Approximation methods for infinite Bayesian Stackelberg games: modeling distributional payoff uncertainty

Game theory is fast becoming a vital tool for reasoning about complex real-world security problems, including critical infrastructure protection. The game models for these applications are constructed using expert analysis and historical data to estimate the values of key parameters, including the preferences and capabilities of terrorists. In many cases, it would be natural to represent uncertainty over these parameters using continuous distributions (such as uniform intervals or Gaussians). However, existing solution algorithms are limited to considering a small, finite number of possible attacker types with different payoffs. We introduce a general model of infinite Bayesian Stackelberg security games that allows payoffs to be represented using continuous payoff distributions. We then develop several techniques for finding approximate solutions for this class of games, and show empirically that our methods offer dramatic improvements over the current state of the art, providing new ways to improve the robustness of security game models.

[1]  Günther Palm,et al.  Evolutionary stable strategies and game dynamics for n-person games , 1984 .

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

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

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

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

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

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

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

[9]  J. Szep,et al.  Games with incomplete information , 1985 .

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

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

[12]  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.

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

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

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

[16]  Manish Jain,et al.  Quality-bounded solutions for finite Bayesian Stackelberg games: scaling up , 2011, AAMAS.

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

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

[20]  Howard Raiffa,et al.  Games And Decisions , 1958 .

[21]  References , 1971 .

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

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

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

[27]  Kevin Chlebik Terrorism and Game Theory: From the Terrorists’ Point of View , 2010 .

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

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