Improving resource allocation strategies against human adversaries in security games: An extended study

Stackelberg games have garnered significant attention in recent years given their deployment for real world security. Most of these systems, such as ARMOR, IRIS and GUARDS have adopted the standard game-theoretical assumption that adversaries are perfectly rational, which is standard in the game theory literature. This assumption may not hold in real-world security problems due to the bounded rationality of human adversaries, which could potentially reduce the effectiveness of these systems. In this paper, we focus on relaxing the unrealistic assumption of perfectly rational adversary in Stackelberg security games. In particular, we present new mathematical models of human [email protected]? behavior, based on using two fundamental theory/method in human decision making: Prospect Theory (PT) and stochastic discrete choice model. We also provide methods for tuning the parameters of these new models. Additionally, we propose a modification of the standard quantal response based model inspired by rank-dependent expected utility theory. We then develop efficient algorithms to compute the best response of the security forces when playing against the different models of adversaries. In order to evaluate the effectiveness of the new models, we conduct comprehensive experiments with human subjects using a web-based game, comparing them with models previously proposed in the literature to address the perfect rationality assumption on part of the adversary. Our experimental results show that the [email protected]? responses follow the assumptions of our new models more closely than the previous perfect rationality assumption. We also show that the defender strategy produced by our new stochastic discrete choice model outperform the previous leading contender for relaxing the assumption of perfect rationality. Furthermore, in a separate set of experiments, we show the benefits of our modified stochastic model (QRRU) over the standard model (QR).

[1]  Kevin Leyton-Brown,et al.  Beyond equilibrium: predicting human behaviour in normal form games , 2010, AAAI.

[2]  A. Tversky,et al.  Prospect theory: an analysis of decision under risk — Source link , 2007 .

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

[4]  Robert T. Clemen,et al.  Subjective Probability Assessment in Decision Analysis: Partition Dependence and Bias Toward the Ignorance Prior , 2005, Manag. Sci..

[5]  Ya'akov Gal,et al.  A study of computational and human strategies in revelation games , 2014, Autonomous Agents and Multi-Agent Systems.

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

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

[8]  Jonathan Gratch,et al.  The effect of expression of anger and happiness in computer agents on negotiations with humans , 2011, AAMAS.

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

[10]  R. McKelvey,et al.  Quantal Response Equilibria for Normal Form Games , 1995 .

[11]  Vincent Conitzer,et al.  Stackelberg vs. Nash in Security Games: An Extended Investigation of Interchangeability, Equivalence, and Uniqueness , 2011, J. Artif. Intell. Res..

[12]  A. Tversky,et al.  Prospect theory: analysis of decision under risk , 1979 .

[13]  Miguel A. Costa-Gomes,et al.  Cognition and Behavior in Normal-Form Games: An Experimental Study , 1998 .

[14]  Nick Feltovich,et al.  Reinforcement-based vs. Belief-based Learning Models in Experimental Asymmetric-information Games , 2000 .

[15]  Amos Azaria,et al.  Strategic Information Disclosure to People with Multiple Alternatives , 2011, AAAI.

[16]  Manish Jain,et al.  Risk-Averse Strategies for Security Games with Execution and Observational Uncertainty , 2011, AAAI.

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

[18]  Peter P. Wakker,et al.  On the Intuition of Rank-Dependent Utility , 2000 .

[19]  Rong Yang,et al.  Improving Resource Allocation Strategy against Human Adversaries in Security Games , 2011, IJCAI.

[20]  R. Wilcox.  Applying Contemporary Statistical Techniques , 2003 .

[21]  D. McFadden.  Econometric analysis of qualitative response models , 1984 .

[22]  Ya'akov Gal,et al.  Modeling Reciprocal Behavior in Human Bilateral Negotiation , 2007, AAAI.

[23]  D. McFadden.  A Method of Simulated Moments for Estimation of Discrete Response Models Without Numerical Integration , 1989 .

[24]  Milind Tambe,et al.  Approximation methods for infinite Bayesian Stackelberg games: modeling distributional payoff uncertainty , 2011, AAMAS.

[25]  J. Kagan,et al.  Rational choice in an uncertain world , 1988 .

[26]  A. Tversky,et al.  Advances in prospect theory: Cumulative representation of uncertainty , 1992 .

[27]  Avi Pfeffer,et al.  Simultaneously modeling humans' preferences and their beliefs about others' preferences , 2008, AAMAS.

[28]  Bo An,et al.  GUARDS and PROTECT: next generation applications of security games , 2011, SECO.

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

[30]  H. Simon,et al.  Rational choice and the structure of the environment. , 1956, Psychological review.

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

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

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

[34]  Colin Camerer,et al.  A Cognitive Hierarchy Model of Games , 2004 .

[35]  Sarit Kraus,et al.  Robust solutions to Stackelberg games: Addressing bounded rationality and limited observations in human cognition , 2010, Artif. Intell..

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

[37]  Milind Tambe,et al.  Urban security: game-theoretic resource allocation in networked physical domains , 2010, AAAI 2010.

[38]  Mrinal K. Sen,et al.  Global Optimization Methods in Geophysical Inversion , 1995 .

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

[40]  R FoxCraig,et al.  Subjective Probability Assessment in Decision Analysis , 2005 .

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

[42]  D. Stahl,et al.  Experimental evidence on players' models of other players , 1994 .

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

[44]  James R. Callan,et al.  Nonlinear least squares methods: A direct grid search approach , 1968 .

[45]  C. Starmer.  Developments in Non-expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk , 2000 .

[46]  Yevgeniy Vorobeychik,et al.  Computing Randomized Security Strategies in Networked Domains , 2011, Applied Adversarial Reasoning and Risk Modeling.

[47]  Miguel A. Costa-Gomes,et al.  Cognition and Behavior in Normal-Form Games: An Experimental Study , 1998 .

[48]  Kelly E. See,et al.  Between ignorance and truth: Partition dependence and learning in judgment under uncertainty. , 2006, Journal of experimental psychology. Learning, memory, and cognition.

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