Combining Graph Contraction and Strategy Generation for Green Security Games

Many real-world security problems can be modeled using Stackelberg security games SSG, which model the interactions between a defender and attacker. Green security games focus on environmental crime, such as preventing poaching, illegal logging, or detecting pollution. A common problem in green security games is to optimize patrolling strategies for a large physical area such as a national park or other protected area. Patrolling strategies can be modeled as paths in a graph that represents the physical terrain. However, having a detailed graph to represent possible movements in a very large area typically results in an intractable computational problem due to the extremely large number of potential paths. While a variety of algorithmic approaches have been explored in the literature to solve security games based on large graphs, the size of games that can be solved is still quite limited. Here, we introduce abstraction methods for solving large graph-based security games and integrate these methods with strategy generation techniques. We demonstrate empirically that the combination of these methods results in dramatic improvements in solution time with modest impact on solution quality.

[1]  C. Field,et al.  The Distribution of the Larger Herbivores in the Queen Elizabeth National Park, Uganda , 1970 .

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

[3]  A. Haurie,et al.  Sequential Stackelberg equilibria in two-person games , 1985 .

[4]  Steven Skiena,et al.  Implementing discrete mathematics - combinatorics and graph theory with Mathematica , 1990 .

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

[6]  Tuomas Sandholm,et al.  A Competitive Texas Hold'em Poker Player via Automated Abstraction and Real-Time Equilibrium Computation , 2006, AAAI.

[7]  Tuomas Sandholm,et al.  A Texas Hold'em poker player based on automated abstraction and real-time equilibrium computation , 2006, AAMAS '06.

[8]  Tomas Holmern,et al.  Local law enforcement and illegal bushmeat hunting outside the Serengeti National Park, Tanzania , 2007, Environmental Conservation.

[9]  Tuomas Sandholm,et al.  Better automated abstraction techniques for imperfect information games, with application to Texas Hold'em poker , 2007, AAMAS '07.

[10]  Tuomas Sandholm,et al.  Lossless abstraction of imperfect information games , 2007, JACM.

[11]  Troels Bjerre Lund,et al.  Potential-Aware Automated Abstraction of Sequential Games, and Holistic Equilibrium Analysis of Texas Hold'em Poker , 2007, AAAI.

[12]  Michael H. Bowling,et al.  Regret Minimization in Games with Incomplete Information , 2007, NIPS.

[13]  Peter Sanders,et al.  Contraction Hierarchies: Faster and Simpler Hierarchical Routing in Road Networks , 2008, WEA.

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

[15]  Troels Bjerre Lund,et al.  A heads-up no-limit Texas Hold'em poker player: discretized betting models and automatically generated equilibrium-finding programs , 2008, AAMAS.

[16]  Manish Jain,et al.  Security applications: lessons of real-world deployment , 2009, SECO.

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

[18]  Peter Sanders,et al.  Time-Dependent Contraction Hierarchies and Approximation , 2010, SEA.

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

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

[21]  Peter Sanders,et al.  Exact Routing in Large Road Networks Using Contraction Hierarchies , 2012, Transp. Sci..

[22]  Nicola Basilico,et al.  Patrolling security games: Definition and algorithms for solving large instances with single patroller and single intruder , 2012, Artif. Intell..

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

[24]  Tuomas Sandholm,et al.  Lossy stochastic game abstraction with bounds , 2012, EC '12.

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

[26]  Rong Yang,et al.  Scaling-up Security Games with Boundedly Rational Adversaries: A Cutting-plane Approach , 2013, IJCAI.

[27]  Manish Jain,et al.  Efficiently Solving Joint Activity Based Security Games , 2013, IJCAI.

[28]  Milind Tambe,et al.  Addressing Scalability and Robustness in Security Games with Multiple Boundedly Rational Adversaries , 2014, GameSec.

[29]  Tuomas Sandholm,et al.  Potential-Aware Imperfect-Recall Abstraction with Earth Mover's Distance in Imperfect-Information Games , 2014, AAAI.

[30]  Tuomas Sandholm,et al.  Extensive-form game abstraction with bounds , 2014, EC.

[31]  Milind Tambe,et al.  Robust Protection of Fisheries with COmPASS , 2014, AAAI.

[32]  Rong Yang,et al.  Adaptive resource allocation for wildlife protection against illegal poachers , 2014, AAMAS.

[33]  Milind Tambe,et al.  When Security Games Go Green: Designing Defender Strategies to Prevent Poaching and Illegal Fishing , 2015, IJCAI.

[34]  Tuomas Sandholm,et al.  Hierarchical Abstraction, Distributed Equilibrium Computation, and Post-Processing, with Application to a Champion No-Limit Texas Hold'em Agent , 2015, AAAI Workshop: Computer Poker and Imperfect Information.

[35]  Noa Agmon,et al.  Making the Most of Our Regrets: Regret-Based Solutions to Handle Payoff Uncertainty and Elicitation in Green Security Games , 2015, GameSec.

[36]  Hirokazu Anai,et al.  Simplifying Urban Network Security Games with Cut-Based Graph Contraction , 2016, AAMAS.

[37]  Bo An,et al.  Deploying PAWS: Field Optimization of the Protection Assistant for Wildlife Security , 2016, AAAI.

[38]  Milind Tambe,et al.  PAWS: Game Theory Based Protection Assistant for Wildlife Security , 2017 .