Technology Evolutionary Games in Complex Transportation Systems in the Face of Adaptive Adversaries

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CREATE Research Archive Non-published Research Reports 2011 Technology Evolutionary Games in Complex Transportation Systems in the Face of Adaptive Adversaries Jun Zhuang University of Buffalo, The

1 CREATE Research Archive Non-published Research Reports 2011 Technology Evolutionary Games in Complex Transportation Systems in the Face of Adaptive Adversaries Jun Zhuang University of Buffalo, The State University of New York, Elizabeth A. Newell University of Buffalo, The State University of New York Follow this and additional works at: Recommended Citation Zhuang, Jun and Newell, Elizabeth A., "Technology Evolutionary Games in Complex Transportation Systems in the Face of Adaptive Adversaries" (2011). Non-published Research Reports. Paper This Article is brought to you for free and open access by CREATE Research Archive. It has been accepted for inclusion in Non-published Research Reports by an authorized administrator of CREATE Research Archive. For more information, please contact

2 Technology Evolutionary Games in Complex Transportation Systems in the Face of Adaptive Adversaries May 5, 2011 Jun Zhuang Center for Risk and Economic Analysis of Terrorism Events (CREATE) Department of Industrial and Systems Engineering, University at Buffalo, SUNY Assistant Professor 403 Bell Hall, Buffalo, NY Elizabeth Newell Department of Industrial and Systems Engineering, University at Buffalo, SUNY Undergraduate Researcher 438 Bell Hall, Buffalo, NY This project was funded through the CREATE Center of Excellence by a grant from the United States Department of Homeland Security, Science and Technology Directorate, Office of University Programs.

3 Technology Evolutionary Games 2 Abstract There exists an evolutionary game between transportation systems and adaptive adversaries. The strategic interactions have high impacts on complex transportation systems, not only to security infrastructure, technologies, and costs, but also to the general public s travel pattern and welfare. In this research, we utilize evolutionary game theory to model the interactions between adaptive adversaries (such as terrorists) and transportation systems (including transportation authorities, companies, and the general public). All players adapt their strategies to the other players previous choices. By this, players maximize their own payoffs or welfare according to their preferences, and are subject to their own budget constraints. This research provides a general theoretical framework for decision-making in complex transportation systems in the face of adaptive adversaries, and provides managerial insights on when and where to adopt what technology in order to maximize the (long-run) social welfare of transportation systems. Keywords: Adaptive adversaries; Decision making; Evolutionary games; Security games; Technology Adoption Transportation systems

4 Technology Evolutionary Games 3 Technology Evolutionary Games in Complex Transportation Systems in the Face of Adaptive Adversaries Introduction There exists an evolutionary game between transportation systems and adaptive adversaries. For example, airport security can be modeled as an evolutionary game between transportation authorities and adaptive adversaries (e.g., terrorists) (Transportation Security Administration 2011). This evolutionary game started when three Romanian terrorists killed an aircrew member on board a Romanian Airline flight on July 25, On January 6, 1960, following the mid-air explosion by a suicide bomber who killed all thirty-four passengers on board a National Airline plane, transportation authorities started using baggage inspection devices. The United States government began using armed guards on commercial planes in response to the American airline flight being diverted to Cuba in May As well, U.S. President John F. Kennedy also signed legislation that made air piracy punishable by imprisonment or even death in 1961, in response to the Cuban flight diversion. The Federal Aviation Administration (FAA) developed profiling and metal detectors in screening passengers in response to eight airlines that were hijacked to Cuba early in Following the August 1969 hijacking of a United States aircraft flying outside the Western Hemisphere to Israel and being diverted to Syria, U.S. President Richard Nixon established an enforcement program known as the Customs Air Security Officers Program, or better known as the Sky Marshal Program, that attempts to stop hijacking. In March 1972, a Los Angeles bound flight from the John F. Kennedy International Airport was notified that they had a bomb on board. Minutes before it was set to detonate, a bomb-sniffing dog discovered a bomb, and thus, the FAA Explosives Detection Canine Team Program was created. But up until this point, immense loss

5 Technology Evolutionary Games 4 of human life due to adaptive adversaries had not occurred; planes were used as political messages, not as weapons. Following the September 11, 2001 terrorist attacks, this changed. Four planes were hijacked on that day; two flown into the Manhattan World Trade Centers, one flown into the Pentagon, and another, fortunately, crashed in Pennsylvania due to courageous passengers and crewmembers. About three thousand people were killed due to the attack. After, stricter security measures were put into effect. All passenger airplanes flying to the United States were required to have reinforced cockpit doors. The Transportation Security Administration (TSA) was created. Following these developments and other terrorist attacks since September 11, 2001, evolving terrorism methods have included box cutters, knives, shoe bombers, liquid-based explosives, and underwear bombers. The correspondingly evolving security measures following these methods include prohibiting knives, nail clippers, lighters, liquids and gels, and the recently adopted advanced imaging technology, full body scanners, and pat downs. Such strategic interactions and evolutionary measures have high impacts on the complex transportation systems, not only to the security infrastructure, technologies, and costs, but also to the general public s travel pattern and welfare. It is critical to understand the evolutionary dynamics from a system perspective, and understand when and where to adopt what technology in order to maximize the long-run social welfare of transportation systems. In this research, we provide a basic framework for technology evolutionary games in complex transportation systems in the face of adaptive adversaries.

6 Technology Evolutionary Games 5 Discussion In this section, we provide the problem statement, potential solution, and research methodology. We also include in this section results and challenges, who would benefit from this research, and a brief conclusion of our research. Statement of the Problem We propose to utilize evolutionary game theory (Sandholm 2002, 2010) to model the interactions between adaptive adversaries (such as terrorists) and transportation systems (including transportation authorities and the general public). Evolutionary game theory is a branch of game theory that applies to the evolving interactions between strategically dependent players. It began as a mathematical way to model complex changes in biological systems in 1930 (Fisher, 1930), and evolved to applications in economics, sociology, anthropology and philosophy and other social sciences. Its applications have been used to model social norms and beliefs, and how they have evolved over time depending on the moves and interactions of different players in the system. When viewing the changing technology as an evolutionary game, we are able to better study the changes that occur between the transportation systems and the adaptive adversary. To the best of our knowledge, there is no previous work utilizing evolutionary games to study the strategic interactions between terrorists and transportation systems. Statement of the Potential Solution and the Research Methodology First, we model the evolutionary game by specifying the following four critical factors: 1) Players: a. Transportation Authorities (Defenders): Such as the U.S. Transportation Security Administration (TSA), and other federal and local authorities.

7 Technology Evolutionary Games 6 b. Transportation Users (Private Citizens): Such as private citizens, commercial/business users, and government employees. c. Adaptive Adversaries (Attackers): Including terrorist organizations who would be interested in attacking transportation systems. 2) Objectives/payoffs for each player, including measures of, and preferences for, defense costs and potential casualties and economic losses (for the transportation authorities), and psychological, economic, political, religious, and financial costs and benefits (for adaptive adversaries). Multi-attribute utility theory will be used to model these objectives (Keeney and Raiffa 1976; Keeney 2007). (3) Options for each player, including the transportation authorities decision on when, what technology/security measures to adopt (such as metal detectors, full body scanners, and patdowns) and where to adopt (urban areas such as New York City, Washington, DC, Los Angeles, Miami, Chicago, Philadelphia, Buffalo, Tampa); the transportation users travel choices (such as air flights, subways, trains, buses, ferries and personal cars); and adaptive adversaries options of when and where to use what methods of attack, including the scenarios of attacking a mass transit system in a major United States city, attacking a major transportation infrastructure component such as a large suspension bridge, and using transportation as an attack vector such as to spread contagious diseases or dissemination of other chemical, biological, nuclear, radiological or explosive agents. (4) Information and uncertainties: human-terrain data, previous observed and unobserved actions, and possible information disclosure strategies (such as secrecy, truthful and deceptive disclosure, as studied previously by the author; see Zhuang and Bier 2010, and Zhuang et al. 2010). Those previous works show that when the first mover possesses some private

8 Technology Evolutionary Games 7 information, he/she may prefer to use secrecy or deception to mislead the second mover. We will assume that the players have uncertainties about other players attributes using subjective probability distributions, and update their beliefs in a Bayesian manner during the duration of the game. Consider a discrete-time horizon, where. There are N types of methods of defense and M types of methods of attack on K targets. In the beginning of period t, the defense level is D n,k,t-1 for each of the defense methods n=1,,n on each target k=1,, K, where D n,k,0 is the original defense level for method type n on target k. The attacker observes those defense levels and finds certain weaknesses in the system D k,t-1 ={D n,k,t-1 ; n=1,,n} and chooses the attack method for target k=1,,k, where A k,t =0 implies no attack. The defender observes the attack levels A k,t that it created through its preparation and mitigation stages, and responds by defense levels D t (A t, D t-1 ), where A t ={A k,t ; k=1,,k} and D t ={A k,t ; k=1,,k}; following the adaptive adversaries attack, the defender will recover, and choose whether and how to retaliate. Finally, the private citizens (travelers) observe the attack and defense levels and methods on each target, and select their travel pattern P t based off their assumptions in safety and in transportation hassle. Then the game evolves to the next period t+1. The sequence of move is illustrated in Image 1.

Technology Evolutionary Games 8 IMAGE 1: Sequence of Actions for the T-period Evolutionary Game The discount factors are denoted as,, and for the attacker, the defender, and private citizens,

9 Technology Evolutionary Games 8 IMAGE 1: Sequence of Actions for the T-period Evolutionary Game The discount factors are denoted as,, and for the attacker, the defender, and private citizens, respectively. When the discount factors equal zero, the players are fully myopic and only care about the payoffs for the current periods. When the discount factors equal one, the players are fully farsighted and equally value the payoffs for the current and the future periods. As a starting point, we assume each player is fully strategic, and we want to maximize the longrun discounted payoffs by choosing the optimal choices at each period. That is, for the attacker, we have the total discounted payoffs equal to: T t"1 $ U A = #! A & t=1 % K # k=1 ' u A,k (A k,t, D k,t"1 )) ( where u A,k is the attacker s payoff obtained from target k, as a function of the previous-period defense and current-period attack. The payoff function includes the costs of the attack effort, and the (expected) benefits from a successful attack. We have u A,k (A k,t, D k,t-1 ) decreases in D k,t-1 and may increase or decrease in A k,t, depending on the costs of the attack effort. By modeling the

10 Technology Evolutionary Games 9 costs of attacks, we implicitly model or at least approximate the budget constraints for the attacker. For the defender, we have the total discounted payoffs equal to: T t"1 $ U D = #! D & t=1 % K # k=1 ' u D,k (D k,t, P t (A t, D t ) A k,t, D k,t"1 )) ( where u D,k is the defender s payoff obtained from target k, as a function of the current-period defense and potential private citizens response P t (A t, D t ), given previous period defense and current-period attack efforts. The payoff function includes the cost of operating the current technology level, and researching and developing new technology, as well as retaliating for the attack costs. We have u D,k decreases in A k,t. By modeling the costs of defense, we implicitly model or at least approximate the budget constraints for the defender. For the private citizens, we have the total discounted payoffs equal to: where u P is the private citizens payoff as a function of the reaction P t given attack and defense levels. The payoff function could include costs and inconveniences/congestion (Wang and Zhuang 2011) due to the changes of travel patterns. We define the subgame perfect Nash equilibrium such that at each decision point, each player chooses the options that maximize the total discounted future payoffs. Statement of the End Users/Customers/ Who Would Benefit Following the above work that is introduced in this white paper, the Department of Homeland Security/Transportation Security Administration (DHS/TSA) would benefit. In particular, this research will provide a general theoretical framework for decision making in such complex transportation systems in the face of adaptive adversaries. This model could be verified

11 Technology Evolutionary Games 10 and evaluated using historical data. Using simulation, this research will provide some novel insights on possible future evolutionary paths; e.g., when and where to adopt what technology, in order to maximize the long-run social welfare of transportation systems. Statement of the Challenges in Attaining the Solution and Results There are multiple challenges in modeling the evolutionary games and attaining the solution and results. First, even the current model has already specified when (the time period) and where (the target) to use what technology (defense method), and there are many more important factors that need to be considered. This includes incomplete information, risk attitudes, possible secrecy and deception, multiple types of players and players possible non-strategic behavior (Hao et al. 2009) and errors (Zhuang, 2010). Second, the sets of potential attack/defense methods, potential targets, and time periods could be uncertain by themselves, further complicating the modeling of incomplete information. Third, it may be difficult to get data for estimating the parameters in the models. Finally, it could be computationally intractable in attaining the solution and results, especially at real-world scale. Conclusion In this work, we provide a basic framework for technology evolutionary games in complex transportation systems in the face of adaptive adversaries. In the future, we would like to mathematically solve the game, verify, and evaluate the models using historical and simulated data. Through this work, we expect to provide insights to the following question: what is the cost-benefit analysis of adopting particular technologies, considering the adaptive traveler and adversary behavior. For example, we expect to find the following results: (a) the defender may not always want to adopt the most advanced technology to fix the most vulnerable parts of the system, especially when the attacker has an alternative attacking method or targets at relatively

12 Technology Evolutionary Games 11 low costs, or when the private citizen would change travel patterns in a unfavorable manner responding to such adoption; (b) the defender may not want to invest in technology on certain targets, if the technology/target is not the most vulnerable (or most attractive to the terrorist) component of the system; and (c) the defender may want to strategically delay the adoption of technology, if doing so would prevent the adaptive adversary behavior from evolving to a more detrimental path.

13 Technology Evolutionary Games 12 References Fisher, R. A. (1930) The Genetic Theory of Natural Selection. Clarendon Press. Oxford, UK. Hao, M., S. Jin and J. Zhuang. (2009) Robustness of Optimal Defensive Resource Allocations in the Face of Less than Fully Rational Attackers, Proceedings of the 2009 Industrial Engineering Research Conference, p.p Keeney, R.L. Modeling values for anti-terrorism analysis, Risk Analysis, 27(3): , Keeney, R.L. and H. Raiffa. Decisions with Multiple Objectives: Preferences and Value Tradeoffs. Wiley, New York, NY, Sandholm, W. H. (2002). Evolutionary Implementation and Congestion Pricing. Review of Economic Studies, 69, Sandholm, W. H. (2010). Population Games and Evolutionary Dynamics. MIT Press. Cambridge, MA. Transportation Security Administration. (2011). Checkpoint Evolution. URL: Accessed April 25, Wang, X. and J. Zhuang. (2011). Balancing Congestion and Security in the Presence of Strategic Applicants with Private Information. European Journal of Operational Research, 212(1): , Zhuang, J. (2010). Impacts of Subsidized Security on Stability and Total Social Costs of Equilibrium Solutions in an N-Player Game with Errors. The Engineering Economist, 55(2), Zhuang, J. and V.M. Bier. (2010). Reasons for Secrecy and Deception in Homeland-Security Resource Allocation. Risk Analysis, 30(12),

14 Technology Evolutionary Games 13 Zhuang, J., V.M. Bier, and O. Alagoz. (2010). Modeling Secrecy and Deception in a Multipleperiod Attacker-Defender Signaling Game. European Journal of Operational Research, 203(2),

Stochastic Game Models for Homeland Security

CREATE Research Archive Research Project Summaries 2008 Stochastic Game Models for Homeland Security Erim Kardes University of Southern California, kardes@usc.edu Follow this and additional works at: http://research.create.usc.edu/project_summaries