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 defender's 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.

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 such fines 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 has begun trials of TRUSTS.

Multipath Switching systems (MPS) are intensely used in state-of-the-art core routers to provide terabit or even petabit switching capacity. One of the most intractable issues in designing MPS is how to load balance traffic across its multiple paths while not disturbing the intraflow packet orders. Previous packet-based solutions either suffer from delay penalties or lead to O(N^2 ) hardware complexity, hence do not scale. Flow-based hashing algorithms also perform badly due to the heavy-tailed flow-size distribution. In this paper, we develop a novel scheme, namely, Flow Slice (FS) that cuts off each flow into flow slices at every intraflow interval larger than a slicing threshold and balances the load on a finer granularity. Based on the studies of tens of real Internet traces, we show that setting a slicing threshold of 1-4 {\rm ms}, the FS scheme achieves comparative load-balancing performance to the optimal one. It also limits the probability of out-of-order packets to a negligible level (10^{ - 6}) on three popular MPSes at the cost of little hardware complexity and an internal speedup up to two. These results are proven by theoretical analyses and also validated through trace-driven prototype simulations.

Attacker-defender Stackelberg games have become a popular game-theoretic approach for security with deployments for LAX Police, the FAMS and the TSA. Unfortunately, most of the existing solution approaches do not model two key uncertainties of the real-world: there may be noise in the defender's execution of the suggested mixed strategy and/or the observations made by an attacker can be noisy. In this paper, we provide a framework to model these uncertainties, and demonstrate that previous strategies perform poorly in such uncertain settings. We also provide RECON, a novel algorithm that computes strategies for the defender that are robust to such uncertainties, and provide heuristics that further improve RECON's efficiency.

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.

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.

Law enforcement agencies frequently must allocate limited resources to protect targets embedded in a network, such as important buildings in a city road network. Since intelligent attackers may observe and exploit patterns in the allocation, it is crucial that the allocations be randomized. We cast this problem as an attacker-defender Stackelberg game: the defender’s goal is to obtain an optimal mixed strategy for allocating resources. The defender’s strategy space is exponential in the number of resources, and the attacker’s exponential in the network size. Existing algorithms are therefore useless for all but the smallest networks. We present a solution approach based on two key ideas: (i) A polynomial-sized game model obtained via an approximation of the strategy space, solved efficiently using a linear program; (ii) Two efficient techniques that map solutions from the approximate game to the original, with proofs of correctness under certain assumptions. We present in-depth experimental results, including an evaluation on part of the Mumbai road network.

Multi-Path Switching systems (MPS) are intensively used in the state-of-the-art core routers. One of the most intractable issues is how to load-balance traffic across its multiple paths while not disturbing the intra-flow packet orders. In this paper, based on the studies of tens of real Internet traces, we develop a novel scheme, namely Flow-Slice (FS), which cuts off each flow into flow-slices at every intra-flow interval larger than a slicing threshold set to 1ms 4ms and balances the load on the finer granularity. Through theoretical analyses and comprehensive trace-driven simulations, we show that FS achieves impressive load-balancing performance with little hardware cost while limiting the packet out-of-order chances to a negligible level (below 10 -6).