Gossip, in fact, turns out to be a crucial outcome of game theory in action, for it's at the heart of understanding human social behavior, the Code of Nature that made it possible for civilization to establish itself out of the selfish struggles to survive in the jungle. For it is in biology that game theory has demonstrated its power most dramatically, in explaining otherwise mysterious outcomes of Darwinian evolution. After all, people may not always play game theory the way you'd expect, but animals do, where the Code of Nature really is the law of the jungle.
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Smith's Strategies Evolution, altruism, and cooperation
The stunning variety of life forms that surround us, as well as the beliefs, practices, techniques, and behavioral forms that constitute human culture, are the product of evolutionary dynamics.
—Herbert Gintis, Game Theory Evolving
To understand human sociality we have much to learn from primates, birds, termites, and even dung beetles and pond scum.
—Herbert Gintis, Game Theory Evolving
In the winter of 1979, Cambridge University biologist David Harper decided it would be fun to feed the ducks.
A flock of 33 mallards inhabited the university's botanical garden, hanging out at a particular pond where they foraged for food. Daily foraging is important for ducks, as they must maintain a minimum weight for low-stress flying. Unlike landlubber animals that can gorge themselves in the fall and live off their fat in the winter, ducks have to be prepared for takeoff at any time. They therefore ought to be good at finding food fast, in order to maintain an eat-as-you-go lifestyle.
Harper wanted to find out just how clever the ducks could be at maximizing their food intake. So he cut up some white bread into precisely weighed pieces and enlisted some friends to toss the pieces onto the pond.
The ducks, naturally, were delighted with this experiment, so they all rapidly paddled into position. But then Harper's helpers began tossing the bread onto two separated patches of the pond. At one spot, the bread tosser dispensed one piece of bread every five seconds. The second was slower, tossing out the bread balls just once every 10 seconds.
Now, the burning scientific question was, if you're a duck, what do you do? Do you swim to the spot in front of the fast tosser or the slow tosser? It's not an easy question. When I ask people what they would do, I inevitably get a mix of answers (and some keep changing their mind as they think about it longer).
Perhaps (if you were a duck) your first thought would be to go for the guy throwing the bread the fastest. But all the other ducks might have the same idea. You'd get more bread for yourself if you switched to the other guy, right? But you're probably not the only duck who would realize that. So the choice of the optimum strategy isn't immediately obvious, even for people. To get the answer you have to calculate a Nash equilibrium.
After all, foraging for food is a lot like a game. In this case, the chunks of bread are the payoff. You want to get as much as you can. So do all the other ducks. As these were university ducks, they were no doubt aware that there is a Nash equilibrium point, an arrangement that gets every duck the most food possible when all the other ducks are also pursuing a maximum food-getting strategy.
Knowing (or observing) the rate of tosses, you can calculate the equilibrium point using Nash's math. In this case the calculation is pretty simple: The ducks all get their best possible deal if one-third of them stand in front of the slow tosser and the other two-thirds stand in front of the fast tosser.
And guess what? It took the ducks about a minute to figure that out. They split into two groups almost precisely the size that game theory predicted. Ducks know how to play game theory!
When the experimenters complicated things—by throwing bread chunks of different sizes—the ducks needed to consider both the rate of tossing and the amount of bread per toss. Even then, the ducks eventually sorted themselves into the group sizes that Nash equilibrium required, although it took a little longer.1
Now you have to admit, that's a little strange. Game theory was designed to describe how "rational" humans would maximize their utility. And now it turns out you don't need to be rational, or even human.2 The duck experiment shows, I think, that there's more to game theory than meets the eye. Game theory is not just a clever way to figure out how to play poker. Game theory captures something about how the world works.
At least the biological world. And it was in fact the realization that game theory describes biology that gave it its first major scientific successes. Game theory, it turns out, captures many features of biological evolution. Many experts believe that it explains the mystery of human cooperation, how civilization itself could emerge from individuals observing the laws of the jungle. And it even seems to help explain the origin of language, including why people like to gossip.
LIFE AND MATH
I learned about evolution and game theory by visiting the Institute of Advanced Study in Princeton, home of von Neumann during game theory's infancy. Long recognized as one of the world's premier centers for math and physics, the institute had been slow to acknowledge the ascent of biology in the hierarchy of scientific disciplines. By the late 1990s, though, the institute had decided to plunge into the 21st century a little early by initiating a program in theoretical biology.
Just as the newborn institute had reached across the Atlantic to bring von Neumann, Einstein, and others to America, it recruited a director for its biology program from Europe—Martin Nowak, an Austrian working at the University of Oxford in England. Nowak was an accomplished mathematical biologist who had mixed biochemistry with math during his student years at the University of Vienna, where he earned his doctorate in 1988. He soon moved on to Oxford, where he eventually became head of the mathematical biology program. I visited him in Princeton in the fall of 1998 to inquire about the institute's plans for mixing math with the science of life.
Nowak described a diverse research program, touching on everything from the immune system—deciphering the math behind fighting the AIDS virus, for instance—to inferring the origins of human language. Underlying much of his work was a common theme that at the time I really didn't appreciate: the pervasive relevance of game theory.
It makes sense, of course. In biology almost everything involves interaction. The sexes interact to reproduce, obviously. There are the fierce interactions of immune system cells battling viruses, or toxic molecules tangling with DNA to cause cancer. And humans, of course, always interact—cooperatively or contentiously, or just by talking to each other.
Evolutionary processes shape the way that such interactions occur and what their outcomes will be. And that's a key point: Evolution is not just about the origin of new species from common ancestors. Evolution is about virtually everything in biology— the physiology of individuals, the diversity of appearances within groups, the distribution of species in an ecosystem, and the behavior of individuals in response to other individuals or groups interacting with other groups. Evolution underlies all the biological action, and underlying evolution's power is the mathematics of game theory. "Game theory has been very successfully used in evolution," Nowak told me. "An overwhelming number of problems in evolution are of a game-theoretic nature."3
In particular, game theory helps explain the evolution of social behavior in the animal (including humans) kingdom, solving a perplexing mystery in the original formulation of Darwinism: Why do animals cooperate? You'd think that the struggle to survive would put a premium on selfishness. Yet cooperation is common in the biological world, from symbiotic relationships between parasites and their hosts to out-and-out altruism that people often exhibit toward total strangers. Human civilization could never have developed as it has without such widespread cooperation; finding the Code of Nature describing human social behavior will not be possible without understanding how that cooperation evolved. And the key clues to that understanding are coming from game theory.
GAMES OF LIFE
In the 1960
s, even before most economists took game theory seriously, several biologists noticed that it might prove useful in explaining aspects of evolution. But the man who really put evolutionary game theory on the scientific map was the British biologist John Maynard Smith.
He was "an approachable man with unruly white hair and thick glasses," one of his obituaries noted, "remembered by colleagues and friends as a charismatic speaker but deadly debater, a lover of nature and an avid gardener, and a man who enjoyed nothing better than discussing scientific ideas with young researchers over a glass of beer in a pub."4 Unfortunately I never had a chance to have a beer with him. He died in 2004.
Maynard Smith was born in 1920. As a child, he enjoyed collecting beetles and bird-watching, foreshadowing his future biological interests. At Eton College he was immersed in mathematics and then specialized in engineering at Cambridge University. During World War II he did engineering research on airplane stability, but after the war he returned to biology, studying zoology under the famed J. B. S. Haldane at University College London.
In the early 1970s, Maynard Smith received a paper to review that had been submitted to the journal Nature by an American researcher named George Price. Price had attempted to explain why animals competing for resources did not always fight as ferociously as they might have, a puzzling observation if natural selection really implied that they should fight to the death if only the fittest survive. Price's paper was too long for Nature, but the issue remained in the back of Maynard Smith's mind. A year later, while visiting the theoretical biology department at the University of Chicago, he studied game theory and began to explore the ways in which evolution is like a game.5
Eventually, Maynard Smith showed that game theory could illuminate how organisms adopt different strategies to survive the slings and arrows of ecological fortune and produce offspring to carry the battle on to future generations. Evolution is a game that all life plays. All animals participate; so do plants, so do bacteria. You don't need to attribute any rationality or reasoning power to the organisms—their strategy is simply the sum of their properties and propensities. Is it a better strategy to be a short tree or a tall tree? To be a super speedy quadruped or a slower but smarter biped? Animals don't choose their strategies so much as they are their strategies.
This is a curious observation, I think. If every animal (plant, bug) is a different strategy, then why are there so many different forms of life out there, why so many different strategies for surviving? Why isn't there one best strategy? Why doesn't one outperform all the others, making it the sole survivor, the winner of the ultimate fitness sweepstakes? Darwin, of course, had dealt with that issue, explaining how different kinds of survival advantages could be exploited by natural selection to diversify life into a smorgasbord of species (like the specialization of workers in Adam Smith's pin factory). Maynard Smith, though, took the Darwinian explanation to greater depths, using game theory to demonstrate with mathematical rigor why evolution is not a winner-takes-all game.
In doing so, Maynard Smith perceived the need to modify classical game theory in two ways: substituting the evolutionary ideas of "fitness" for utility and "natural selection" for rationality. In economic game theory, he noted, "utility" is somewhat artificial; it's a notion that attempts "to place on a single linear scale a set of qualitatively distinct outcomes" such as a thousand dollars, "losing one's girl friend, losing one's life." In biology, though, "fitness, or expected number of offspring, may be difficult to measure, but it is unambiguous. There is only one correct way of combining different components—for example, chances of survival and of reproduction."6 And "rationality" as a strategy for human game players exhibits two "snags," Maynard Smith noted: "It is hard to decide what is rational, and in any case people do not behave rationally." Consequently, he asserted, "the effect of these changes is to make game theory more readily applicable in biology than in the human sciences."7
To illustrate his insight, he invented a clever but simple animal-fighting game. Known as the hawk-dove game, it showed why one single strategy would not produce a stable population. Imagine such a world, a "bird planet" populated solely by birds. These birds are capable of behaving either like hawks (aggressive, always ready to fight over food), or doves (always peaceful and passive). Now suppose these birds all decide that being hawkish is the best survival strategy. Whenever two of them encounter some food, they fight over it—the winner eats, the loser nurses his wounds, starves, and maybe even dies. But even the winner may suffer some injuries, incurring a cost that diminishes its benefits from getting the food.
Now suppose one of these hawkish birds decides that all this fighting is … well, for the birds. He starts behaving like a dove. Upon encountering some food, he eats only if no other bird is around. If one of those hawks shows up, the "dove" flies away. The dove might miss a few meals, but at least he's not losing his feathers in fights. Furthermore, suppose a few other birds try the dove approach. When they meet each other, they share the food. While the hawks are chewing each other up, the doves are chewing on dinner.
Consequently, Maynard Smith noted, an all-hawk population is not an "evolutionary stable strategy." An all-hawk society is susceptible to invasion by doves. On the other hand, it is equally true that an all-dove society is not stable, either. The first hawk who comes along will eat pretty well, because all the other birds will fly away at the sight of him. Only when more hawks begin to appear will there be any danger of dying in a fight. So the question is, what is the best strategy? Hawk or dove?
It turns out that the best strategy for surviving depends on how many hawks there are in the population. If hawks are rare, a hawkish strategy is best because most of the opponents will be doves and will run from a fight. If hawks are plentiful, though, they will get into many costly fights—yielding an advantage for dovish behavior. So a society should evolve to include a mix of hawks and doves. The higher the cost of fighting, the fewer the number of hawks. Maynard Smith showed how game theory described this situation perfectly, with an evolutionary stable strategy being the biological counterpart of a Nash equilibrium.
While an evolutionary stable strategy is analogous to a Nash equilibrium, it is not always precisely equivalent. In many sorts of games there can be more than one Nash equilibrium, and some of them may not be evolutionary stable strategies. An ecosystem composed of various species with a fixed set of behavioral strategies could be at a Nash equilibrium without being immune to invasion by a mutant capable of introducing a new strategy into the competition. Such an ecosystem would not be evolutionarily stable.8 But the birds are unlikely to appreciate that distinction. In any case, the birds have to choose to play hawk or dove just as the ducks had to decide which bread tosser to favor. The best mix—the evolutionary stable strategy—will be a split population, some percentage doves, some hawks.
Exactly what those percentages are depends on the precise costs of fighting compared to the food you miss by fleeing. Here's one game matrix showing a possible weighting of the costs:
If two hawks meet, both are losers (getting "scores" of –2) because they beat each other up. If Bird 1 is a hawk and Bird 2 a dove, the dove flies away and gets 0, the hawk gets all the food (2). But if two doves meet, they share the food and both get 1 point. (Or you could say that one dove defers to the other half the time, the 1 point each signifying a 50-50 chance of either bird getting the food.) If you calculate it out, you find that the best mix of strategies (for these values of the costs) is that two-thirds should be doves and one-third hawks.9 (Keep in mind that, mathematically, you could have a mix of hawks and doves, or just birds that play mixed strategies. In other words, if you're a bird in this scenario, your best bet is to behave like a hawk one-third of the time and behave like a dove two-thirds of the time.)10
Obviously this is a rather simplified view of biology. Hawks and doves are not the only possible behavioral strategies, even for birds. But you can see the basic idea, and you should also be able to see how game theo
ry could describe situations with added complexity.
Suppose, for instance, "spectator birds" watched as other birds battled. In fact, like human boxing or football fans, some birds do like to watch the gladiators of their group slug it out in a good fight (as do certain fishes). And that desire to view violence may offer a clue to why societies provide so much violence to view. Spectating may be wired into animal genes by evolutionary history, and maybe game theory has something to do with it.
At first glance, spectating offers one obvious survival advantage—you're less likely to get killed watching than fighting. But you don't have to be a spectator to avoid the danger of a fight. You can simply get as far away from any fighting as you can. So why watch? The answer emerges naturally from game theory. You may find yourself in an unavoidable fight someday, in which case it would be a good idea to know your opponent's record.
Face it: You can't always run from a fight. The wimps who retreat from every encounter don't really enhance their chance of survival, for they will lose out in the competition for food, mates, and other essential resources. On the other hand, looking for a fight at every opportunity is not so smart, either—the battle may exact a greater cost than the benefit of acquiring the resource. You would expect clever birds to realize that they might have to fight someday, so they better scout their potential opponents by observing them in battle. The observers (or "eavesdroppers" in biolingo) could choose to be either a hawk or a dove when it's their turn to fight—depending on what they've observed about their adversary.
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