Multidefender Security Games

Current Stackelberg security game models primarily focus on isolated systems in which only one defender is present, despite being part of a more complex system with multiple players. However, many real systems such as transportation networks and the power grid exhibit interdependencies among targets and, consequently, between decision makers jointly charged with protecting them. To understand such multidefender strategic interactions present in security scenarios, the authors investigate security games with multiple defenders. Unlike most prior analyses, they focus on situations in which each defender must protect multiple targets, so even a single defender's best response decision is, in general, nontrivial. Considering interdependencies among targets, the authors develop a novel mixed-integer linear programming formulation to compute a defender's best response, and approximate Nash equilibria of the game using this formulation. Their analysis shows how network structure and the probability of failure spread determine the propensity of defenders to over- or underinvest in security.

[1]  Yevgeniy Vorobeychik,et al.  Computing Optimal Security Strategies for Interdependent Assets , 2012, UAI.

[2]  Vincent Conitzer,et al.  Stackelberg vs. Nash in Security Games: An Extended Investigation of Interchangeability, Equivalence, and Uniqueness , 2011, J. Artif. Intell. Res..

[3]  Manish Jain,et al.  Security Games with Arbitrary Schedules: A Branch and Price Approach , 2010, AAAI.

[4]  David P. Morton,et al.  Stochastic Network Interdiction , 1998, Oper. Res..

[5]  H. Kunreuther,et al.  Interdependent Security , 2003 .

[6]  Milind Tambe,et al.  Unleashing Dec-MDPs in Security Games: Enabling Effective Defender Teamwork , 2014, ECAI.

[7]  Huifu Xu,et al.  A Stochastic Multiple-Leader Stackelberg Model: Analysis, Computation, and Application , 2009, Oper. Res..

[8]  David L. Woodruff,et al.  Network Interdiction and Stochastic Integer Programming , 2013 .

[9]  Jon Kleinberg,et al.  Maximizing the spread of influence through a social network , 2003, KDD '03.

[10]  Sarit Kraus,et al.  Using Game Theory for Los Angeles Airport Security , 2009, AI Mag..

[11]  Volkan Rodoplu,et al.  Computation of a Nash Equilibrium of Multiple-Leader Stackelberg Network Games , 2010, 2010 Fifth International Conference on Systems and Networks Communications.

[12]  Bo An,et al.  PROTECT: a deployed game theoretic system to protect the ports of the United States , 2012, AAMAS.

[13]  Manish Jain,et al.  Software Assistants for Randomized Patrol Planning for the LAX Airport Police and the Federal Air Marshal Service , 2010, Interfaces.

[14]  Kalyanmoy Deb,et al.  Finding optimal strategies in a multi-period multi-leader-follower Stackelberg game using an evolutionary algorithm , 2013, Comput. Oper. Res..

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

[16]  Asuman E. Ozdaglar,et al.  Network Security and Contagion , 2013, PERV.

[17]  Sven Leyffer,et al.  Solving multi-leader–common-follower games , 2010, Optim. Methods Softw..

[18]  Luis E. Ortiz,et al.  Interdependent Defense Games: Modeling Interdependent Security under Deliberate Attacks , 2012, UAI.

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

[20]  Yevgeniy Vorobeychik,et al.  Noncooperatively Optimized Tolerance: Decentralized Strategic Optimization in Complex Systems , 2011, Physical review letters.

[21]  Sarit Kraus,et al.  Bayesian stackelberg games and their application for security at Los Angeles international airport , 2008, SECO.

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

[23]  Hanif D. Sherali,et al.  A Multiple Leader Stackelberg Model and Analysis , 1984, Oper. Res..

[24]  Gerald G. Brown,et al.  Solving Defender-Attacker-Defender Models for Infrastructure Defense , 2011, ICS 2011.

[25]  Milind Tambe,et al.  Defender (Mis)coordination in Security Games , 2013, IJCAI.

[26]  Ankur A. Kulkarni,et al.  A Shared-Constraint Approach to Multi-Leader Multi-Follower Games , 2012, 1206.2968.

[27]  Michael P. Wellman,et al.  Stochastic Search Methods for Nash Equilibrium Approximation in Simulation-based Games , 2022 .

[28]  Moez Draief,et al.  Contagion and observability in security domains , 2013, 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[29]  Yevgeniy Vorobeychik,et al.  Equilibrium Analysis of Multi-Defender Security Games , 2015, IJCAI.