An emergent type of geopolitical warfare in recent years has been coined "Gray Zone competition," "competition short of armed conflict", or simply "competition," because it sits in a nebulous area between peace and conventional conflict. As such, the Gray Zone (GZ) "is a conceptual space between peace and war, occurring when actors use instruments of power to achieve political-security objectives ... [that] ... fall below the level of large-scale direct military conflict". It's not openly declared or defined; it's slower and is prosecuted more subtly using social, psychological, religious, information, cyber and other means to achieve physical or cognitive objectives, with or without violence. The lack of clarity of intent in competition activity makes it challenging to detect, characterize, and counter an enemy fighting this way.

Security is a critical concern around the world. In many domains from counter-terrorism to sustainability, limited security resources prevent full security coverage at all times; instead, these limited resources must be scheduled, while simultaneously taking into account different target priorities, the responses of the adversaries to the security posture and potential uncertainty over adversary types. Computational game theory can help design such security schedules. Indeed, casting the problem as a Bayesian Stackelberg game, we have developed new algorithms that are now deployed over multiple years in multiple applications for security scheduling. These applications are leading to real-world use-inspired research in the emerging research area of “security games”; specifically, the research challenges posed by these applications include scaling up security games to large-scale problems, handling significant adversarial uncertainty, dealing with bounded rationality of human adversaries, and other interdisciplinary challenges.

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Security is a critical concern around the world, whether it is the challenge of protecting ports, airports and other critical infrastructure, interdicting the illegal flow of drugs, weapons and money, protecting endangered wildlife, forests and fisheries, suppressing urban crime or security in cyberspace. Unfortunately, limited security resources prevent full security coverage at all times; instead, we must optimize the use of limited security resources. To that end, a new “security games” framework was developed, which led to building of decision-aids for security agencies around the world. Security games is a novel area of research that is based on computational and behavioral game theory, while also incorporating elements of AI planning under uncertainty and machine learning. Today securitygames based decision aids for infrastructure security are deployed in the US and internationally; examples include deployments at ports and ferry traffic with the US coast guard, for security of air traffic with the US Federal Air Marshals, and for security of university campuses, airports and metro trains with police agencies in the US and other countries. Moreover, recent work on “green security games” has led decision aids to be deployed, assisting NGOs in protection of wildlife; and “opportunistic crime security games” have focused on suppressing urban crime. In the cyber-security domain, the interaction between the defender and adversary is quite complicated with a high degree of incomplete information and uncertainty. Recently, applications of game theory to provide quantitative and analytical tools to network administrators through defensive algorithm development and adversary behavior prediction to protect cyber infrastructures has also received significant attention. This chapter provides an overview of use-inspired research in security games including algorithms for scaling up security games to real-world sized problems, handling multiple types of uncertainty, and dealing with bounded rationality and bounded surveillance of human adversaries.

Research on security games has focused on settings where the defender must protect against either a single adversary or multiple, independent adversaries. However, there are a variety of real-world security domains where adversaries may benefit from colluding in their actions against the defender, e.g., wildlife poaching, urban crime and drug trafficking. Given such adversary collusion may be more detrimental for the defender, she has an incentive to break up collusion by playing off the self-interest of individual adversaries. As we show in this paper, breaking up such collusion is difficult given bounded rationality of human adversaries; we therefore investigate algorithms for the defender assuming both rational and boundedly rational adversaries. The contributions of this paper include (i) collusive security games (COSGs), a model for security games involving potential collusion among adversaries, (ii) SPECTRE-R, an algorithm to solve COSGs and break collusion assuming rational adversaries, (iii) observations and analyses of adversary behavior and the underlying factors including bounded rationality, imbalanced- resource-allocation effect, coverage perception, and individualism/collectivism attitudes within COSGs with data from 700 human subjects, (iv) a learned human behavioral model that incorporates these factors to predict when collusion will occur, (v) SPECTRE-BR, an enhanced algorithm which optimizes against the learned behavior model to provide demonstrably better performing defender strategies against human subjects compared to SPECTRE-R.

An effective way of preventing attacks in secure areas is to screen for threats (people, objects) before entry, e.g., screening of airport passengers. However, screening every entity at the same level may be both ineffective and undesirable. The challenge then is to find a dynamic approach for randomized screening, allowing for more effective use of limited screening resources, leading to improved security. We address this challenge with the following contributions: (1) a threat screening game (TSG) model for general screening domains; (2) an NP-hardness proof for computing the optimal strategy of TSGs; (3) a scheme for decomposing TSGs into subgames to improve scalability; (4) a novel algorithm that exploits a compact game representation to efficiently solve TSGs, providing the optimal solution under certain conditions; and (5) an empirical comparison of our proposed algorithm against the current state-of-the-art optimal approach for large-scale game-theoretic resource allocation problems.

Security is a critical concern around the world. In many domains from counter-terrorism to sustainability, limited security resources prevent full security coverage at all times; instead, these limited resources must be scheduled, while simultaneously taking into account different target priorities, the responses of the adversaries to the security posture and potential uncertainty over adversary types. Computational game theory can help design such security schedules. Indeed, casting the problem as a Bayesian Stackelberg game, we have developed new algorithms that are now deployed over multiple years in multiple applications for security scheduling. These applications are leading to real-world use-inspired research in the emerging research area of “security games”; specifically, the research challenges posed by these applications include scaling up security games to large-scale problems, handling significant adversarial uncertainty, dealing with bounded rationality of human adversaries, and other interdisciplinary challenges.

Threat Screening Games (TSGs) are used in domains where there is a set of individuals or objects to screen with a limited amount of screening resources available to screen them. TSGs are broadly applicable to domains like airport passenger screening, stadium screening, cargo container screening, etc. Previous work on TSGs focused only on the Bayesian zero-sum case and provided the MGA algorithm to solve these games. In this paper, we solve Bayesian general-sum TSGs which we prove are NP-hard even when exploiting a compact marginal representation. We also present an algorithm based upon a adversary type hierarchical tree decomposition and an efficient branch-and-bound search to solve Bayesian general-sum TSGs. With this we provide four contributions: (1) GATE, the first algorithm for solving Bayesian general-sum TSGs, which uses hierarchical type trees and a novel branch-and-bound search, (2) the Branch-and-Guide approach which combines branch-and-bound search with the MGA algorithm for the first time, (3) heuristics based on properties of TSGs for accelerated computation of GATE, and (4) experimental results showing the scalability of GATE needed for real-world domains.

Leather is an integral part of the world economy and a substantial income source for developing countries. Despite government regulations on leather tannery waste emissions, inspection agencies lack adequate enforcement resources, and tanneries’ toxic wastewaters wreak havoc on surrounding ecosystems and communities. Previous works in this domain stop short of generating executable solutions for inspection agencies. We introduce NECTAR the first security game application to generate environmental compliance inspection schedules. NECTAR’s game model addresses many important real-world constraints: a lack of defender resources is alleviated via a secondary inspection type; imperfect inspectors are modeled via a heterogeneous failure rate; and uncertainty, in traveling through a road network and in conducting inspections, is addressed via a Markov Decision Process. Previously unexplored in security game literature, NECTAR features a novel explanation system to improve user understanding of inspection schedules; understandability is a critical component to build trust and facilitate user adoption. This explanation system generalizes to any security game type, and we demonstrate its application to NECTAR. To evaluate our model, we conduct a series of simulations and analyze their policy implications. We also conduct a preliminary survey to assess explanation systems’ potential impact on understandability.

Several models have been proposed for Stackelberg security games (SSGs) and protection against perfectly rational and bounded rational adversaries; however, none of these existing models have addressed the cooperation mechanism between adversaries. In a large number of studies related to SSGs, there is one leader and one follower in the game such that the leader takes action and the follower responds accordingly. These studies fail to take into account the possibility of existence of more than one group of adversaries who can cooperate and cause synergistic loss to the security agents (defenders). The first contribution of this paper is formulating a new type of Stackleberg security game involving a beneficial cooperation mechanism among adversaries. The second contribution of this paper is to develop a parametric human behavior model which is able to capture the bounded rationality of adversaries in this type of cooperative games. This model is proposed based on human subject experiments with participants on Amazon Mechanical Turk (AMT).

Several models have been proposed for Stackelberg security games (SSGs) and protection against perfectly rational and bounded rational adversaries; however, none of these existing models addressed the destructive cooperation mechanism between adversaries. SPECTRE (Strategic Patrol planner to Extinguish Collusive ThREats) takes into account the synergistic destructive collusion among two groups of adversaries in security games. This framework is designed for the purpose of efficient patrol scheduling for security agents in security games in presence of collusion and is mainly build up on game theoretic approaches, optimization techniques, machine learning methods and theories for human decision making under risk. The major advantage of SPECTRE is involving real world data from human subject experiments with participants on Amazon Mechanical Turk (AMT).

Several models have been proposed for Stackelberg security games (SSGs) and protection against perfectly rational and bounded rational adversaries; however, none of these existing models addressed the collusion mechanism between adversaries. In a large number of studies related to SSGs, there is one leader and one follower in the game such that the leader takes action and the follower responds accordingly. These studies fail to take into account the possibility of existence of group of adversaries who can collude and cause synergistic loss to the security agents (defenders). The first contribution of this paper is formulating a new type of Stackleberg security game involving a beneficial collusion mechanism among adversaries. The second contribution of this paper is to develop a parametric human behavior model which is able to capture the bounded rationality of adversaries in this type of collusive games. This model is proposed based on human subject experiments with participants on Amazon Mechanical Turk (AMT).

Security agencies including the US Coast Guard, the Federal Air Marshal Service and the Los Angeles Airport police are several major domains that have been deploying Stackelberg security games and related algorithms to protect against a single adversary or multiple, independent adversaries strategically. However, there are a variety of real-world security domains where adversaries may benefit from colluding in their actions against the defender. Given the potential negative effect of these collusive actions, the defender has an incentive to break up collusion by playing off the self-interest of individual adversaries. This paper deals with problem of collusive security games for rational and bounded rational adversaries. The theoretical results verified with human subject experiments showed that behavior model which optimizes against bounded rational adversaries provides demonstrably better performing defender strategies against human subjects.

Leather is an integral part of the world economy and a substantial income source for developing countries. Despite government regulations on leather tannery waste emissions, inspection agencies lack adequate enforcement resources, and tanneries' toxic wastewaters wreak havoc on surrounding ecosystems and communities. Previous works in this domain stop short of generating executable solutions for inspection agencies. We introduce NECTAR - the first security game application to generate environmental compliance inspection schedules. NECTAR's game model addresses many important real-world constraints: a lack of defender resources is alleviated via a secondary inspection type; imperfect inspections are modeled via a heterogeneous failure rate; and uncertainty, in traveling through a road network and in conducting inspections, is addressed via a Markov Decision Process. To evaluate our model, we conduct a series of simulations and analyze their policy implications.

Security is a critical concern around the world. In many domains from cybersecurity to sustainability, limited security resources prevent complete security coverage at all times. Instead, these limited resources must be scheduled (or allocated or deployed), while simultaneously taking into account the importance of different targets, the responses of the adversaries to the security posture, and the potential uncertainties in adversary payoffs and observations, etc. Computational game theory can help generate such security schedules. Indeed, casting the problem as a Stackelberg game, we have developed new algorithms that are now deployed over multiple years in multiple applications for scheduling of security resources. These applications are leading to real-world use-inspired research in the emerging research area of “security games.” The research challenges posed by these applications include scaling up security games to real-world-sized problems, handling multiple types of uncertainty, and dealing with bounded rationality of human adversaries. In cybersecurity domain, the interaction between the defender and adversary is quite complicated with high degree of incomplete information and uncertainty. While solutions have been proposed for parts of the problem space in cybersecurity, the need of the hour is a comprehensive understanding of the whole space including the interaction with the adversary. We highlight the innovations in security games that could be used to tackle the game problem in cybersecurity.

After more than a decade of fighting in Afghanistan and Iraq, terror groups and enemies of the United States remain at large. The United States Army has refined its doctrine to resemble a fighting force that has been entrenched in protracted war. Through its development of Unified Land Operations (ULO) defined in Army Doctrine Publication (ADP) 3-0 and Army Doctrine Reference Publication (ADRP) 3-0, the Army has also taken steps within its doctrine to ensure readiness for a conventional conflict that may require the synchronization of assets across multiple spectrums of operations. The future is often unpredictable, which makes the readiness of an army, and the constant refinement of its doctrine, all the more important. While doctrine shapes decisions made on the battlefield, the random variability inherent to any conflict suggests a need for additional aids to assist commanders in making sound decisions.History has shown many examples of conventional and unconventional warfare. In some cases, conventional wars have degraded into unconventional wars that prolonged for many years. Many books have been written that describe and analyze the nature of different unconventional wars and insurgencies that have taken place throughout history. While no two insurgencies are the same, analyzing these past conflicts can result in the realization of many similarities. The Army’s current counterinsurgency (COIN) doctrine, Field Manual (FM) 3-24, attempts to capture these similarities in Chapters 4 and 5 (US Dept. of the Army and US Marine Corps. 2014).

This paper proposes the Multi-Operation Patrol Scheduling System (MOPSS), a new system to generate patrols for transit system. MOPSS is based on five contributions. First, MOPSS is the first system to use three fundamentally different adversary models for the threats of fare evasion, terrorism and crime, generating three significantly different types of patrol schedule. Second, to handle uncertain interruptions in the execution of patrol schedules, MOPSS uses Markov decision processes (MDPs) in its scheduling. Third, MOPSS is the first system to account for joint activities between multiple resources, by employing the well known SMART security game model that tackles coordination between defender's resources. Fourth, we are also the first to deploy a new Opportunistic Security Game model, where the adversary, a criminal, makes opportunistic decisions on when and where to commit crimes. Our fifth, and most important, contribution is the evaluation of MOPSS via real-world deployments, providing data from security games in the field.

This paper presents actual results from the field using a novel deployed system referred to as the Multi-Operation Patrol Scheduling System (MOPSS). MOPSS generates patrols for a transit system considering three different threats: fare evasion (FE), terrorism (CT) and crime (CR). In so doing, this paper present four contributions: (i) we propose the first multi-operation patrolling system; (ii) MOPSS uses Markov decision processes (MDPs) to handle uncertain interruptions in the execution of patrol schedules; (iii) we are the first to deploy a new Opportunistic Security Game model, where the adversary, a criminal, makes opportunistic decisions on when and where to commit crimes and, finally (iv) we evaluate MOPSS in the real-world, providing some of the first actual data from security games in the field.

Boundedly rational human adversaries pose a serious challenge to security because they deviate from the classical assumption of perfect rationality. An emerging trend in security game research addresses this challenge by using behavioral models such as quantal response (QR) and subjective utility quantal response (SUQR). These models improve the quality of the defender's strategy by more accurately modeling the decisions made by real human adversaries. Work on incorporating human behavioral models into security games has typically followed two threads. The first thread, scalability, seeks to develop efficient algorithms to design patrols for large-scale domains that protect against a single adversary. However, this thread cannot handle the common situation of multiple adversary types with heterogeneous behavioral models. Having multiple adversary types introduces considerable uncertainty into the defender's planning problem. The second thread, robustness, uses either Bayesian or maximin approaches to handle this uncertainty caused by multiple adversary types. However, the robust approach has so far not been able to scale up to complex, large-scale security games. Thus, each of these two threads alone fails to work in key real world security games. Our present work addresses this shortcoming and merges these two research threads to yield a scalable and robust algorithm, MIDAS (MaxImin Defense Against SUQR), for generating game-theoretic patrols to defend against multiple boundedly rational human adversaries. Given the size of the defender's optimization problem, the key component of MIDAS is incremental cut and strategy generation using a master/slave optimization approach. Innovations in MIDAS include (i) a maximin mixed-integer linear programming formulation in the master and (ii) a compact transition graph formulation in the slave. Additionally, we provide a theoretical analysis of our new model and report its performance in simulations. In collaboration with the United States Coast Guard (USCG), we consider the problem of defending fishery stocks from illegal fishing in the Gulf of Mexico and use MIDAS to handle heterogeneity in adversary types (i.e., illegal fishermen) in order to construct robust patrol strategies for USCG assets.

The burgeoning area of security games has focused on real-world domains where security agencies protect critical infrastructure from a diverse set of adaptive adversaries. In such domains, decision makers have multiple competing objectives they must consider which may take different forms that are not readily comparable including safety, cost, and public perception. Thus, it can be difficult to know how to weigh the different objectives when deciding on a security strategy. To address the challenges of these domains, we propose a fundamentally different solution concept, multi-objective security games (MOSGs). Instead of a single optimal solution, MOSGs have a set of Pareto optimal (non-dominated) solutions referred to as the Pareto frontier, which can be generated by solving a sequence of constrained single-objective optimization problems (CSOPs). The Pareto frontier allows the decision maker to analyze the tradeoffs that exist between the multiple objectives. Our contributions include: (i) an algorithm, Iterative-ε-Constraints,, for generating the sequence of CSOPs; (ii) an exact approach for solving an mixed-integer linear program (MILP) formulation of a CSOP; (iii) heuristics that achieve speed up by exploiting the structure of security games to further constrain the MILP; (iv) an approximate approach for solving a CSOP built off those same heuristics, increasing the scalability of our approach with quality guarantees. Additional contributions of this paper include proofs on the level of approximation, detailed experimental evaluation of the proposed approaches and heuristics, as well as a discussion on techniques for visualizing the Pareto frontier.