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

Science News, July 24, 2004 by Erica Klarreich

He and Chao measured how the two strains' interactions affect their fitness. "It falls out that these selfish viruses take over the system, but when that happens, the average fitness of the population drops," Turner says. "It fits in exactly with the predictions of the prisoner's dilemma."

TIT FOR TAT Things look rosier for cooperation in situations where a participant plays the prisoner's dilemma repeatedly with the same opponent and learns from previous games. After all, it can be risky to exploit someone you know you're going to encounter again.

In 1980, political scientist Robert Axelrod of the University of Michigan in Ann Arbor held a tournament in which he invited game theorists to submit strategies for repeated prisoner's-dilemma encounters. The computer-simulated tournament produced a surprise: The hands-down winner was one of the simplest strategies, a tit-for-tat rule.

A player using the tit-for-tat strategy cooperates in the first round and then in each subsequent round mimics the opponent's behavior in the previous round. In a population containing a mix of defectors and tit-for-tat players, the latter generally do better, provided there are enough of them. When they meet another tit-for-tat player, both cooperate and get a high payoff. When they meet a defector, they get suckered once, but only once. If repeatedly losing the game translates into low fitness, often the defectors do so poorly that they eventually die out, leaving an entirely cooperative population.

In 1987, Manfred Milinski of the Max Planck Institute of Limnology in Ploen, Germany, found indications that stickleback fish may play the tit-for-tat strategy during a daring maneuver caned predator inspection. If a dangerous predator, such as a pike, enters the sticklebacks' neighborhood, two sticklebacks often swim together toward the open mouth of the predator, presumably to gather information on whether it poses an immediate threat.

The situation looked to Milinski like a classic case of prisoner's dilemma. Cooperating--approaching the pike in synchrony--is best for the group, since it divides the risk evenly and increases the chance that at least one stickleback will survive to return to the group. Yet each individual has a strong incentive to hang back a little and let the other stickleback take more of the risk. A stickleback that lags by just half a body length cuts its risk from 50 percent to 10 percent, Milinski says.

Milinski noticed that when the sticklebacks approached the pike, one would advance a bit and then check whether the other had followed. "Each step was one round of the game, Milinski says.

To test whether the sticklebacks were using a tit-for-tat policy, Milinski placed a lone stickleback in a tank with a pike and positioned a mirror to give the stickleback the illusion that there was a second stickleback nearby. Depending on the angle of the mirror, this imaginary fish appeared to be either swimming apace or dawdling.

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.