ANN ARBOR—Whether you are an investor in the stock market or a coyote hunting for dinner, it often pays to do something different from your competitors, says University of Michigan scientist Robert Savit.

But exactly how do successful investors and savvy coyotes make choices that, most of the time, are rewarded with a big financial profit or a fat tasty rabbit? Not only do scientists not know the answer, they are just beginning to understand the question, says Savit, a professor of physics who directs the U-M Program for the Study of Complex Systems.

In a paper to be published in the March 8 issue of Physical Review Letters, Savit and co-authors Radu Manuca and Rick Riolo describe a simple computer model they studied which mimics some of the behaviors of complex adaptive systems commonly found in society, business or ecology. In these systems, independent agents compete for resources and by their competition alter the environment.

The U-M study is fascinating, but it raises more questions than it answers. “Frankly,” says Savit, “at first we were completely mystified by the results.”

In the computer model, a specific number of agents plays a simple game. At every time step in the game, each agent must join one of two groups labeled zero or one. Agents choosing the group that turns out to be in the minority receive one point; agents in the majority group get nothing. The larger the minority group, the more total points awarded. The system performs best when almost 50 percent of the agents are in the minority group, because resources (points) are then distributed to the agents at a maximal rate.

Agents “decide” which group to join by choosing from one of several random strategy tables made up of zeros and ones, which are randomly assigned to the agents. In a given game, each agent “remembers” whether zero or one was the minority group for a specified number of previous time steps in the game. Based on that information, each agent makes its next choice from one of the strategy tables.

“There is no human logic or predictive ability built into the strategy tables whatsoever,” Savit emphasizes. “The zeros and ones in the strategy tables are as random as coin flips.”

Since each agent’s assigned choices are meaningless and arbitrary, you assume the behavior of the agents will be, too. But as the game continues, something remarkable happens.

“If the amount of information the agents remember is just right, then the agents’ choices become coordinated, so the number of agents successfully choosing the minority group is just under 50 percent and a large number of points are distributed to the agents altogether,” Savit says.

“The model shows the importance of balancing the amount of information available with the total population in the system,” Savit adds. “For any given population of agents, there is an optimal amount of information for which they can coordinate their choices and the average agent can earn a lot of points. If the agents don’t have enough information, their choices are maladaptive. If they have too much information to coordinate effectively, their choices are poor and they don’t earn many points. In other words, more information is not necessarily better.”

Assuming that the computer model is an accurate, although simplified, depiction of how adaptive systems work in the real world, it has left Savit with many questions to ponder. For example:

Savit and colleagues are now studying a new computer model that includes evolution; that is, agents can develop new strategies throughout the course of the game based on the effectiveness of past strategies.

“In the evolutionary model, resource distribution becomes an order of magnitude better coordinated,” Savit says. “Minority groups almost always equal 49 percent to 50 percent of the total number of agents—very close to the theoretical maximum you could achieve if you played God and explicitly controlled the size of the minority group. This suggests a number of exciting possibilities; for example, new methods of emergent control of Internet traffic or of vehicular traffic on crowded roadways.”

Continued support for the study of complex adaptive system models is being provided by the U-M. Radu Manuca, a former U-M graduate student, is now at the College of William and Mary. Rick Riolo is director of the U-M Program for the Study of Complex System’s computer laboratory.

Physical Review Letters