Review of “hidden games”: secret equations
Why do peacock feathers – a flashing “Dine Here” sign for predators – attract peacocks? Why are we often satisfied with excuses that we know are not sincere? Why did some snipers in WWI trenches intentionally miss their enemies? The answers, and more, can be found – who knew? – in mathematics. Specifically, in the mathematical models used in “game theory”, a rigorous approach to studying strategic interactions.
It turns out that a few simple equations can illuminate a vast array of social phenomena – economic, political, moral and sexual. That doesn’t mean humans are dumb. This means that, in day-to-day decisions, we can intelligently simmer situations down to their most essential principles.
In “Hidden Games,” Moshe Hoffman of the Max Planck Institute for Evolutionary Biology and Erez Yoeli of MIT do a valiant job of applying game theory to seemingly irrational behavior. Each chapter takes a single game or a theme common to many games and follows it through a mix of real-life examples, psychological experiments, hypotheses, and technical analysis.
Game theory is not for board games like Monopoly but rather for much simpler scenarios. One chapter looks at the hawk-dove game: two players independently decide whether to attack (play hawk) or acquiesce (play dove). If both assault, each has an equal shot at the resources up for grabs, but they both pay the combat cost. If both accept, they each have an equal shot, free of charge. 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 their outcome by unilaterally changing strategies. In hawk-dove, if the cost of the fight is more than half the price value, a Nash equilibrium exists when there is a hawk and a dove.
Which player should back down? It doesn’t matter as long as everyone agrees. MM. Hoffman and Yoeli report that even speckled woodland butterflies have come to this conclusion. When fighting for territory, insects perform a “spiral flight”, a brief battle with a predetermined winner, who happens to be whoever 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 fighting and human rights, which the authors argue are not based on logic but on convention.
Another game explains conspicuous consumption. The principle here is called expensive signage. It often makes sense to do something unnecessary, like buying luxuries, if the relative cost to you is less than the relative cost to someone of more modest means. It shows that you can afford to throw money away, thereby attracting potential partners or allies. In the same way, illustrious feathers that risk attracting predators paradoxically testify to the health of a peacock.
Hidden Games: The Surprising Power of Game Theory to Explain Irrational Human Behavior
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Expensive signage explains human aesthetic judgments; intricate rhyme schemes constrain rap lyricists, making expert verses all the more impressive. Now, why do Brown graduates say they went to school “in Providence” rather than naming their prestigious alma mater? Modesty is also a costly signal, showing that you can manage without showing your laurels.
The book also explains spin-hypes on Instagram and cable news. Viewers expect an exaggeration, so to portray reality would actually be underselling. Meanwhile, overconfidence and other forms of self-deception make it easier for us to deceive others.
One of the most famous economic games is called the iterated prisoner’s dilemma. Each turn, each of the two players can offer to cooperate or try to exploit the other. In the long run, it makes sense that the two continue to cooperate. This is why, during World War I, some snipers aimed at opponents’ walls, not their heads. A chapter on justice gives an extended re-reading of the tragicomic Hatfield-and-McCoy saga and provides a template for revenge. There are repercussions to looking beyond a transgression. “In repeated games,” the authors write, “the past must matter.”
Higher-order beliefs are inferences about the beliefs of others, and they play a key role in many games. They explain categorical standards, such as prohibitions on chemical weapons. Targeting discrete actions (chemical or non-chemical attacks) makes it easier for observers to accept punishment. They know that others know that they or they find out what the abuser did.
Higher-order beliefs also explain indirect speech (“Would you like to come up for a coffee?”), allowing for plausible deniability. And the symbolism. “Symbolic gestures are confusing,” write MM. Hoffman and Yoeli, “because the things that don’t matter question: we place enormous weight on simple words like I’m sorry and I like You and spare no expense for rituals, ceremonies, and elaborate displays that convey no new information. Both public apologies and royal coronations allow for coordination, harmonizing everyone on who is in debt or serving whom.
“Hidden Games” features a conversational style, including humorous asides and lyrics from popular songs. He also has math. My eyes widened when I saw expanses of Greek letters. Fortunately, there is 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 calculations, but in reality the calculations take the regular reader one step further, explaining Why behaviors make sense to us.
We seem to make complex calculations intuitively, like an outfielder determining the trajectory of a flying ball without a slide rule. Genetic and cultural evolution have done the hard work of analysis for us, leaving us with practical instincts and standards. Either way, the equations are likely to be useful to researchers who want to develop new ideas or generate new hypotheses.
On paper, game theory isn’t as fun as it looks. All math, no Monopoly money. But as it’s lived, it’s even more fun. We have a sense of the serious game to thank for the floridity of Eminem’s lyrics, humble Instagram brags, awkward flirtation and royal family drama. Game on.
Mr Hutson is the author of “The 7 Laws of Magical Thinking: How Irrational Beliefs Keep Us Happy, Healthy and Sane”.
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