Linear-Time Resource Allocation in Security Games with Identical Fully Protective Resources

Game theory has become an important tools for making resource allocations decision in security domains, including critical infrastructure protection. Many of these games are formulated as Stackelberg security games. We present new analysis and algorithms for a class of Stackelberg security games with identical, fully protective defender resources. The first algorithm has worst-case complexity linear in the number of possible targets, but works only for a restricted case. The second algorithm can find and optimal resource allocation for the general case in time O(n ċ log(n)).

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

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

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

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

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

[6]  K. Bagwell.  Commitment and observability in games , 1995 .

[7]  R. K. Shyamasundar,et al.  Introduction to algorithms , 1996 .

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

[9]  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).

[10]  Milind Tambe,et al.  GUARDS: game theoretic security allocation on a national scale , 2011, AAMAS.

[11]  Tim Roughgarden.  Stackelberg Scheduling Strategies , 2004, SIAM J. Comput..

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

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

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

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

[16]  Vincent Conitzer,et al.  Multi-Step Multi-Sensor Hider-Seeker Games , 2009, IJCAI.

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

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

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

[20]  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.

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

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

[23]  Ronald L. Rivest,et al.  Introduction to Algorithms, third edition , 2009 .

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