Methods and Algorithms for Infinite Bayesian Stackelberg Security Games - (Extended Abstract)

Recently there has been significant interest in applications of game-theoretic analysis to analyze security resource allocation decisions. Two examples of deployed systems based on this line of research are the ARMOR system in use at the Los Angeles International Airport [20], and the IRIS system used by the Federal Air Marshals Service [25]. Game analysis always begins by developing a model of the domain, often based on inputs from domain experts or historical data. These models inevitably contain significant uncertainty--especially in security domains where intelligence about adversary capabilities and preferences is very difficult to gather. In this work we focus on developing new models and algorithms that capture this uncertainty using continuous payoff distributions. These models are richer and more powerful than previous approaches that are limited to small finite Bayesian game models. We present the first algorithms for approximating equilibrium solutions in these games, and study these algorithms empirically. Our results show dramatic improvements over existing techniques, even in cases where there is very limited uncertainty about an adversaries' payoffs.

[1]  Tansu Alpcan,et al.  Security Games with Incomplete Information , 2009, 2009 IEEE International Conference on Communications.

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

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

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

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

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

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

[8]  D. McFadden Quantal Choice Analysis: A Survey , 1976 .

[9]  Nicola Basilico,et al.  Computing Bayes-Nash Equilibria through Support Enumeration Methods in Bayesian Two-Player Strategic-Form Games , 2009, 2009 IEEE/WIC/ACM International Joint Conference on Web Intelligence and Intelligent Agent Technology.

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

[11]  E. Maasland,et al.  Auction Theory , 2021, Springer Texts in Business and Economics.

[12]  Jean-Francois Richard,et al.  Approximation of Nash equilibria in Bayesian games , 2008 .

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

[14]  P. Taylor,et al.  Evolutionarily Stable Strategies and Game Dynamics , 1978 .

[15]  John C. Harsanyi,et al.  Games with Incomplete Information Played by "Bayesian" Players, I-III: Part I. The Basic Model& , 2004, Manag. Sci..

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

[17]  T. Basar,et al.  A game theoretic approach to decision and analysis in network intrusion detection , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[18]  J. Harsanyi Games with Incomplete Information Played by 'Bayesian' Players, Part III. The Basic Probability Distribution of the Game , 1968 .

[19]  Dimitris Bertsimas,et al.  Robust game theory , 2006, Math. Program..

[20]  Sarit Kraus,et al.  Adversarial Uncertainty in Multi-Robot Patrol , 2009, IJCAI.

[21]  Milind Tambe,et al.  Robust Bayesian methods for Stackelberg security games , 2010, AAMAS.

[22]  Peter R. Wurman,et al.  Monte Carlo Approximation in Incomplete Information, Sequential Auction Games , 2003, Decis. Support Syst..

[23]  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.

[24]  Michael P. Wellman,et al.  Computing Best-Response Strategies in Infinite Games of Incomplete Information , 2004, UAI.

[25]  Nicola Basilico,et al.  Leader-follower strategies for robotic patrolling in environments with arbitrary topologies , 2009, AAMAS.

[26]  Jean-Francois Richard,et al.  Approximation of Bayesian Nash Equilibrium , 2008 .