Science 1663

Agent-Based Computer Models

Since 9/11 policymakers have been interested in new tools to help guide responses to unexpected events. Here Rob Axtell, Associate Director for the Center for Social Complexity in the Department of Computational Social Science at George Mason University and Ed MacKerrow, a Los Alamos scientist and expert in agent-based modeling, discuss how computer experiments using interacting agents are being used to develop appropriate policies and approaches.

1663: Agent-based computer models have become a hot item in Washington policy circles. Can you explain what they are and why they're important?

Axtell: Agent-based computer models are a new way of working on social science issues. They are used to simulate complex social systems composed of interacting agents—either individuals (consumers, voters, commuters) or social groupings (families, firms, cities, nations).

Ed MacKerrow

MacKerrow: Basically, the simulations amount to science experiments in which we have full transparency into the rules of behavior and can control variables relative to each other. For example, a corporate manager might tell us what factors, including emotional ones, influence his decisions. We then encode those rules of behavior into "if-then" algorithms in the agent-based model. By including rules of behavior for lots of different interacting agents and running the model many times, we can generate a group of virtual corporate histories. We then examine the interesting ones to discover how and why the agents behaved as they did in different situations.

Our goal is to capture the differences in behavioral drivers across a variety of people.

1663: This seems like a radical way to do social science.

Axtell: As a method, it's actually more empirically based than most. The social sciences have many armchair theories about why people do what they do, how institutions work, or why the stock market gyrates the way it does. But those theories are based mostly on speculation because experiments in the social sciences are hard to do.

MacKerrow: The agent-based approach actually prompts us to collect information about people's motivations and their personal incentives. Whereas personal incentives may be difficult to include in equation-based approaches, they are quite naturally represented in computational algorithms.

Axtell: We take the individual-level behaviors and try to figure out what's going to happen at the macroscopic level—the level of the company, the institution, or the whole society. Chris Langdon of the Santa Fe Institute described this modeling approach as a kind of "macroscope," as opposed to a microscope.

MacKerrow: Perhaps your model of retirement would be a good example to describe.

Rob Axtell

Axtell: The basic question is what causes people to retire. The standard economic view is that people are completely autonomous actors who make unilateral decisions based on their assets, age, current employment—basically their economic status.

What's missing is any sense of sociality, of wanting to conform to what your friends, neighbors, and co-workers are doing. So we built a model in which you don't feel like working anymore if all your buddies are retired and playing golf. And conversely, if your friends are all still working hard, then maybe you don't retire even though you'd like to.

Certain peculiarities in the historical retirement data seem more in line with our model than with the conventional models. For example, when retirement policy shifted in 1960 to permit people to retire at 62 but with reduced Social Security benefits, there wasn't an abrupt shift to the early retirement age or a smooth steady shift downward. Instead, there was an irregular pattern of abrupt changes from year to year that settled down in the late '90s, with the most-common retirement age at around 62 instead of 65. Our model produces those kinds of abrupt, irregular changes as individuals try to coordinate with those around them.

MacKerrow: Rob calls it a cascading model. Interestingly, it's not unlike the way a nuclear fission reaction can cause a cascade. A few particles create more particles, and there's a sudden amplification process.

In this simulation of Axtell’s retirement model, there are 100 agents (squares) for each age from 19 to 100 (only ages 55 and above are shown). Purple agents are "rationals" and retire at age 65, the earliest possible retirement age. Blue agents are "imitators" who imitate the people in their social network. Yellow agents are "randoms," they have some probability of retiring at 65 or later. Red agents are retired, white agents have died. Initially (left), retirement at age 65 is not yet the "norm," and lots of agents retire after age 75. Over time (right), 65 becomes the norm as imitators follow rationals.

Axtell: Another example where agent-based models really work is in reproducing certain mystifying empirical regularities, like the distribution of city sizes and business firm sizes (in number of people), which have remained the same for hundreds of years.

The distributions don't follow the standard bell curve (Gaussian). If they did, the number of cities or firms that were bigger than average would decrease very rapidly. Instead, the number decreases more slowly

1663: Like a power law? The number of cities of a given size equals the size to a certain power?

Agent-based models explain why the number of large cities is disproportionately high.

Axtell: Exactly. There are many more large cities, firms, or what have you than a bell curve would predict.

MacKerrow: It's interesting that the variance around the average city or firm size is not well defined. For example, if you calculated an average U.S. firm size from measured data (there are 120 million workers and 6 million firms), the answer would be 20 people. In reality, there are an unexpectedly large number of firms with hundreds and even thousands of employees.

Axtell: That also means that large firms have a disproportionate influence on the economy compared with average-sized firms.

1663: So what kinds of behaviors do you have to allow in the models to get those power law distributions?

Axtell: Most economic theorists start with a model in which the system is in static equilibrium: people can't make changes that allow them to do better because they're already making all the possible tradeoffs. Those models can't produce the large fluctuations at the high end of the distribution that we see for firm and city sizes.

Because we see power law distributions across the social sciences, many of us think that social processes should not be modeled as equilibrium systems. They should be modeled as systems in a state of perpetual evolution or fluctuation in which people are constantly trying to better themselves and their living conditions—nothing is really stationary.

1663: What qualities allow people to better themselves? Do they have different skills and abilities? And do they fill in new niches, with opportunities expanding because of that diversity?

Axtell: When we talk about people bettering themselves and their situation, we're actually examining the difference between growth—simply getting bigger—and development. Whereas mathematics does not lend itself to building models with different qualities of growth, we can do that by giving the agents in our models some distribution of skills. And then we can ask: Which kinds of skills are present after a hundred years in the economy? Which kinds of skills have died out? How does technology evolve? The computational models can help us answer those questions.

1663: Are the agent-based methods being accepted?

MacKerrow: There's a pretty wide-scale acceptance across a variety of fields. The models give decision makers in Washington something tangible. It's not just someone's speculation.

Axtell: Plus, policymakers have a big appetite for models that give them some leverage on long-term problems or new ways of thinking about old problems.

For example, the epidemiology community, driven mostly by demands that arose following 9/11, is using agent-based models to determine the best U.S. response to bioterrorism. Who gets vaccinated and in what order? Should you shut down interstate trucking or all schools and universities?

Agent-based traffic models have also gained a foothold. Models of the entire transportation system give you much higher fidelity than do equation-based simulations, and the policymakers want that because they need to know what to do.

In Washington there's also a lot of interest in modeling certain kinds of military operations, both logistical movements and person-to-person combat, in which every weapon the soldier will have is represented.

The models simulate various military rules of engagement to determine which are likely to produce successful scenarios, and the results are decision aids for policymakers.

1663: Do you think decision makers have a realistic view of what models can do?

Axtell: In some cases, they may be jumping the gun. They want substantive and quantitative results, but you can't get such results from agent modeling without first gathering data on the agents.

A Pashtun wedding.

MacKerrow: Yes. Our Washington customers often ask us to do what I call general models. What causes terrorism, and will we see more? Will Al-Qaeda form into new Al-Qaedas? We've had little success in answering those questions because terrorism is used for different reasons in different contexts.

However, if we focus on specific cases, for example, a particular tribe of Pashtuns [an ethno-linguistic group with populations in Afghanistan] and have good data on what they've been doing for the last 50 years, we may be able to simulate what might happen to the tribe in the future.

For example, suppose a new warlord is suddenly running the village. We could address specific questions: How might that warlord affect opium farming in the region, and how might changes in opium production affect that tribe's relative regional power? If we couldn't talk to the tribal members directly, we would work with anthropologists who have studied that tribe or similar tribes. When we focus on specific situations, with knowledge of the relevant behavioral drivers, agent-based simulation makes sense.

Axtell: Yes, making a good model is always hard. You have to know your sources and the people you're trying to model. I spent 5 years working on a model of 1,000 Anasazi Native Americans who lived in a northeastern Arizona valley from 500 A.D. to 1200 A.D. We had to learn a lot about their archaeology and anthropology.

1663: And what question were you answering?

Axtell: We were trying to adjudicate a longstanding debate about the demise of the Anasazi. Was it due primarily to microclimatic fluctuations or to social factors like war, an epidemic, or even a religious cult?

Our model showed that most of the fluctuations in their population could be understood with the environmental story. The tree rings gave us a record of how much rain actually fell, and so by linking that to their environment and lifestyle in a credible way—the calories they needed to survive, the typical number of offspring per person, life expectancy, and so on—we could get the ebb and flow of the population about right without adding in factors like war or pestilence. The final decline of their last few years, with the last 50 people, probably involved sociality, but their overall decline could be explained by drought caused by microclimatic shifts.

MacKerrow: The nice thing about agent-based models is that you can run the simulations many times to see the macro results, such as total population, time after time, and then compare the results of all the runs with each other and with historical fact.

Axtell: In essence, history represents only one run of the model. You hope that if you run the model 1,000 times, a typical run will agree with history. Of course there's always the possibility of extreme events, like the birth of an Adolph Hitler on steroids who totally annihilates a population.

I always think of the agents as abstract particles with personality.

MacKerrow: But fundamental social science still can't explain why someone born in London ends up as a suicide bomber in Iraq. We sort of understand how attitude diffusion occurs, and we're learning about suicide bombing, but we're still in the dark about the basic drivers behind the behavior. It's like living in a time before the apple fell on Newton's head and being asked to analyze thousands of bits of video data on the trajectories of baseballs. You need Newton's laws of mechanics before you can really explain those trajectories.

The Pashtuns follow patrilineal marriage rules, with greater age conferring greater honor (age increases tward the right). Ideally, the oldest son (far right) would marry a daughter of his oldest uncle (blue arrows) but he (pink arrow) indicates his desire to marry the cousin who has no sisters and is likely to have a larger dowry. Marrying her, however, would dishonor the oldest uncle's family, possibly leading to violent fueds. Rivalry between male cousins causes many tribes to split into sub-tribes ("khels").

Axtell: Right. The social sciences are really pre-Newtonian. We don't even know the right units of analysis. If we actually knew how the 25 or 50 main components of the brain work and interact, we could build a model that would have deep behavioral significance. We don't have that information yet.

MacKerrow: All is not grim though. We are really in a renaissance period for the social sciences. Vast amounts of attitude data are sitting out on the Internet. We have empirical observations from experimental economics studies. Functional magnetic resonance imaging even allows us to directly observe a thinking brain in action. If all that information can be coupled to the experimental analysis of computational social science, we could see great advancements. The major national security issues today revolve on worldwide social-cultural dynamics. Which group will become violent next? Which coalitions will form or break up? Which social identity groups will support, oppose, or react violently to proposed policies? Agent-based simulation may provide a new "algebra" to better represent the way people really behave.