Zhengyu Yin

Stackelberg vs. Nash in security games: an extended investigation of interchangeability, equivalence, and uniqueness

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 followers 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 defenders uncertainty about the attackers ability to observe explicit.

Stackelberg vs. Nash in security games: interchangeability, equivalence, and uniqueness

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; for example, these games are at the heart of major applications such as the ARMOR program deployed for security at the LAX airport since 2007 and the IRIS program in use by the US Federal Air Marshals (FAMS). The foundational assumption for using Stackel-berg 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, the followers may act without observation of the leaders strategy, essentially converting the game into a simultaneous-move game model. Previous work fails to address how a leader should compute her strategy given this fundamental uncertainty about the type of game faced. Focusing on the complex games that are directly inspired by real-world security applications, the paper provides four contributions in the context of a general class of security games. First, exploiting the structure of these security games, the paper shows that the Nash equilibria in security games are interchangeable, thus alleviating the equilibrium selection problem. Second, resolving the leaders dilemma, it shows that 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 real-world 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, our experimental results emphasize positive properties of games that do not fit our restrictions. Our contributions have major implications for the real-world applications.

TRUSTS: Scheduling Randomized Patrols for Fare Inspection in Transit Systems Using Game Theory

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.

Game-theoretic security patrolling with dynamic execution uncertainty and a case study on a real transit system

Attacker-Defender Stackelberg security games (SSGs) have emerged as an important research area in multi-agent systems. However, existing SSGs models yield fixed, static, schedules which fail in dynamic domains where defenders face execution uncertainty, i.e., in domains where defenders may face unanticipated disruptions of their schedules. A concrete example is an application involving checking fares on trains, where a defenders schedule is frequently interrupted by fare evaders, making static schedules useless. To address this shortcoming, this paper provides four main contributions. First, we present a novel general Bayesian Stackelberg game model for security resource allocation in dynamic uncertain domains. In this new model, execution uncertainty is handled by using a Markov decision process (MDP) for generating defender policies. Second, we study the problem of computing a Stackelberg equilibrium for this game and exploit problem structure to reduce it to a polynomial-sized optimization problem. Shifting to evaluation, our third contribution shows, in simulation, that our MDP-based policies overcome the failures of previous SSG algorithms. In so doing, we can now build a complete system, that enables handling of schedule interruptions and, consequently, to conduct some of the first controlled experiments on SSGs in the field. Hence, as our final contribution, we present results from a real-world experiment on Metro trains in Los Angeles validating our MDP-based model, and most importantly, concretely measuring the benefits of SSGs for security resource allocation.

Continuous time planning for multiagent teams with temporal constraints

Continuous state DEC-MDPs are critical for agent teams in domains involving resources such as time, but scaling them up is a significant challenge. To meet this challenge, we first introduce a novel continuous-time DEC-MDP model that exploits transition independence in domains with temporal constraints. More importantly, we present a new locally optimal algorithm called SPAC. Compared to the best previous algorithm, SPAC finds solutions of comparable quality substantially faster; SPAC also scales to larger teams of agents.

Two decades of multiagent teamwork research: past, present, and future

This paper discusses some of the recent cooperative multiagent systems work in the TEAMCORE lab at the University of Southern California. Based in part on an invited talk at the CARE 2010 workshop, we highlight how and why execution-time reasoning has been supplementing, or replacing, planning-time reasoning in such systems.

Game theory and human behavior: challenges in security and sustainability

Security and sustainability are two critical global challenges that involve the interaction of many intelligent actors. Game theory provides a sound mathematical framework to model such interactions, and computational game theory in particular has a promising role to play in helping to address key aspects of these challenges. Indeed, in the domain of security, we have already taken some encouraging steps by successfully applying game-theoretic algorithms to real-world security problems: our algorithms are in use by agencies such as the US coast guard, the Federal Air Marshals Service, the LAX police and the Transportation Security Administration. While these applications of game-theoretic algorithms have advanced the state of the art, this paper lays out some key challenges as we continue to expand the use of these algorithms in real-world domains. One such challenge in particular is that classical game theory makes a set of assumptions of the players, which may not be consistent with real-world scenarios, especially when humans are involved. To actually model human behavior within game-theoretic framework, it is important to address the new challenges that arise due to the presence of human players: (i) human bounded rationality; (ii) limited observations and imperfect strategy execution; (iii) large action spaces. We present initial solutions to these challenges in context of security games. For sustainability, we lay out our initial efforts and plans, and key challenges related to human behavior in the loop.