Stackelberg Security Games Research Articles

Stackelberg Security Game for Optimizing Cybersecurity Decisions in Cloud Computing

As it is difficult to cover all cybersecurity threats, an optimal defense strategy is one of the focal issues in cloud computing due to its dynamic abstraction and scalability. On this basis, Stackelberg security games (SSG) have received significant attention for their better deployment of limited security. To deal with uncertainty and incomplete information, we introduce a modified quantal response (Mod-QR) approach that incorporates bounded rationality and preference into the decision-making process. Formally, this can be done by using the quantal response equilibrium (QRE) framework to find a trade-off between the effectiveness and operating costs of cloud computing. In this case, the most effective countermeasures to defend the cloud can be viewed as a mixed strategy in which all the actions of the defender are played with a nonzero probability. This framework has been evaluated using an experimental study on MATLAB optimization toolbox to understand the behavioral aspects of cybersecurity actors and then to proactively protect cloud computing.

Equilibrium analysis for multi-defender Stackelberg security games under a logit tie-breaking rule

We introduce a general multi-defender Stackelberg security game where multiple independent defenders jointly protect a same set of targets from being attacked by a common attacker. In the game, Strong Stackelberg Equilibrium is fundamentally problematic, because the notion of ‘breaking ties in defender's favour’ is no longer well defined, as we must specify which defender will receive the favour. To address this issue, we define a new equilibrium concept under a newly defined tie-breaking rule. We characterise Logit Stackelberg Multi-Defender Equilibrium, corresponding to a logit tie-breaking rule, as well as an equivalent Nash Equilibrium among defenders, and exhibit algorithms for computing the equilibrium solutions. We find that Logit Stackelberg Multi-Defender Equilibrium and its' equivalent Nash Equilibrium may not exist, which motivates us to find an approximate equilibrium. We design a revised exclusion algorithm to find the approximate ε-Nash Equilibrium in which no defender gains more than ε by deviating.

Duel-based neuroevolutionary method for Stackelberg Security Games with boundedly rational Attacker

This paper considers the problem of finding optimal strategies in Stackelberg Security Games when playing against a non-perfectly rational Attacker. To this end, a novel Duel-based NeuroEvolutionary approach to Security Games (DNESG) is proposed, which utilizes the Strategy Comparison Neural Network (SCNN) as a surrogate model to compare pairs of Defender’s strategies. SCNN is trained on historical data (past attack attempts) and does not require any direct information about the Attacker’s preferences regarding targets, payoff distribution, or decision-making model. SCNN is embedded in the Evolutionary Algorithm framework and implements a tournament-based selection method in place of a time-consuming direct strategy evaluation. The effectiveness of DNESG is assessed on a set of 90 benchmark Deep Packet Inspection games inspired by real cybersecurity scenarios. The proposed method provides high-quality solutions and outperforms state-of-the-art approaches (both exact and approximate) with statistical significance when playing against non-perfectly rational Attacker. Moreover, DNESG offers excellent time scalability, being two orders of magnitude faster than the state-of-the-art Mixed-Integer Linear Programming method.

Behavioral Learning in Security Games: Threat of Multi-Step Manipulative Attacks

This paper studies the problem of multi-step manipulative attacks in Stackelberg security games, in which a clever attacker attempts to orchestrate its attacks over multiple time steps to mislead the defender's learning of the attacker's behavior. This attack manipulation eventually influences the defender's patrol strategy towards the attacker's benefit. Previous work along this line of research only focuses on one-shot games in which the defender learns the attacker's behavior and then designs a corresponding strategy only once. Our work, on the other hand, investigates the long-term impact of the attacker's manipulation in which current attack and defense choices of players determine the future learning and patrol planning of the defender. This paper has three key contributions. First, we introduce a new multi-step manipulative attack game model that captures the impact of sequential manipulative attacks carried out by the attacker over the entire time horizon. Second, we propose a new algorithm to compute an optimal manipulative attack plan for the attacker, which tackles the challenge of multiple connected optimization components involved in the computation across multiple time steps. Finally, we present extensive experimental results on the impact of such misleading attacks, showing a significant benefit for the attacker and loss for the defender.

Stackelberg Security Games with Contagious Attacks on a Network: Reallocation to the Rescue

In the classic network security games, the defender distributes defending resources to the nodes of the network, and the attacker attacks a node, with the objective of maximizing the damage caused. In this paper, we consider the network defending problem against contagious attacks, e.g., the attack at a node u spreads to the neighbors of u and can cause damage at multiple nodes. Existing works that study shared resources assume that the resource allocated to a node can be shared or duplicated between neighboring nodes. However, in the real world, sharing resource naturally leads to a decrease in defending power of the source node, especially when defending against contagious attacks. Therefore, we study the model in which resources allocated to a node can only be transferred to its neighboring nodes, which we refer to as a reallocation process. We show that the problem of computing optimal defending strategy is NP-hard even for some very special cases. For positive results, we give a mixed integer linear program formulation for the problem and a bi-criteria approximation algorithm. Our experimental results demonstrate that the allocation and reallocation strategies our algorithm computes perform well in terms of minimizing the damage due to contagious attacks.

CROSS: A framework for cyber risk optimisation in smart homes

This work introduces a decision support framework, called Cyber Risk Optimiser for Smart homeS (CROSS), which advises both smart home users and smart home service providers on how to select an optimal portfolio of cyber security controls to counteract cyber attacks in a smart home including traditional cyber attacks and adversarial machine learning attacks. CROSS is based on a multi-objective bi-level two-stage optimisation. In stage-one optimisation, the problem is modelled as a multi-leader-follower game that considers both security and economic objectives, where the provider selects a security portfolio to protect both itself and its users, while rational attackers target the weakest path. Stage-two optimisation is a Stackelberg security game that focuses on additional user security controls under the remit of smart home users. While CROSS can potentially be applied to other similar use cases, in this paper, our aim is to address threats against artificial intelligence (AI) applications as the use of AI in smart Internet of Things (IoT) devices introduces new cyber threats to home environments. Specifically, we have implemented and assessed CROSS in a smart heating use case in a prototypical AI-enabled IoT environment that combines characteristics and vulnerabilities currently present on existing commercial off-the-shelf (COTS) devices, demonstrating the selection of optimal decisions.

Playing Stackelberg Security Games in Perfect Formulations

Playing Stackelberg Security Games in Perfect Formulations

Learning attack-defense response in continuous-time discrete-states Stackelberg Security Markov games

ABSTRACT Researchers have become interested in security games in recent decades as a result of its successful application in real-world security issues. The security model is based on the Stackelberg Security Game (SSG), in which defenders (leaders) select a defensive strategy based on the optimal reaction of attackers (followers), who, at equilibrium, select the predicted assaulting strategy as a response. These applications, on the other hand, do not account for the time constraints posed by the game’s players’ journey time. Furthermore, players should be able to cope with dynamic settings in which their knowledge of the environment changes on a regular basis, allowing them to perform more effectively. This research proposes a security model based on a continuous-time Reinforcement Learning (RL) approach implemented using a temporal difference method that takes prior information into account to address these issues. We use a controlled, ergodic continuous-time Markov game to model the SSG. The game framework model assumes that all information is available. We calculate the number of transitions over a time interval divided by the entire value of the holding time to estimate the transition rates. The arithmetic mean of the observed cost of the individual players is used to estimate the cost for defenders and attackers. An iterated proximal/gradient approach is used to calculate the SSG equilibrium point. We offer a continuous-time random walk method for game implementation. In a numerical case relevant to rain-forest hazards, we analyze the performance of the suggested RL security solution and discuss the problems that should be considered in future.

Defense coordination in security games: Equilibrium analysis and mechanism design

Real-world security scenarios sometimes involve multiple defenders: security agencies of two or more countries might patrol the same border areas, and domestic security agencies might also operate in the same locations when their areas of jurisdiction overlap. Motivated by these scenarios and the observation that uncoordinated movements of the defenders may lead to an inefficient defense, we introduce a model of multi-defender security games and explore the possibility of improving efficiency by coordinating the defenders — specifically, by pooling the defenders' resources and allocating them jointly. The model generalizes the standard model of Stackelberg security games, where a defender (now a group of defenders) allocates security resources to protect a set of targets, and an attacker picks the best target to attack. In particular, we are interested in the situation with heterogeneous defenders, who may value the same target differently. Our task is twofold. First, we need to develop a good understanding of the uncoordinated situation, as the baseline to be improved. To this end we formulate a new equilibrium concept, and prove that an equilibrium under this concept always exists and can be computed efficiently. Second, to coordinate the heterogeneous defenders we take a mechanism design perspective and aim to find a mechanism to generate joint resource allocation strategies. We seek a mechanism that improves the defenders' utilities upon the uncoordinated baseline, achieves Pareto efficiency, and incentivizes the defenders to report their true incentives and execute the recommended strategies. Our analysis establishes several impossibility results, which indicate the intrinsic difficulties of defense coordination. Specifically, we show that even the basic properties listed above are in conflict with each other: no mechanism can simultaneously satisfy them all, or even some proper subsets of them. In terms of positive results, we present mechanisms that satisfy all combinations of the properties that are not ruled out by our impossibility results, thereby providing a comprehensive profile of the mechanism design problem with respect to the properties considered.

Choices Are Not Independent: Stackelberg Security Games with Nested Quantal Response Models

The quantal response (QR) model is widely used in Stackelberg security games (SSG) to model a bounded rational adversary. The QR model is a model of human response from among a large variety of prominent models known as discrete choice models. QR is the simplest type of discrete choice models and does not capture commonly observed phenomenon such as correlation among choices. We introduce the nested QR adversary model (based on nested logit model in discrete choice theory) in SSG which addresses shortcoming of the QR model. We present tractable approximation of the resulting equilibrium problem with nested QR adversary. We do so by deriving an interesting property of the equilibrium problem, namely a loosely coupled split into nested problems that mirrors the nested decision making by the adversary in the nested QR model. We show that each separate nested problem can be approximated efficiently and that the loosely coupled overall problem can be solved approximately by formulating it as a discretized version of a continuous dynamic program. Finally, we conduct experiments that show the scalability and parallelizability of our approach, as well as advantages of the nested QR model.

When Can the Defender Effectively Deceive Attackers in Security Games?

This paper studies defender patrol deception in general Stackelberg security games (SSGs), where a defender attempts to alter the attacker's perception of the defender's patrolling intensity so as to influence the attacker's decision making. We are interested in understanding the complexity and effectiveness of optimal defender deception under different attacker behavior models. Specifically, we consider three different attacker strategies of response (to the defender's deception) with increasing sophistication, and design efficient polynomial-time algorithms to compute the equilibrium for each. Moreover, we prove formal separation for the effectiveness of patrol deception when facing an attacker of increasing sophistication, until it becomes even harmful to the defender when facing the most intelligent attacker we consider. Our results shed light on when and how deception should be used in SSGs. We conduct extensive experiments to illustrate our theoretical results in various game settings.

Developing a Stackelberg security game for circular supply chain network

Developing a Stackelberg security game for circular supply chain network

Learning machiavellian strategies for manipulation in Stackelberg security games

Learning machiavellian strategies for manipulation in Stackelberg security games

Reveling misleading information for defenders and attackers in repeated Stackelberg Security Games

Critical infrastructure protection has become a major problem in today’s economy. Furthermore, the ongoing attacks on the population have piqued interest in resource allocation models in the face of societal dangers. Attacker–Defender Stackelberg Security Games (SSGs) have emerged as a critical field of study and development for resolving this issue.A game-theoretic model for SSGs with incomplete information is presented in this study. The objective is to reduce the knowledge and ingenuity of attackers when it comes to selecting a target, location, and time for an assault. For security resource allocation, we present a Bayesian-Stackelberg game-theoretic framework. The defenders’ diverse preferences create a decision-making dilemma, which needs the development of a system to devise strategies that encourages coordination. We construct an incentive-compatible optimum mechanism that maximizes benefits while incentivizing participants to implement the offered strategies. Our findings demonstrate that is possible to compute a mechanism able to obtain effective defensive coordination in security games under certain restrictions. In this approach, attackers and defenders learn their behavior by seeing private information in a Markov process-restricted game. The artificial intelligence technology chosen to perform the learning process is Reinforcement Learning (RL) approach. We provide an algorithm and evaluate the repeating game using myopic players as attackers and defenders. Experiments on SSGs can be managed using a random walk technique. The suggested framework’s efficacy and efficiency are demonstrated using a numerical example.

Single-Leader-Multiple-Followers Stackelberg Security Game With Hypergame Framework

In this paper, we employ a hypergame framework to analyze the single-leader-multiple-followers (SLMF) Stackelberg security game with two typical misinformed situations: misperception and deception. We provide a stability criterion with the help of hyper Nash equilibrium (HNE) to investigate both strategic stability and cognitive stability of equilibria in SLMF games with misinformation. In fact, we find mild stable conditions such that the equilibria with misperception and deception can become HNE. Moreover, we discuss the robustness of the equilibria to reveal whether players have the ability to keep their profits under the influence of some misinformation.

Stackelberg security game to mitigate the DoS attack in vehicular ad-hoc networks

Stackelberg security game to mitigate the DoS attack in vehicular ad-hoc networks

The Deployment-to-Saturation Ratio in Security Games

Stackelberg security games form the backbone of systems like ARMOR, IRIS and PROTECT, which are in regular use by the Los Angeles International Police, US Federal Air Marshal Service and the US Coast Guard respectively. An understanding of the runtime required by algorithms that power such systems is critical to furthering the application of game theory to other real-world domains. This paper identifies the concept of the deployment-to-saturation ratio in random Stackelberg security games, and shows that problem instances for which this ratio is 0.5 are computationally harder than instances with other deployment-to-saturation ratios for a wide range of different equilibrium computation methods, including (i) previously published different MIP algorithms, and (ii) different underlying solvers and solution mechanisms. This finding has at least two important implications. First, it is important for new algorithms to be evaluated on the hardest problem instances. We show that this has often not been done in the past, and introduce a publicly available benchmark suite to facilitate such comparisons. Second, we provide evidence that this computationally hard region is also one where optimization would be of most benefit to security agencies, and thus requires significant attention from researchers in this area. Furthermore, we use the concept of phase transitions to better understand this computationally hard region. We define a decision problem related to security games, and show that the probability that this problem has a solution exhibits a phase transition as the deployment-to-saturation ratio crosses 0.5. We also demonstrate that this phase transition is invariant to changes both in the domain and the domain representation, and that the phase transition point corresponds to the computationally hardest instances.

Coalition Formation in Multi-defender Security Games

We study Stackelberg security game (SSG) with multiple defenders, where heterogeneous defenders need to allocate security resources to protect a set of targets against a strategic attacker. In such games, coordination and cooperation between the defenders can increase their ability to protect their assets, but the heterogeneous preferences of the self-interested defenders often make such cooperation very difficult. In this paper, we approach the problem from the perspective of cooperative game theory and study coalition formation among the defenders. Our main contribution is a number of algorithmic results for the computation problems that arise in this model. We provide a poly-time algorithm for computing a solution in the core of the game and show that all of the elements in the core are Pareto efficient. We show that the problem of computing the entire core is NP-hard and then delve into a special setting where the size of a coalition is limited up to some threshold. We analyse the parameterized complexity of deciding if a coalition structure is in the core under this special setting, and provide a poly-time algorithm for computing successful deviation strategies for a given coalition.

Using Game Theory in Public Domains: The Potential and Limitations of Security Games

Abstract Since its origins, when it was mainly connected to the field of economics, game theory has brought important theoretic insights into many domains. Besides biology, philosophy or computer science, its findings have been applied to various fields of public policy. One specific area of public policy is that of security. Within the last two decades we have been witnesses to a significant increase in efforts to model security issues using tools of game theory and to derive political implications. The paper deals with the model of a Stackelberg security game and its real-world applications in security domains. The main aim and purpose of the paper is to provide a survey of selected cases of real-world deployed applications of the game-theoretic Stackelberg model in the area of public security and, based on the literature analysis, to discuss the potential and limitations of the model for policy- and decision-makers that are dealing with security measures on various governmental levels. Existing cases clearly indicate that the model can contribute to a better design and implementation of the security policy and help implement a better allocation of resources and thus potentially improve the effectiveness of security measures. On the other hand, the paper also discusses some limitations and potential future adjustments of the model together with points for further research.

A game theory approach for RTL security verification resources allocation

Many Trojan detection technologies are too time-consuming to cover the entire state space in complex designs. The valuable verification resources should be allocated to regions vulnerable to security threats. However, there are few studies on security verification resources allocation. To fill in this gap, we design a security game framework to guide the security verification resources allocation. The framework utilizes the Trojan vulnerability measurement as player utilities, so the utility value determination doesn't need any expert prior knowledge to the specific design under test. A new Stackelberg security game specific to hardware security is also proposed. The new game model minimizes the defender utility loss with the limited verification resources restriction. Due to the lack of study on RTL Trojan vulnerability measurement, we also propose a RTL security vulnerability measurement to measure each logic propagation path vulnerability quantitatively and efficiently. We apply the proposed Stackelberg security game framework to Trust-hub Trojan benchmarks written by Verilog RTL code. The experiments demonstrate that the most suspicious logic propagation path is one part of Trojan in most cases and the proposed RTL security vulnerability measurement is effective. Also, the allocation strategy calculated by security game could get security confidence as high as possible with all available resources and may also cover the Trojan even when the carefully design Trojan evade the vulnerability measurement.