Generous players: game theory explores the Golden Rule's place in biology

Science News,  July 24, 2004  by Erica Klarreich

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Milinski found that when the imaginary stickleback seemed to be defecting, the. real stickleback hung back. "What the experimental fish did corresponded very well to the predicted strategy," Milinski says.

In their recent mathematical analysis reported in Nature, researchers have shown that a single tit-for-tat player in a population of defectors can sometimes get a toehold and then drive the defectors to extinction, provided the population is fairly small.

The researchers' reasoning goes like this. Although a single tit-for-tat player surrounded by defectors does worse than the defectors do, and so has less chance than the defectors of producing offspring, the chance is not zero. If that single player is lucky enough to have an offspring, there are now two tit-for-tat players in the population.

In a large population--say, 1 million--having a second tit-for-tat player doesn't give either one much of a boost, since their odds of running into each other are practically nil. But in a small population--say, 10--the two tit-for-tat players have an excellent chance of encountering each other, cooperating, and getting a high payoff. Depending on the particular payoffs of the game, their fitness levels may soar, and they can expect to have more offspring with each generation.

Martin Nowak of Harvard University and his collaborators have now shown that for a wide range of game parameters and population sizes, a lone tit-for-tat player actually has a better chance of its descendants eventually taking over the entire population than any individual defector does.

ANOTHER FRAMEWORK The prisoner's dilemma has long hogged the limelight when it comes to game theory as a tool to study cooperation. Christoph Hauert and Michael Doebeli of the University of British Columbia in Vancouver argue that researchers should pay more attention to the snowdrift game, which depicts a slightly less stark version of the cooperation paradox.

In this game, two cars are stuck in a massive snowdrift. Each driver can either shovel snow (cooperate) or simply sit in his ear (defect). Unlike the prisoner's dilemma, in which defecting is the better strategy no matter what your opponent does, the snowdrift game requires each player to take into account the other's actions. If the other driver is shoveling, it's tempting to sit back and let him do all the work. However, if your opponent refuses to leave his car, then you'd better get out your shovel and start digging.

The snowdrift game, Hauert says, is a "promising framework for studying cooperation under less-stringent conditions than the prisoner's dilemma--ones where the cooperator gets a share of the benefits." Many animal interactions may fall into this category, he says.

Although researchers have long considered the behavior of animals and other organisms in terms of the prisoner's dilemma, few interactions have been proved conclusively to mirror that game, observes Hauert.

"I think it would be worthwhile to go through the experimental evidence [on animal interactions] again and discuss the findings with respect to the snowdrift game," Hauert says.