; these auctions create an incentive for honesty.

Why is all this better than flipping a coin? Because coin tosses produce jealousy between the disputants—whoever’s on the losing end of the flip winds up envying the winner. The auction, on the other hand, produces an outcome that’s envy-free. What's more, with auctions the person who values the object most gets it every time, assuming that everyone starts with the same amount of "money"—or whatever type of stake that happens to be.

Now that you've got a couple of auctions to choose from, there’s only one thing left for an auctioneer to decide: What should you pay with? Nobody said payments have to be in dollars and cents.

So instead of using money, parents might consider making their spouses pay with chores; managers may want to put less enjoyable tasks or assignments on the table. Not only does this guarantee that whoever gets the prize really is the one who wants it more, but it also helps get something necessary, if mildly unpleasant, done at the same time. Win-win is always better than heads-tails.

This article is adapted from 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 by Paul Raeburn and Kevin Zollman (Scientific American/FSG, April 5, 2016). It is reprinted with permission.

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