Predictable allocations of security resources such as police officers, canine units, or checkpoints are vulnerable to exploitation by attackers. Recent work has applied game-theoretic methods to find optimal randomized security policies, including a fielded application at the Los Angeles International Airport (LAX). This approach has promising applications in many similar domains, including police patrolling for subway and bus systems, randomized baggage screening, and scheduling for the Federal Air Marshal Service (FAMS) on commercial flights. However, the existing methods scale poorly when the security policy requires coordination of many resources, which is central to many of these potential applications.We develop new models and algorithms that scale to much more complex instances of security games. The key idea is to use a compact model of security games, which allows exponential improvements in both memory and runtime relative to the best known algorithms for solving general Stackelberg games. We develop even faster algorithms for security games under payoff restrictions that are natural in many security domains. Finally, introduce additional realistic scheduling constraints while retaining comparable performance improvements. The empirical evaluation comprises both random data and realistic instances of the FAMS and LAX problems. Our new methods scale to problems several orders of magnitude larger than the fastest known algorithm.

There has been significant recent interest in game-theoretic approaches to security, with much of the recent research focused on utilizing the leader-follower Stackelberg game model. Among the major applications are the ARMOR program deployed at LAX Airport and the IRIS program in use by the US Federal Air Marshals (FAMS). The foundational assumption for using Stackelberg games is that security forces (leaders), acting first, commit to a randomized strategy; while their adversaries (followers) choose their best response after surveillance of this randomized strategy. Yet, in many situations, a leader may face uncertainty about the follower's surveillance capability. Previous work fails to address how a leader should compute her strategy given such uncertainty.We provide five contributions in the context of a general class of security games. First, we show that the Nash equilibria in security games are interchangeable, thus alleviating the equilibrium selection problem. Second, under a natural restriction on security games, any Stackelberg strategy is also a Nash equilibrium strategy; and furthermore, the solution is unique in a class of security games of which ARMOR is a key exemplar. Third, when faced with a follower that can attack multiple targets, many of these properties no longer hold. Fourth, we show experimentally that in most (but not all) games where the restriction does not hold, the Stackelberg strategy is still a Nash equilibrium strategy, but this is no longer true when the attacker can attack multiple targets. Finally, as a possible direction for future research, we propose an extensive-form game model that makes the defender's uncertainty about the attacker's ability to observe explicit.

The increasing threat of terrorism makes security at major locations of economic or political importance a major concern. Limited security resources prevent complete security coverage, allowing adversaries to observe and exploit patterns in patrolling or monitoring, and enabling them to plan attacks that avoid existing patrols. The use of randomized security policies that are more difficult for adversaries to predict and exploit can counter their surveillance capabilities. We describe two applications, ARMOR and IRIS, that assist security forces in randomizing their operations. These applications are based on fast algorithms for solving large instances of Bayesian Stackelberg games. Police at the Los Angeles International Airport deploy ARMOR to randomize the placement of checkpoints on roads entering the airport and the routes of canine unit patrols within the airport terminals. The Federal Air Marshal Service has deployed IRIS in a pilot program to randomize the schedules of air marshals on international flights. This paper examines the design choices, information, and evaluation criteria that were critical to developing these applications.

Artículo de publicación ISIStackelberg 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 adversaries’ 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 subjects’ 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)

Security is a concern of major importance to governments and companies throughout the world. With limited resources, complete coverage of potential points of attack is not possible. Deterministic allocation of available law enforcement agents introduces predictable vulnerabilities that can be exploited by adversaries. Strategic randomization is a game theoretic alternative that we implement in Intelligent Randomization In Scheduling (IRIS) system, a software scheduling assistant for the Federal Air Marshals (FAMs) that provide law enforcement aboard U.S. commercial flights.In IRIS, we model the problem as a Stackelberg game, with FAMS as leaders that commit to a flight coverage schedule and terrorists as followers that attempt to attack a flight. The FAMS domain presents three challenges unique to transportation network security that we address in the implementation of IRIS. First, with tens of thousands of commercial flights per day, the size of the Stackelberg game we need to solve is tremendous. We use ERASER-C, the fastest known algorithm for solving this class of Stackelberg games. Second, creating the game itself becomes a challenge due to number of payoffs we must enter for these large games. To address this, we create an attribute-based preference elicitation system to determine reward values. Third, the complex scheduling constraints in transportation networks make it computationally prohibitive to model the game by explicitly modeling all combinations of valid schedules. Instead, we model the leader's strategy space by incorporating a representation of the underlying scheduling constraints.The scheduling assistant has been delivered to the FAMS and is currently undergoing testing and review for possible incorporation into their scheduling practices. In this paper, we discuss the design choices and challenges encountered during the implementation of IRIS.

The Stackelberg Security Game (SSG) model has been immensely influential in security research since it was introduced roughly a decade ago. Furthermore, deployed SSG-based applications are one of most successful examples of game theory applications in the real world. We present a broad survey of recent technical advances in SSG and related literature, and then look to the future by highlighting the new potential applications and open research problems in SSG.

Security games, and important class of Stackelberg games, are used in deployed decision-support tools in use by LAX police and the Federal Air Marshals Service. The algorithms used to solve these games find optimal randomized schedules to allocate security resources for infrastructure protection. Unfortunately, the state of the art algorithms either fail to scale or to provide a correct solution for large problems with arbitrary scheduling constraints. We introduce ASPEN, a branch-and-price approach that overcomes these limitations based on two key contributions: (i) A columngeneration approach that exploits a novel network flow representation, avoiding a combinatorial explosion of schedule allocations; (ii) A branch-and-bound algorithm that generates bounds via a fast algorithm for solving security games with relaxed scheduling constraints. ASPEN is the first known method for efficiently solving massive security games with arbitrary schedules.

In proof-of-payment transit systems, passengers are legally required to purchase tickets before entering but are not physically forced to do so. Instead, patrol units move about the transit system, inspecting the tickets of passengers, who face fines if caught fare evading. The deterrence of fare evasion depends on the unpredictability and effectiveness of the patrols. In this paper, we present TRUSTS, an application for scheduling randomized patrols for fare inspection in transit systems. TRUSTS models the problem of computing patrol strategies as a leader-follower Stackelberg game where the objective is to deter fare evasion and hence maximize revenue. This problem differs from previously studied Stackelberg settings in that the leader strategies must satisfy massive temporal and spatial constraints; moreover, unlike in these counterterrorism-motivated Stackelberg applications, a large fraction of the ridership might realistically consider fare evasion, and so the number of followers is potentially huge. A third key novelty in our work is deliberate simplification of leader strategies to make patrols easier to be executed. We present an efficient algorithm for computing such patrol strategies and present experimental results using real-world ridership data from the Los Angeles Metro Rail system. The Los Angeles County Sheriff’s department is currently carrying out trials of TRUSTS.