Protecting Moving Targets with Multiple Mobile Resources

In recent years, Stackelberg Security Games have been successfully applied to solve resource allocation and scheduling problems in several security domains. However, previous work has mostly assumed that the targets are stationary relative to the defender and the attacker, leading to discrete game models with finite numbers of pure strategies. This paper in contrast focuses on protecting mobile targets that leads to a continuous set of strategies for the players. The problem is motivated by several real-world domains including protecting ferries with escort boats and protecting refugee supply lines. Our contributions include: (i) A new game model for multiple mobile defender resources and moving targets with a discretized strategy space for the defender and a continuous strategy space for the attacker. (ii) An efficient linear-programming-based solution that uses a compact representation for the defender's mixed strategy, while accurately modeling the attacker's continuous strategy using a novel sub-interval analysis method. (iii) Discussion and analysis of multiple heuristic methods for equilibrium refinement to improve robustness of defender's mixed strategy. (iv) Discussion of approaches to sample actual defender schedules from the defender's mixed strategy. (iv) Detailed experimental analysis of our algorithms in the ferry protection domain.

[1]  Gerald Tesauro,et al.  Playing repeated Stackelberg games with unknown opponents , 2012, AAMAS.

[2]  Andreas Krause,et al.  Randomized Sensing in Adversarial Environments , 2011, IJCAI.

[3]  Milind Tambe,et al.  TRUSTS: Scheduling Randomized Patrols for Fare Inspection in Transit Systems , 2012, IAAI.

[4]  Milind Tambe,et al.  Optimal patrol strategy for protecting moving targets with multiple mobile resources , 2013, AAMAS.

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

[6]  Peter Bro Miltersen,et al.  Computing Proper Equilibria of Zero-Sum Games , 2006, Computers and Games.

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

[8]  Maxwell B. Stinchcombe,et al.  Equilibrium Refinement for Infinite Normal-Form Games , 1995 .

[9]  Sarit Kraus,et al.  Multi-robot perimeter patrol in adversarial settings , 2008, 2008 IEEE International Conference on Robotics and Automation.

[10]  Sarit Kraus,et al.  Game-theoretic randomization for security patrolling with dynamic execution uncertainty , 2013, AAMAS.

[11]  Michal Pechoucek,et al.  Using Agents to Improve International Maritime Transport Security , 2011, IEEE Intelligent Systems.

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

[13]  Shlomo Zilberstein,et al.  Anytime Planning for Decentralized POMDPs using Expectation Maximization , 2010, UAI.

[14]  Milind Tambe,et al.  Towards Flexible Teamwork , 1997, J. Artif. Intell. Res..

[15]  Milind Tambe,et al.  Game-theoretic patrol strategies for transit systems: the TRUSTS system and its mobile app , 2013, AAMAS.

[16]  Sarit Kraus,et al.  Deployed ARMOR protection: the application of a game theoretic model for security at the Los Angeles International Airport , 2008, AAMAS.

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

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

[19]  Vincent Conitzer,et al.  Solving Security Games on Graphs via Marginal Probabilities , 2013, AAAI.

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

[21]  Yevgeniy Vorobeychik,et al.  Computing Stackelberg Equilibria in Discounted Stochastic Games , 2012, AAAI.

[22]  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.

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

[24]  Sarit Kraus,et al.  Security in multiagent systems by policy randomization , 2006, AAMAS '06.

[25]  Bo An,et al.  Security Games with Limited Surveillance , 2012, AAAI.

[26]  Sarit Kraus,et al.  Ad Hoc Autonomous Agent Teams: Collaboration without Pre-Coordination , 2010, AAAI.

[27]  S. Alpern Infiltration games on arbitrary graphs , 1992 .

[28]  P. Hudson Search Games , 1982 .

[29]  Milind Tambe,et al.  Continuous Time Planning for Multiagent Teams with Temporal Constraints , 2011, IJCAI.

[30]  Joshua Letchford,et al.  Computational Aspects of Stackelberg Games , 2013 .

[31]  Bo An,et al.  Refinement of Strong Stackelberg Equilibria in Security Games , 2011, AAAI.

[32]  Vladik Kreinovich,et al.  Security games with interval uncertainty , 2013, AAMAS.

[33]  M. Dufwenberg Game theory. , 2011, Wiley interdisciplinary reviews. Cognitive science.

[34]  Kevin Leyton-Brown,et al.  Computational analysis of perfect-information position auctions , 2009, EC '09.

[35]  E. Damme Stability and perfection of Nash equilibria , 1987 .

[36]  Milind Tambe,et al.  Security and Game Theory - Algorithms, Deployed Systems, Lessons Learned , 2011 .

[37]  Vincent Conitzer,et al.  Complexity of Computing Optimal Stackelberg Strategies in Security Resource Allocation Games , 2010, AAAI.

[38]  Branislav Bosanský,et al.  Computing time-dependent policies for patrolling games with mobile targets , 2011, AAMAS.

[39]  Milind Tambe,et al.  Patrol Strategies to Maximize Pristine Forest Area , 2012, AAAI.

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

[41]  S. Matthew Weinberg,et al.  Symmetries and optimal multi-dimensional mechanism design , 2012, EC '12.

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

[43]  Asuman E. Ozdaglar,et al.  Separable and low-rank continuous games , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

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

[45]  E. Vandamme Stability and perfection of nash equilibria , 1987 .

[46]  Vincent Conitzer,et al.  Security Games with Multiple Attacker Resources , 2011, IJCAI.

[47]  Michal Pechoucek,et al.  Using Multi-agent Simulation to Improve the Security of Maritime Transit , 2011, MABS.