John Nash Versus the Taxi Drivers of Bangalore

The altruistic human hunters and altruistic babbler birds are two outcomes of a very important evolutionary process called "equilibrium selection." It is an intimidating term, not widely understood even by biologists who have read some game theory. But I think the idea can clarify many mysteries, not only in evolution but in human culture.

To understand equilibrium selection, we first have to understand a little about equilibria and game theory. Game theory is the study of strategic decision-making, where your payoff for doing something depends not only on what you do, but on what other people do. A "game" is any social situation in which there are incentives to pick one's own strategy in anticipation of the strategies favored by others—but where their strategies will in turn depend on their anticipations of your own behavior. This sounds like an infinite regress: I anticipate that you anticipate that I anticipate that you anticipate ... How can game theory make any progress in predicting human behavior in such games, when games seem like hopeless muddles?

Around 1950, the economist John Nash cut through this Gordian knot by developing the idea of an "equilibrium" (now known as a Nash Equilibrium). An equilibrium is a set of strategies, one for each player, that has a simple property. The property is that no player has an incentive to switch to a different strategy, given what the other players are already doing. An equilibrium tends to keep players playing the same strategies. The idea of an equilibrium is the foundation of modern game theory, and therefore of modern economics, business strategy, and military strategy. For his insight, Nash received a share of the 1994 Nobel Prize for Economics.

Driving on the left side of the road is a good example of an equilibrium. If everybody else is already driving on the left, as in Britain, no rational individual has a good reason to start driving on the right—such rebels against convention would quickly be eliminated from the population of drivers. But driving on the right side of the road is also an equilibrium, apparently favored by some former British colonies in North America as a mark of their independence. There is a third equilibrium in the driving game, which consists of driving on the left 50 percent of the time and on the right 50 percent of the time. If everybody is already doing that, you might as well too. This randomized equilibrium seems to be favored in Britain's former colonies in south Asia, especially by the taxi drivers of Bangalore. Nash realized that in most realistic games there are many equilibria. We cannot necessarily predict which equilibrium will be played, but we can predict that players will coordinate their behavior on one of the equilibria. In the driving game, different countries play different equilibria.

Equilibrium selection is the gradual process by which an equilibrium becomes established for a particular game. Imagine an anarchic country without cars that suddenly starts importing cars. People would start driving without knowing which side of the road other drivers will favor. Some would pick the left consistently (the British equilibrium), others would pick the right consistently (the American equilibrium), and still others would toss a coin every day to decide (the Bangalore equilibrium). Now we have a process of competition between three strategies that would each produce a different equilibrium. Suppose that every head-on collision kills both drivers involved. If left-driver meets left-driver, they both survive. If right meets right, they both survive. If Bangalore meets Bangalore, they both die half the time. If right-driver meets left-driver, they both die. There is no rational basis for predicting which equilibrium will become established. Every equilibrium is equally "rational" in the sense that every individual is doing as well as possible given what everyone else is already doing. Although rationality cannot select between equilibria, the contingencies of history can. We can be virtually certain that within several weeks, either the drive-left equilibrium or the drive-right equilibrium will win out. Which of them wins will be due to chance, but one of them will win. (There is only a very small chance that the Bangalore equilibrium will win.)

In this example, the equilibrium selection problem is solved not by rational logic but by historical contingency. When species evolve to play one equilibrium rather than another in the game of courtship, evolutionary contingency can play the role of historical chance. It is easy to simulate this process in a computer, as Brian Skyrms did in his wonderfully lucid 1997 book Evolution of the Social Contract The same equilibrium selection processes must happen all the time in real biological evolution. Most interactions between animals can be interpreted in strategic terms, and so can be modelled using game theory. But for most realistically complex games, there are vast numbers of equilibria: not just three equilibria as in the driving game, but hundreds or thousands of possible equilibria. For realistic games with many equilibria, equilibrium selection processes become absolutely crucial to understanding and predicting behavior.

In our sports example, we considered two possible equilibria in the game of displaying athletic fitness: club-fighting and hunting. If everyone is already club-fighting, you can attract a mate only by club-fighting too, so you have no reason to do anything else, and that makes club-fighting an equilibrium. But if everyone is already hunting, you can only attract a mate by hunting well, so hunting is an equilibrium too. The mate preferences that favor good hunters or good fighters tend to be genetically and culturally conservative, and this sexual conservatism maintains the equilibrium.

Club-fighting and hunting are equally rational from the individual point of view, but hunting is the equilibrium with the higher payoff for everyone. With the Arabian babblers, we saw that altruistic behaviors such as food-sharing and alarm-calling could work as an equilibrium in the game of displaying fitness. The general point is that courtship games have many possible equilibria, and some of them will include a lot of apparently altruistic behavior. Most of them do not, because most ways of wasting energy to display one's fitness do not transfer any benefits to others. The peacock's tail simply wastes one peacock's energy to display his fitness, without transferring that energy to any other peacocks or peahens. But in some species, such as Arabian babblers and humans, our costly courtship displays actually bring some benefits to others.

Anthropologist James Boone described how equilibrium selection can favor altruistic displays in his 1998 paper "The Evolution of Magnanimity." He envisioned different groups playing different equilibria in the game of conspicuous display:

Now imagine that, in some of these groups, elites signal their power by piling up their year's agricultural surplus in the plaza and burning it up in front of their subordinates. In other groups, elites engage in status displays by staging elaborate feasts and handing out gifts to their subjects. After several generations of intense warfare, which type of display behavior is likely to survive in the population? One might expect that the "feasters" would be much more successful at attracting supporters than the "burners."

Competition between groups would favor a magnanimous equilibrium over a wasteful equilibrium. Yet this would not be "group selection," as traditionally defined by biologists, in which individuals incur an individual cost to produce a group benefit. In this case, every individual is acting selfishly and rationally in trying to gain high status and sexual attractiveness through their costly display. The individual sexual benefits, not the group benefits, maintain the equilibrium: group competition merely picks between equilibria. Anthropologists Robert Boyd and Peter Richerson have argued that this sort of interaction between equilibrium selection and group competition is extremely important, not only in genetic evolution but in cultural history. Their ideas offer a new foundation for the comparative analysis of human cultures and social institutions, and I wish I had more space to discuss them further here.

In summary, evolution sometimes favors courtship equilibria in which animals are very generous to others. This does not mean that evolution favors truly selfless altruism, simply that the hidden benefit of generosity is reproductive rather than nepotistic or reciprocal. In principle, evolution could sustain very high levels of altruism by rewarding the altruistic with high social status and improved mating opportunities. Without sexual selection, generosity to unrelated individuals unable to reciprocate would be very unlikely to evolve. With sexual selection, such generosity can evolve easily as long as the capacity for generosity reveals the giver's fitness. In our species, the fact that we find kindness and generosity so appealing in sexual partners suggests that our ancestors converged on a rare, and wonderful equilibrium in the game of courtship.

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