Software Assistants for Randomized Patrol Planning for the LAX Airport Police and the Federal Air Marshal Service

The increasing threat of terrorism makes security at major locations of economic or political importance a major concern. Limited security resources prevent complete security coverage, allowing adversaries to observe and exploit patterns in patrolling or monitoring, and enabling them to plan attacks that avoid existing patrols. The use of randomized security policies that are more difficult for adversaries to predict and exploit can counter their surveillance capabilities. We describe two applications, ARMOR and IRIS, that assist security forces in randomizing their operations. These applications are based on fast algorithms for solving large instances of Bayesian Stackelberg games. Police at the Los Angeles International Airport deploy ARMOR to randomize the placement of checkpoints on roads entering the airport and the routes of canine unit patrols within the airport terminals. The Federal Air Marshal Service has deployed IRIS in a pilot program to randomize the schedules of air marshals on international flights. This paper examines the design choices, information, and evaluation criteria that were critical to developing these applications.

[1]  H. Stackelberg,et al.  Marktform und Gleichgewicht , 1935 .

[2]  W. A. Wagenaar Generation of random sequences by human subjects: A critical survey of literature. , 1972 .

[3]  R. Selten,et al.  A Generalized Nash Solution for Two-Person Bargaining Games with Incomplete Information , 1972 .

[4]  RICHARD C. LARSON,et al.  A hypercube queuing model for facility location and redistricting in urban emergency services , 1974, Comput. Oper. Res..

[5]  G. Leitmann On generalized Stackelberg strategies , 1978 .

[6]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .

[7]  A. Haurie,et al.  Sequential Stackelberg equilibria in two-person games , 1985 .

[8]  M. Treisman,et al.  Generation of random sequences by human subjects: Cognitive operations or psychological process? , 1987 .

[9]  Drew Fudenberg,et al.  Game theory (3. pr.) , 1991 .

[10]  Ariel Rubinstein,et al.  A Course in Game Theory , 1995 .

[11]  M. Jones The Element of Surprise , 1996, Tropical doctor.

[12]  T. Başar,et al.  Dynamic Noncooperative Game Theory, 2nd Edition , 1998 .

[13]  Jonathan F. Bard,et al.  Practical Bilevel Optimization: Algorithms and Applications , 1998 .

[14]  Herbert Gintis,et al.  Game Theory Evolving: A Problem-Centered Introduction to Modeling Strategic Interaction - Second Edition , 2009 .

[15]  Daphne Koller,et al.  Multi-Agent Influence Diagrams for Representing and Solving Games , 2001, IJCAI.

[16]  Henry H. Willis,et al.  Estimating Terrorism Risk , 2002 .

[17]  Bernhard von Stengel,et al.  Chapter 51 Inspection games , 2002 .

[18]  R. Looney Economic Costs to the United States Stemming From the 9-11 Attacks; Strategic Insights: v.1, issue 6 (August 2002) , 2002 .

[19]  T. Sandler,et al.  Terrorism & Game Theory , 2003 .

[20]  Jeannette M. Wing,et al.  Game strategies in network security , 2005, International Journal of Information Security.

[21]  B. Stengel,et al.  Leadership with commitment to mixed strategies , 2004 .

[22]  Gerald G. Brown,et al.  A Two-Sided Optimization for Theater Ballistic Missile Defense , 2005, Oper. Res..

[23]  Johannes O. Royset,et al.  On the Complexity of Delaying an Adversary’s Project , 2005 .

[24]  Sui Ruan,et al.  Patrolling in a Stochastic Environment , 2005 .

[25]  Richard Mesic,et al.  Implementing Security Improvement Options at Los Angeles International Airport , 2006 .

[26]  Gerald G. Brown,et al.  Defending Critical Infrastructure , 2006, Interfaces.

[27]  Li Lin,et al.  Passenger grouping under constant threat probability in an airport security system , 2006, Eur. J. Oper. Res..

[28]  Jonathan F. Bard,et al.  Practical Bilevel Optimization: Algorithms and Applications (Nonconvex Optimization and Its Applications) , 2006 .

[29]  Vincent Conitzer,et al.  Computing the optimal strategy to commit to , 2006, EC '06.

[30]  Mikel Buesa,et al.  The Economic Cost of March 11: Measuring the Direct Economic Cost of the Terrorist Attack on March 11, 2004 in Madrid , 2007 .

[31]  Kevin Leyton-Brown,et al.  A Polynomial-Time Algorithm for Action Graph Games , 2006, AAAI.

[32]  Sarit Kraus,et al.  Security in multiagent systems by policy randomization , 2006, AAMAS '06.

[33]  V. Bier Choosing What to Protect , 2007, Risk analysis : an official publication of the Society for Risk Analysis.

[34]  Sarit Kraus,et al.  An efficient heuristic approach for security against multiple adversaries , 2007, AAMAS '07.

[35]  C. Drury,et al.  Optimal Placement of Suicide Bomber Detectors , 2007 .

[36]  Nicola Gatti,et al.  Game Theoretical Insights in Strategic Patrolling: Model and Algorithm in Normal-Form , 2008, ECAI.

[37]  Sarit Kraus,et al.  Playing games for security: an efficient exact algorithm for solving Bayesian Stackelberg games , 2008, AAMAS.

[38]  Sarit Kraus,et al.  Deployed ARMOR protection: the application of a game theoretic model for security at the Los Angeles International Airport , 2008, AAMAS 2008.

[39]  D. Piomelli Bedside to Bench: The element of surprise , 2008, Nature Medicine.

[40]  Sarit Kraus,et al.  The impact of adversarial knowledge on adversarial planning in perimeter patrol , 2008, AAMAS.

[41]  V. Georgiev Using Game Theory to Analyze Wireless Ad Hoc Networks . ” , 2008 .

[42]  Milind Tambe,et al.  Effective solutions for real-world Stackelberg games: when agents must deal with human uncertainties , 2009, AAMAS 2009.

[43]  Milind Tambe,et al.  Is There a Chink in Your ARMOR? Towards Robust Evaluations for Deployed Security Systems ? , 2009 .

[44]  Manish Jain,et al.  Computing optimal randomized resource allocations for massive security games , 2009, AAMAS 2009.

[45]  Lawrence M. Wein,et al.  OR Forum - Homeland Security: From Mathematical Models to Policy Implementation: The 2008 Philip McCord Morse Lecture , 2009, Oper. Res..

[46]  Milind Tambe,et al.  A Framework for Evaluating Deployed Security Systems: Is There a Chink in your ARMOR? , 2010, Informatica.

[47]  Milind Tambe,et al.  Security and Game Theory: IRIS – A Tool for Strategic Security Allocation in Transportation Networks , 2011, AAMAS 2011.