An Agent-Based Model of Terrorist Activity William M. Bulleit Michigan Technological University
[email protected] Matthew W. Drewek Michigan Technological University
[email protected] Abstract Prediction of where terrorists are most likely to strike is an issue that concerns planners, law enforcement and government agencies at various levels, and engineers who must design facilities of all kinds. The present work is an effort to use agent-based modeling to examine the interaction of civilians, terrorists, and security to determine the types of facilities (resource locations) that are most susceptible to attack. The ultimate goal is to be able to estimate the probability of attack for various types of facilities in a population center so that resources can be allocated for hardening or otherwise protecting those facilities. We have approached the modeling of the community beginning with the basic concepts of resources, metabolism, and vision [Epstein & Axtell 1996]. The terrorist agents evolve from the civilian agents using a tag mediated procedure derived from that used by Axelrod [1997]. The number and location of security agents are determined based on the wealth and level of fear in the civilian agent population. The preliminary results from this model show terrorist activity occurring near, but not on, locations of maximum resources and on the routes that the civilian agents use to move back and forth between resource locations. Contact: Prof. William M. Bulleit Dept. of Civil and Environmental Engineering Michigan Technological University Houghton, MI 49931-1295 Tel: 1-906-487-2853 Fax: 1-906-487-1620 Email:
[email protected] Key Words: agent-based modeling, terrorism Acknowledgement: We would like to thank both the National Science Foundation and the Michigan Technological University Department of Civil and Environmental Engineering, whose support has made this project possible. Support: This material is based upon work supported under a National Scie nce Foundation Graduate Research Fellowship. Any opinions, findings, conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the National Science Foundation.
An Agent-Based Model of Terrorist Activity William M. Bulleit and Matthew W. Drewek Prediction of where terrorists are most likely to strike is an issue that concerns planners, law enforcement and government agencies at various levels, and engineers who must design facilities of all kinds. The present work represents an effort to use agent-based modeling to examine the interaction of civilians, terrorists, and security to determine the types of facilities (resource locations) that are most susceptible to attack. The ultimate goal is to be able to estimate the probability of attack for various types of facilities in a population center so that resources can be allocated for hardening or otherwise protecting those facilities. Agent models comprise a range of types, of which this one is an extension of the type used by Epstein and Axtell [1996] where the society evolves from resources on the environment, agent metabolism for those resources, and agent vision of the environment (knowledge). The present view of our model is that it represents a community in which civilians evolve to become radicals who may become active terrorists committing attacks on the community. The concept of using agent models to simulate terrorism has been suggested by previous work [Epstein 2002].
Community Environment The environment on which this community evolves consists of a rectangular grid on which lie a numb er of piles of resources. Each civilian agent requires a set amount of each different resource. The resource piles can be isolated in the sense that there may not be a resource gradient between the piles. This lack of gradient is important to the design of the civilian agents. A second aspect of the environment that should be mentioned here relates to the effects on the environment of a terrorist attack. A terrorist attack, modeled as a suicide bomber, results in the destruction of all resources on the grid point where the terrorist was at the time of the attack plus all agents and all resources on the Moore neighborhood of that grid point.
Civilian Agents Civilian agents evolve on the environment. Each agent is randomly assigned a metabolism for each different resource on the environment and a vision, the numb er of grid points that it can see in the four cardinal directions from its current location. The agents are also randomly assigned an amount of each of the different resources on the environment. The agents move around the environment in search of resources that they need to live. Agents have a gender, and when male and female agents meet they procreate, if each of them has reached a fertile age and is wealthy enough. Wealth is measured in units we refer to as “generalized resources.” The generalized resource is the amount of time that an agent can live if it collects no more resources, given that the agent dies if the amount of any single resource drops below zero. Procreation allows the agents to evolve vision and metabolism. Because the environment does not have a resource gradient at all locations, the agents were given memory. Without this memory, it is difficult to evolve a stable population. The memory is simple – the agent remembers the grid point where the maximum of each of the different resources that it has encountered in it travels around the environment is located. Thus, if there are three different resources on the environment, then the agent stores the location and amount of the maximum value of each of the three resources it has encountered. It updates these values as it finds a better source (larger value) of a specific resource. As well as allowing a stable population to evolve, this simple memory allows agents to evolve patterns of travel between resource locations; for instance the path between two resources could represent travel between home and work in a real community.
Terrorist Agents and Terrorist Attacks Terrorist agents evolve from the civilian agent population. The evolution of a civilian agent to a terrorist is performed using a tag mediated process that is based on the approach used by Axelrod [1997]. Each agent is assigned a tag at the beginning of the simulation or at birth. The tag consists of a string of five integers where each integer ranges from 0-9. As the agents move around they interact with other agents. The interaction is controlled by the tags, and the evolution of a civilian to a terrorist is based on the tag values. First, consider interaction. When an agent moves to a grid point, it examines, at random, one of the grid points in its von Neumann neighborhood. If an agent is on that location, they compare the sum of the five numbers in their tag. The closer the two sums are, the larger the probability that the agents interact. If the difference is 45, then the probability is zero that they interact; if the difference is 0 then the probability of interaction is 1.0. The probability of interaction is uniform between these two end points. If the agents interact, then one of the integer locations in the tag is chosen at random – a 0.20
probability that any one of the five is chosen. Once one of the integer locations is chosen, the agents compare the integer they have at that location. If the integers are the same, nothing happens. If the integers are different, then one of two things occur: (1) The agent that moved changes its integer to match the agent that it interacted with, or (2) the agent that moved has a radical conversion with probability based on the difference between each agent’s integer value – the larger the difference, the more likely that a radical change will occur. The agent that moved will change its integer to a 0 or a 9. After the agents have interacted, whether or not an integer change has occurred in either of the above two ways, there is still a small probability that one of the integers on its tag will change by -1 or +1, referred to as an isolated change. This ends the interaction. The agent that moves has the changes occur to it so that there is no possibility that an agent will be changed more than once during any time step [Axelrod 1997]. An agent becomes a terrorist based on the sum of the five integers in its tag. The probability that the agent becomes a terrorist is based on a U-shaped symmetrical polynomial function that passes through 1.0 at a sum of 0, 0.0 at a sum of 22.5, and through 1.0 again at 45. Thus there is some probability that any agent can become a terrorist, but the probability is greatest near the end points of the sum of tag integers. After the agent becomes a terrorist, it remains an inactive terroris t until its age and wealth each reach a specific value that allows it to become active. After every change to the tag, the agent’s new sum is used to determine the probability of becoming a terrorist (if the agent is already a terrorist, the probability is that of remaining a terrorist). An active terrorist agent stops looking for resources and begins to examine the wealth on the von Neumann neighborhood of grid points within its vision. This information, referred to as surveillance data, consists of present agent wealth, grid point resource value, and the moving average of the agent wealth on each grid point over the past 10 time steps. This approach is used because terrorists do not strike just high wealth locations, but locations where wealth passes through, e.g., airports. The active terrorist agent then keeps track of the mean and standard deviation of the largest five surveillance data values that it has seen in its travels. When it finds a grid point that has a surveillance data value that is greater than the mean plus some number of standard deviations (typically 1.0) and the coefficient of variation of its surveillance data set is less than 0.25, it becomes a suicide bomber and explodes destroying wealth on the Moore neighborhood as discussed above. These two criteria for going active allow a terrorist agent to attack when it finds a local region with a relatively consistent high level of wealth.
Security Agents The number of security agents in the community evolves as attacks occur, but cannot drop below a base level of security defined by the user. The number of security agents is based on characteristics of each agent in the population. These characteristics include: the wealth of the agent, the resources the agent collects at each time step, the level of fear that the agent feels at that time step, the maximum and minimum amount of fear that the agent has felt in the past, and the inherent nervousness of the agent. These characteristics are used to determine the amount of resources that the agent is willing to contribute to buying security. Note that the agents do not actually give up any resources. The amount of resources that each agent is willing to give up for security, but does not actually give up, is summed over all agents and divided by the average metabolism of all agents. This procedure gives the number of security agents on the environment at the end of that time step. Security agents search for terrorists in regions of high population. Each security agent moves to the open grid point within their vision that has the most agents on its von Neumann neighborhood. Once on that grid it examines its von Neumann neighborhood. It interacts with (investigates) each agent on the von Neumann neighborhood with a probability related to the number of agents on the neighborhood, e.g., if there were three agents on the von Neumann neighborhood, then it interacts with each of those agents with probability 1/3. If the security agent interacts with an agent, there are two possible outcomes: (1) It releases civilians, or (2) it arrests terrorists (active or inactive) with a probability determined using the U-shaped symmetrical polynomial function described above. Thus, the probability of arresting a terrorist agent increases for more radical agents (sum of tag integers closer to 0 or 45). An arrested terrorist agent is permanently removed from the environment.
Incubation and Steady State The steady-state behavior of the community only becomes apparent after the agents, particularly the civilian agents, have learned to live on the environment. We refer to this as the “incubation period.” After the incubation period the population is reasonably stable, some number of security agents are on the environment, and terrorists are being generated on a regular basis.
Illustration of Simulated Terrorist Activity The process described above was implemented using MatLab [MathWorks 2002]. This illustration is on an environment with two piles of each of two resources. Examination of Figure 1 shows the four piles. The piles in the SW and NE quadrants are the first resource, and the agents have the higher metabolism for this resource, i.e., they need more of it. The piles in the SE and NW quadrants are the second resource, and the agents have a lower metabolism for it. The minimum el vel of security was set at 1.0%. This level is high if each security agent represents one person and each civilian agent represents one person. But, the level may not be too high if one civilian agent represents more than one person. We are not at the stage in our modeling to be able to make this distinction. The results from simulations on this environment, Figure 1, show two terrorist behaviors: (1) Terrorists typically attack near, but not on the resource peaks (1 on Figure 1), and (2) terrorists attack in regions off of the resource peaks on routes where the civilian agents are traveling between resources (2 on Figure 1). On a gross level, this seems realistic since many attacks occur in areas where people and resources move from place to place, e.g., airports and trains. If the base level of security is reduced to 0% (all security agents must be endogenous), then there are more attacks and more of them are closer to the peaks. We view the base level of security as the police force levels prior to the occurrence of any attacks.
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Figure 1: Locations of Terrorist Attacks in Terms of Total Wealth Destroyed References [Axelrod, 1997] Axelrod, Robert, 1997, The Complexity of Cooperation: Agent-Based Models of Competition and Collaboration. Princeton University Press, Princeton, NJ. [Epstein & Axtell, 1996] Epstein, Joshua M.. & Robert Axtell, 1996, Growing Artificial Societies: Social Science from the Bottom Up. The Brookings Institution, Washington, DC. [MathWorks, 2002] The MathWorks, 2002, MatLab Student Version with Simulink , Version 6.5, Release 13, Natick, MA. [Epstein 2002] Epstein, J. M., 2002 Modeling civil violence: An agent-based computational approach. Proceedings of the National Academy of Sciences, Vol. 99, Suppl. 3 (www.pnas.org/cgi/doi/10.1073/pnas.092080199)
