Security and Game Theory: IRIS – A Tool for Strategic Security Allocation in Transportation Networks

Security is a concern of major importance to governments and companies throughout the world. With limited resources, complete coverage of potential points of attack is not possible. Deterministic allocation of available law enforcement agents introduces predictable vulnerabilities that can be exploited by adversaries. Strategic randomization is a game theoretic alternative that we implement in Intelligent Randomization In Scheduling (IRIS) system, a software scheduling assistant for the Federal Air Marshals (FAMs) that provide law enforcement aboard U.S. commercial flights. In IRIS, we model the problem as a Stackelberg game, with FAMS as leaders that commit to a flight coverage schedule and terrorists as followers that attempt to attack a flight. The FAMS domain presents three challenges unique to transportation network security that we address in the implementation of IRIS. First, with tens of thousands of commercial flights per day, the size of the Stackelberg game we need to solve is tremendous. We use ERASERC, the fastest known algorithm for solving this class of Stackelberg games. Second, creating the game itself becomes a challenge due to number of payoffs we must enter for these large games. To address this, we create an attribute-based preference elicitation system to determine reward values. Third, the complex scheduling constraints in transportation networks make it computationally prohibitive to model the game by explicitly modeling all combinations of valid schedules. Instead, we model the leader’s strategy space by incorporating a representation of the underlying scheduling constraints. The scheduling assistant has been delivered to the FAMS and is currently undergoing testing and review for possible incorporation into their scheduling practices. In this paper, we discuss the design choices and challenges encountered during the implementation of IRIS.

[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]  Miss A.O. Penney (b) , 1974, The New Yale Book of Quotations.

[4]  D. Kenney,et al.  Police and Policing: Contemporary Issues , 1999 .

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

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

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

[8]  C. Zandonella Tissue engineering: The beat goes on , 2003, Nature.

[9]  Li Chen,et al.  Survey of Preference Elicitation Methods , 2004 .

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

[11]  Vincent Conitzer,et al.  Mixed-Integer Programming Methods for Finding Nash Equilibria , 2005, AAAI.

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

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

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

[15]  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 .

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

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

[18]  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.

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

[20]  Rudolf Avenhaus,et al.  Inspection Games , 2009, Encyclopedia of Complexity and Systems Science.

[21]  Право Federal Air Marshal Service , 2013 .