‘Hidden Games’ Review: Secret Equations

A few plain equations, it turns out, can shed light on a vast array of social phenomena—economic, political, moral and sexual. That doesn’t mean humans are simpletons. It means that, in everyday decisions, we can smartly simmer situations down to their most essential principles.

In “Hidden Games,” Moshe Hoffman, at the Max Planck Institute for Evolutionary Biology, and Erez Yoeli, at MIT, do a valiant job of applying game theory to seemingly irrational behavior. Each chapter takes a simple game or a theme common to many games and follows it through a mix of real-life examples, psychology experiments, hypotheticals and technical analysis.

Game theory addresses itself not to board games like Monopoly but rather to much simpler scenarios. One chapter looks at the hawk-dove game: two players decide independently whether to aggress (play hawk) or acquiesce (play dove). If both aggress, each has an even shot at the resources up for grabs, but they both pay the cost of fighting. If both acquiesce, they each have an even shot, cost free. If only one plays hawk, that one gets the goods. An important concept in game theory is a Nash equilibrium, a state in which no one can improve his outcome by unilaterally changing strategies. In hawk-dove, if the cost of fighting is more than half the prize’s value, a Nash equilibrium exists when there is one hawk and one dove.

Which player should back down? It doesn’t really matter, so long as everyone agrees. Messrs. Hoffman and Yoeli report that even speckled wood butterflies have come to this conclusion. When fighting over territory, the insects perform a “spiral flight,” a brief battle with a predetermined winner, which happens to be the one who was there first. “The main feature of the hawk-dove model,” the authors write, “is the importance of shared expectations, which, once established, are self-fulfilling.” The model applies to insect fights and human rights, which, the authors argue, are grounded not in logic but in convention.

Another game explains conspicuous consumption. The principle here is called costly signaling. It often makes sense to do something wasteful, like buy luxury goods, if the relative cost to you is less than the relative cost to someone of lower means. It shows you can afford to throw money away, thus attracting potential mates or allies. In the same way, illustrious feathers that risk attracting predators paradoxically demonstrate a peacock’s health.

Costly signaling explains human aesthetic judgments; complex rhyme schemes constrain rap lyricists, making expert verses that much more impressive. Now why do Brown grads say they went to school “in Providence” rather than name drop their prestigious alma mater? Modesty, too, is a costly signal, showing you can get by without flaunting your laurels.

The book also explains spin—exaggerations on Instagram and cable news. Viewers expect exaggeration, so portraying reality would actually be to undersell. Meanwhile, overconfidence and other forms of self-deception enable us to better deceive others.

One of the most famous economics games is called iterated prisoner’s dilemma. On every turn, each of two players can offer to cooperate with or try to exploit the other. In the long term, it makes sense for both to keep cooperating. That’s why, during World War I, some snipers aimed at adversaries’ walls, not their heads. A chapter on justice gives an extended replay of the tragicomic Hatfield-and-McCoy saga and provides a model of vengeance. There are repercussions for looking past a transgression. “In repeated games,” the authors write, “bygones must be made to matter.”

Higher-order beliefs are inferences about others’ beliefs, and they play a key role in many games. They explain categorical norms, like prohibitions against chemical weapons. Targeting discrete actions—chemical versus nonchemical attacks—makes it easier for observers to agree to punish. They know that others know that they know what the perpetrator did.

Higher-order beliefs also explain indirect speech (“Would you like to come up for coffee?”), which enables plausible deniability. And symbolism. “Symbolic gestures are puzzling,” Messrs. Hoffman and Yoeli write, “because things that don’t matter matter: we put enormous weight on mere words like I’m sorry and I love you and spare no expense on rituals, ceremonies, and elaborate displays that don’t convey any new information.” Public apologies and royal coronations both enable coordination, harmonizing everyone on who’s in debt or service to whom.

“Hidden Games” exhibits a conversational style, including humorous asides and popular song lyrics. It also has math. My eyes glazed over when I came to spans of Greek letters. Fortunately, there’s usually a common-sense explanation to go along with the equations. The existence of more accessible accounts may suggest that we don’t need the math, but in reality the math takes the diligent reader one step deeper, explaining why the behaviors make sense to us.

We appear to be doing complex calculations intuitively, the way an outfielder determines a fly ball’s trajectory without a slide rule. Genetic and cultural evolution have done the hard analytical work for us, leaving us with handy instincts and norms. In any case, the equations will presumably be useful to scholars who want to develop new insights or generate new hypotheses.

On paper, game theory isn’t as fun as it sounds. All math, no Monopoly money. But as it’s lived, it’s even more fun. We have serious gamesmanship to thank for the floridity of Eminem’s lyrics, Instagram humblebrags, awkward flirtation and the theatrics of the royal family. Game on.

Mr. Hutson is the author of “The 7 Laws of Magical Thinking: How Irrational Beliefs Keep Us Happy, Healthy, and Sane.”