A Beautiful Math

by Tom Siegfried

  "I'd like to give you a word of advice," Gutman whispers to Spade. "I daresay you're going to give her some money, but if you don't give her as much as she thinks she ought to have, my word of advice is, be careful." Gutman knew that people react negatively to the perception of being treated unfairly. He could have predicted the outcome of ultimatum games without game theory or brain scanners, because he was an astute student of human nature.

  So why bother with game theory? If you can figure out human nature just by observing how people behave, whether in the real world or the lab, perhaps game theory is nothing more than superfluous mathematics. Besides, when game theory math incorporates the economists' belief in selfish rationality, it doesn't even predict human behavior correctly.

  Actually, though, game theory provides a more sophisticated and quantitative tool for describing human nature than the intuition of criminals. Looked at in the right way, the ultimatum game does not disprove game theory, but expands it. Fairness, trust, and other social conditions do affect how people play games and make economic choices. But that just means that the standard economic notion of self-interest is too restrictive—life is more than money. Game theory's math doesn't really tell you what people want, but rather how people should behave in order to achieve what they want.

  As economist Jörgen Weibull observes, reports of game theory's death have been exaggerated. "It has many times been claimed that certain game-theoretic solutions—such as Nash equilibrium … —have been violated in laboratory experiments," Weibull writes. "While it may well be true that human subjects do not behave according to these solutions in many situations, few experiments actually provide evidence for this."2

  Early experiments with tests such as the ultimatum game merely assumed that people wanted to maximize their money—which they often failed to do when playing the game. Such tests do not disprove game theory, though; instead, they suggest that something is wrong with the experimenter's assumptions. Later versions of the ultimatum game attempted to include things like fairness, or, more generally, test how a player's social preferences (that is, concerns for others) influence game decisions. Such factors as altruism and spite, Weibull notes, affect the outcome that players prefer to reach, and they make their choices accordingly.

  "Indeed, several laboratory experiments have convincingly— though perhaps not surprisingly for the non-economist—shown that human subjects' preferences are not driven only by the resulting material consequences to the subject."3 In some cases, social context (say, the norms of a person's peer group) dictates choices that appear inconsistent with both personal self-interest and concern for the welfare of others. "Further analysis of preferences of this type seems highly relevant for our understanding of many social behaviors," Weibull observes.4

  THE NATURE OF HUMAN NATURE

  By getting a grip on the nuances of social preferences, game theory enhances its prospects for forging a science of human behavior, a Code of Nature for predicting social phenomena. But there might be a flaw in that plan. It presumes that there is such a thing as "human nature" to begin with for game theory to describe.

  At first glance, experiments such as those using the ultimatum game do seem to provide evidence for a consistent human nature. After all, when economists play the ultimatum game with college students, the results come out pretty much the same, whether in Los Angeles, Pittsburgh, or even Tokyo. And of course, one wellknown battalion of social scientists argues strongly that there most definitely is a universal human nature. They are devotees of a discipline known as evolutionary psychology, a widely publicized field contending that human behavior today reflects the genetic selection imposed on the species during the early days of human evolution. Human nature, this notion implies, is a common heritage of the race, shaping the way people instinctively respond to situations today, based on how they behaved in order to survive in hunter-gatherer times.

  A typical advocate of this view is Harvard psychologist Steven Pinker, who argued his beliefs with considerable passion in a book called The Blank Slate. Viewing the brain as blank at birth, to be shaped totally by experience, is nonsense, he insisted. General features of human nature have been programmed by evolution and stored on a genetic hard drive that guides the brain's development. As a result, human nature today derives from the era of early human evolution. "The study of humans from an evolutionary perspective has shown that many psychological faculties (such as our hunger for fatty food, for social status, and for risky sexual liaisons) are better adapted to the evolutionary demands of our ancestral environment than to the actual demands of the current environment," Pinker wrote.5

  In other words, people today are just hunter-gatherers wearing suits.

  On the surface, it might seem that it would be a good thing for game theory—and the rest of the human sciences—if this idea is right. If the Code of Nature is inscribed into the human genetic endowment, that should improve the prospects for deciphering the rules governing human nature and then predicting human behavior. After all, the concept that a Code of Nature exists might be interpreted to mean that there is some universal behavioral program to which all members of the human species conform.

  Yet with all due respect to much of the intelligent research that has been done in the field of evolutionary psychology, some of the conclusions that have been drawn from it rest on rather shaky ground. And it turns out that rather than bolstering evolutionary psychology, game theory helps to show why it breaks down. Furthermore, the way game theory does it has much in common with the way that Asimov's fictional hero Hari Seldon found the solution to formulating his physics of society, or psychohistory.

  COMPARING CULTURES

  In Prelude to Foundation, the first prequel to Asimov's Foundation Trilogy, a young Hari Seldon delivers a talk at a mathematics conference on the planet Trantor, capital world of the Galactic Empire. Seldon's talk describes his idea of predicting the future via the math of psychohistory, a science that he had just begun to develop. Naturally the emperor receives word of this talk (in the galactic future, politicians pay more attention to science than they do today) and invited Seldon to an audience.

  "What I have done," Seldon told the emperor, "is to show that, in studying human society, it is possible … to predict the future, not in full detail, of course, but in broad sweeps; not with certainty, but with calculable probabilities."6

  But the emperor was dismayed to learn that Seldon couldn't actually predict the future just yet, that he merely had the germ of an idea about how to do so if the mathematics could be properly developed. Seldon, in fact, was skeptical that he would ever succeed.

  "In studying society, we put human beings in the place of subatomic particles, but now there is the added factor of the human mind," Seldon explained. "To take into account the various attitudes and impulses of mind adds so much complexity that there lacks time to take care of all of it."7

  In fact, Seldon pointed out, an effective psychohistory capable of predicting the galactic future would have to account for the interacting human variables on 25 million planets, each containing more than a billion free-thinking minds. "However theoretically possible a psychohistorical analysis may be, it is not likely that it can be done in any practical sense," he admitted.8

  By displeasing the emperor with such pessimism, Seldon soon found himself a fugitive, roaming from one sector to another on the planet Trantor—the urban sector of the Imperial capital, a university town, a farming region, an impoverished mining center. By the end of the book Seldon realized that Trantor was a microcosm of the galaxy, home to hundreds of societies each with their own mores and customs. That was his solution to achieving a science of psychohistory! He didn't have to analyze 25 million worlds; he could understand the variations in human behavior by using Trantor itself as a laboratory.

  Toward the end of the 20th century, Earth-bound anthropologists independently arrived at a similar scheme for analyzing human social behavior. By playing the ultimatum game (and some variants)
in small, isolated societies around the planet, those scientists have found that human nature isn't so universal after all. College students in postindustrial society, it turns out, are not perfectly representative of the entire human race.

  This worldwide game-playing project began after anthropologist Joe Henrich, then a graduate student at UCLA, tried out the ultimatum game with the Machiguenga farmers of eastern Peru in 1996. The rules were the same as with college students: One player is given a sum of money and must offer a share of it to the second player. The second player may either accept the offer (and the first player keeps the rest) or the second player may reject the offer, in which case all the money is returned and neither player gets anything.

  By the time Henrich tried the game in Peru, it had been widely played with college students, who usually make offers averaging more than 40 percent of the pot. Such offers are routinely accepted. Sometimes lower amounts would be offered, but they would usually be rejected. Among the Machiguenga, though, Henrich observed that lower amounts were routinely offered—and usually accepted.

  "We both expected the Machiguenga to do the same as everybody else," UCLA anthropologist Robert Boyd told me. "It was so surprisingly different that I didn't know what to expect anymore."9

  Could it be that the Machiguenga actually understood the rational-choice rules of game theory, while everybody else in the world let emotions diminish their payoffs? Or would other isolated cultures behave in the same way? Soon Henrich, Boyd, and others acquired funding from the MacArthur Foundation, and later the National Science Foundation, to repeat the games in 15 smallscale societies on four continents. The results were utterly baffling. From Fiji to Kenya, Mongolia to New Guinea, people played the ultimatum game not just the way college students did, or the way economic theory dictated, but any way they darn well pleased.

  In some cultures, like the Machiguenga, low offers were typical and were often accepted. But in other cultures, low offers were frequently made but typically rejected. In a few cultures the offers would sometimes be extra generous—even more than half. But in some societies such generous offers were likely to be refused. Among other groups, rejections almost never occurred, regardless of the size of the offer.10

  "It really makes you rethink the nature of human sociality," Henrich, now at Emory University in Atlanta, told me. "There's a lot of variation in human sociality. Whatever your theory is about human behavior, you have to account for that variation."11

  CULTURAL DIVERSITY

  This cross-cultural game theory research clearly shows that people in many cultures do not play economic games in the selfish way that traditional economic textbooks envision. And it appears that the differences in behavior are indeed rooted in culture-specific aspects of the group's daily life. Individual differences among the members of a group—such as sex, age, education, and even personal wealth—did not affect the likelihood of rejecting an offer very much. Such choices apparently depend not so much on individual idiosyncrasies as on the sorts of economic activity a society engages in. In particular, average offers seemed to reflect a society's amount of commerce with other groups. More experience participating in markets, the research suggested, produces not cutthroat competition, but a greater sense of fairness.

  The stingy Machiguenga, for instance, are economically detached from most of the world—in fact, they hardly ever interact with anyone outside their own families. So their market-based economic activity is very limited, and their behavior is selfish. In cultures with more "market integration," such as the cattle-trading Orma in Kenya, ultimatum game offers are generally higher, averaging 44 percent of the pot and often are as much as half.

  Orma average offers are similar to those found with American college students. But sometimes students make low offers, and the Orma rarely do. College students find their low offers are usually rejected, but in some societies any offer is accepted, no matter how low. Among the Torguud Mongols of western Mongolia, for example, a low offer is rarely refused. Even so, Torguud offers averaged between 30 and 40 percent—despite the fact that the offerer would surely get more by offering less. Apparently the local Mongolian culture values fairness more than money. At the same time, inflicting punishment (by rejecting an offer) is not highly regarded there, either.

  In society after society, the anthropologists discovered different ways in which cultural considerations dictated unselfish behavior. Among the Aché of Paraguay, for example, hunters often leave the day's game on the outskirts of their village. Members of the tribe then retrieve it for sharing among the villagers. When playing the ultimatum game, the Aché typically make high offers, often more than half. So do the whale-hunting Lamalera of Indonesia, who carefully and fairly divide up the meat from killed whales.

  In other societies, though, the cultural influences play out differently. In Tanzania, the Hadza share meat, but they complain about it and try to get away without sharing when they can. Nonsharers, though, risk ostracism, social scorn, and negative gossip. It makes sense, then, that when playing the ultimatum game, the Hadza make low offers, with high rejection rates.

  On the other hand, high offers do not always signify a culture imbued with altruism. The Au and Gnau of Papua New Guinea often offer more than half the money, but such generosity is frequently rebuffed. The reason, it seems, is that among the Au and Gnau accepting a gift implies an obligation to reciprocate in the future. And an excessively large offer may be interpreted as an insult.

  Colin Camerer, one of the economists collaborating with the anthropologists in the cross-cultural games, observes that this result is just another twist in the cultural influence on economic behavior. "Offering too much money, rather than being extremely generous, is actually being kind of mean—it's demeaning," Camerer explained to me. "So the money is turned down because they don't want to be insulted, and they don't want to be in debt."12

  The surprising results of the cross-cultural game theory experiments showed that the games were not necessarily measuring what the scientists thought they were. Rather than purely testing economic behavior, the games actually tapped into patterns of cultural practice. Players apparently tried to figure out how the game related to their real-world life and then behaved accordingly.

  For instance, the Orma quickly recognized a similarity between real life and a variant of the ultimatum experiment, the public goods game (which we encountered in Chapters 3 and 4). In that game the experimenter (Jean Ensminger of Caltech) offered each of four Orma some money from which they could contribute to a community pot and keep the rest. Ensminger would then double the pot and divide it equally among the four players. When she described the game to her Kenyan assistants, they quickly replied that it was just like harambee—a practice of soliciting contributions for community projects.

  "That really changed our thinking a lot about what was going on when people are in an experiment," Camerer told me in one of our conversations at Caltech. "In game theory, the bias we inherited was the mathematician's bias." In other words, the initial belief was that "when you present the game, it's like a smart kid sitting down to play Monopoly or poker…. They read the rules, figure out what to do—they treat it as like a logic problem. But these subjects treat it as like analogical reasoning—what is this like in my life?"13

  So what the game theory experiments have shown is that life differs in different cultures, and economic behavior reflects those differences in cultural life. Game theory has consequently illuminated the interplay of culture and economic behavior, showing that humankind does not subscribe to a one-size-fits-all mentality. Human culture is not monolithic—it's like a mixed strategy in game theory.

  In an intriguing way, this diversity in cultural behavior around the world parallels the multiplicity of versions of "human nature" found within various academic disciplines. When I visited Boyd in his office—on the third floor of Haines Hall on the UCLA campus—our discussion turned to that problem in pursuing the general notion of human nature and the basic prin
ciples of human behavior. Boyd lamented the academic world's fragmented and inconsistent view of how people tick.

  "We have this weird, I think untenable, situation in the social sciences," he said. "You go over to Bunch Hall and the economists tell the students one thing. And the students come over here to sociology, one floor down, and they get told no, that's all wrong, this is right. And they come up here, and we anthropologists tell them all kinds of different things…. And then they go to the psychology department and they get told something different again. This is not OK. It's not acceptable that the economists are happy with their world and the sociologists are happy with their world, and this persists in an institution which is supposed to be about getting at the truth."14

  Perhaps the rise of game theory as a social science tool, though, will help change that situation. In particular, merging the abstract math of game theory with the real-world immersion of anthropologists and other social scientists has begun to show how disparate views of human nature may be drawn closer to how life really works.

  "Somehow in the last 20 years there's been this emergence," Boyd said, "of people who are interested in doing mathematical theory like game theory, but building it on psychologically real people."

  GAMES, GENES, AND HUMAN NATURE

  The fairness displayed in many societies and the variety of behaviors among them are hard to reconcile with the view that human psychology is universally programmed by the evolutionary past. A hard-line interpretation of evolutionary psychology would predict similar behavior everywhere. The game experiment project argues otherwise, posing a conundrum for evolutionary psychologists.

  "I think that if it had turned out that everywhere in the world people were … ruthlessly selfish, they would have said, ‘See, I told you so,'" said Boyd. "And when it didn't turn out that way … that's not a comfortable fact for them. It's some fairly strong evidence on the other side of the scale." He pointed out, though, that evolution remains important to human psychology. "No educated person should doubt that our psychology is the product of evolution— that's a given," Boyd said. "The question is, how did it work?"