Security Game Model Research Articles

A Study on Enhancing the Information Security of Urban Traffic Control Systems Using Evolutionary Game Theory

In recent years, there has been significant development in intelligent technologies for urban traffic control, such as smart city and vehicle-to-everything (V2X) communication. These advancements aim to provide more efficient and convenient services to participants in urban transportation. As the urban traffic control (UTC) system integrates with various networks and physical infrastructure, the potential threats of malicious attacks and breaches pose significant risks to the safety of individuals and their properties. To address this issue, this academic paper focuses on studying the network structure of the UTC system. A signal security game model is constructed based on the concepts of evolutionary game theory (EGT), involving three parties: attackers, upper computers (UC), and traffic signal machines (TSM). The model aims to analyze the evolutionary stability of the strategies chosen by each party, and to explore the relationships between various factors and the strategy choices of the three parties. Furthermore, the stability of equilibrium points in the three-party game system is analyzed using the Liapunov method. The conditions in which UC and TSM, dependent on detection rates and defense costs, choose to abandon defense at pure-strategy equilibrium points were obtained. Finally, MATLAB is utilized for simulation analysis to validate the impact of attack costs, defense costs, and detection rates on the information security of UTC systems.

Security defense strategy algorithm for Internet of Things based on deep reinforcement learning

Currently, important privacy data of the Internet of Things (IoT) face extremely high risks of leakage. Attackers persistently engage in continuous attacks on terminal devices to obtain private data of crucial importance. Although significant progress has been made in recent years in deep reinforcement learning defense strategies, most defense methods still face problems such as low defense resource allocation efficiency and insufficient defense coordination capabilities. To solve the above problems, this paper constructs a novel adversarial security scenario and proposes a security game model that integrates defense resource allocation and patrol inspection. Regarding the above game model, this paper designs a deep reinforcement learning algorithm named SDSA to calculate its security defense strategy. SDSA calculates the allocation strategy of the best patrolling strategy that is most suitable for the defender by searching the policy on a multi-dimensional discrete action space, and enables multiple defense agents to cooperate efficiently by training a multi-intelligent Dueling Double Deep Q-Network (D3QN) with prioritized experience replay. Finally, the experimental results show that the SDSA-learned security defense strategy can provide a feasible and effective security protection strategy for defenders against attacks compared to the MADDPG and OptGradFP methods.

Evolutionary Game for Confidentiality in IoT-Enabled Smart Grids

We applied evolutionary game theory to extend a resource constrained security game model for confidentiality attacks and defenses in an Advanced Metering Infrastructure (AMI), which is a component of IoT-enabled Smart Grids. The AMI is modeled as a tree structure where each node aggregates the information of its children before encrypting it and passing it on to its parent. As a part of the model, we developed a discretization scheme for solving the replicator equations. The aim of this work was to explore the space of possible behaviors of attackers and to develop a framework where the AMI nodes adaptively select the most profitable strategies. Using this model, we simulated the evolution of a population of attackers and defenders on various cases resembling the real life implementation of AMI. We discuss in depth how to enhance security in AMI using evolutionary game theory either by a priori analysis or as a tool to run dynamic and adaptive infrastructure defense.

Playing repeated security games with multiple attacker types: a Q-iteration on a linear programming approach

This paper investigates infinite horizon repeated security games with one defender and multiple attacker types. The incomplete information brings uncertainty of attackers' behaviour for the defender. Under the uncertainty of attackers' behaviours, we take the worst-case analysis to minimise the defender's regret w.r.t. each attacker type. We wish to keep the regret especially small w.r.t. one attacker type, at the cost of modest additional overhead compared to others. The trade-off among the objectives requires us to build a Multi-Objective Repeated Security Game (MORSG) model. To parameterise the regret Pareto frontier, we combine the different weight vectors with different objectives and build a linear programming approach. By running the Q-iteration procedure on linear programming for each weight vector, the optimal regret Pareto frontier can be computed. We also propose an approximate approach to approximate it. The approximation analysis proves the effectiveness of the approximation approach.

Modeling bluffing behavior in signaling security games

AbstractIn some security domains, the defender holds more private information than the attacker, such as the authenticity of resources. A mock camera can be adopted by the defender to deter potential attackers while the attacker may see it as a real one. This provides an opportunity for a defender with fake resources to bluff, as if all resources she owns are real. We model the bluffing behavior as a signaling game where the attacker is uncertain whether the defender is strong (all resources are real) or weak (fake resources disguised as real resources). We propose a mixed integer cubic programming formulation to solve for the solution concept based on perfect Bayesian equilibrium. We compare our bluffing security game model with a model without signaling. The experiments indicate that our model outperforms the no‐signaling model in terms of the defender's utility.

Toward an integrated dynamic defense system for strategic detecting attacks in cloud networks using stochastic game

In a complex network as a cloud computing environment, security is becoming increasingly based on deception techniques. To date, the static nature of cyber networks offers to adversaries good opportunities to systematically study the network environment, launch a cyber-attack effortlessly and wide-spread and finally defeat the target system. In order to resolve the limitations of the traditional security measures as intrusion prevention or detection systems, firewall, access list, etc., which did not change the attack surface and cannot avoid zero-days attacks, technics that provide dynamic defense, such virtual machine migration and honeypot should be deployed. Despite this, with a virtual machine migration technique, not all virtual machines’ migration between servers enhances security considerably. In this paper, we propose an integrated defense system combining virtual machine migration and honeypot. The effectiveness of the proposed system is discussed in terms of security policies. In addition, our proposed model determines the potential attack paths quantitatively then classifies them into two sub-sets: attack paths explored only and attack paths explored and exploited based on the black box intrusion steps. Thus, to model the interaction attacker–defender, the attack graph combined with the stochastic game theory is used. Finally, we carry out some numerical results to demonstrate the effectiveness of the proposed security game model.

A Game-Theoretic Approach to Cross-Layer Security Decision-Making in Industrial Cyber-Physical Systems

Current security measures in industrial cyber-physical systems (ICPS) lack the active decision capability to defend against highly-organized cyber-attacks. In this paper, a security decision-making approach based on stochastic game model is proposed to characterize the interaction between attackers and defenders in ICPSs and generate optimal defense strategies to minimize system losses. The major distinction of this approach is that it presents a practical way to build a cross-layer security game model for ICPSs by means of quantitative vulnerability analysis and time-based unified payoff quantification. A case study on a hardware-in-the-loop simulation testbed is carried out to demonstrate the feasibility of the proposed approach.

Strategic Coordination of Human Patrollers and Mobile Sensors With Signaling for Security Games

Traditional security games concern the optimal randomized allocation of human patrollers, who can directly catch attackers or interdict attacks. Motivated by the emerging application of utilizing mobile sensors (e.g., UAVs) for patrolling, in this paper we propose the novel Sensor-Empowered security Game (SEG) model which captures the joint allocation of human patrollers and mobile sensors. Sensors differ from patrollers in that they cannot directly interdict attacks, but they can notify nearby patrollers (if any). Moreover, SEGs incorporate mobile sensors' natural functionality of strategic signaling. On the technical side, we first prove that solving SEGs is NP-hard even in zero-sum cases. We then develop a scalable algorithm SEGer based on the branch-and-price framework with two key novelties: (1) a novel MILP formulation for the slave; (2) an efficient relaxation of the problem for pruning. To further accelerate SEGer, we design a faster combinatorial algorithm for the slave problem, which is provably a constant-approximation to the slave problem in zero-sum cases and serves as a useful heuristic for general-sum SEGs. Our experiments demonstrate the significant benefit of utilizing mobile sensors.

Policy Learning for Continuous Space Security Games Using Neural Networks

A wealth of algorithms centered around (integer) linear programming have been proposed to compute equilibrium strategies in security games with discrete states and actions. However, in practice many domains possess continuous state and action spaces. In this paper, we consider a continuous space security game model with infinite-size action sets for players and present a novel deep learning based approach to extend the existing toolkit for solving security games. Specifically, we present (i) OptGradFP, a novel and general algorithm that searches for the optimal defender strategy in a parameterized continuous search space, and can also be used to learn policies over multiple game states simultaneously; (ii) OptGradFP-NN, a convolutional neural network based implementation of OptGradFP for continuous space security games. We demonstrate the potential to predict good defender strategies via experiments and analysis of OptGradFP and OptGradFP-NN on discrete and continuous game settings.

Security Game with Non-additive Utilities and Multiple Attacker Resources

There has been significant interest in studying security games for modeling the interplay of attacks and defenses on various systems involving critical infrastructure, financial system security, political campaigns, and civil safeguarding. However, existing security game models typically either assume additive utility functions, or that the attacker can attack only one target. Such assumptions lead to tractable analysis, but miss key inherent dependencies that exist among different targets in current complex networks. In this paper, we generalize the classical security game models to allow for non-additive utility functions. We also allow attackers to be able to attack multiple targets. We examine such a general security game from a theoretical perspective and provide a unified view. In particular, we show that each security game is equivalent to a combinatorial optimization problem over a set system ε, which consists of defender's pure strategy space. The key technique we use is based on the transformation, projection of a polytope, and the ellipsoid method. This work settles several open questions in security game domain and significantly extends the state-of-the-art of both the polynomial solvable and NP-hard class of the security game.

Security Game with Non-additive Utilities and Multiple Attacker Resources

There has been significant interest in studying security games for modeling the interplay of attacks and defenses on various systems involving critical infrastructure, financial system security, political campaigns, and civil safeguarding. However, existing security game models typically either assume additive utility functions, or that the attacker can attack only one target. Such assumptions lead to tractable analysis, but miss key inherent dependencies that exist among different targets in current complex networks. In this paper, we generalize the classical security game models to allow for non-additive utility functions. We also allow attackers to be able to attack multiple targets. We examine such a general security game from a theoretical perspective and provide a unified view. In particular, we show that each security game is equivalent to a combinatorial optimization problem over a set system ε, which consists of defender's pure strategy space. The key technique we use is based on the transformation, projection of a polytope, and the ellipsoid method. This work settles several open questions in security game domain and extends the state-of-the-art of both the polynomial solvable and NP-hard class of the security game.

A game theoretic approach to cyber security risk management

This paper describes the Cyber Security Game (CSG). Cyber Security Game is a method that has been implemented in software that quantitatively identifies cyber security risks and uses this metric to determine the optimal employment of security methods for any given investment level. Cyber Security Game maximizes a system’s ability to operate in today’s contested cyber environment by minimizing its mission risk. The risk score is calculated by using a mission impact model to compute the consequences of cyber incidents and combining that with the likelihood that attacks will succeed. The likelihood of attacks succeeding is computed by applying a threat model to a system topology model and defender model. Cyber Security Game takes into account the widespread interconnectedness of cyber systems, where defenders must defend all multi-step attack paths and an attacker only needs one to succeed. It employs a game theoretic solution using a game formulation that identifies defense strategies to minimize the maximum cyber risk (MiniMax). This paper discusses the methods and models that compose Cyber Security Game . A limited example of a Point of Sale system is used to provide specific demonstrations of Cyber Security Game models and analyses.

Non-Additive Security Games

Security agencies have found security games to be useful models to understand how to better protect their assets. The key practical elements in this work are: (i) the attacker can simultaneously attack multiple targets, and (ii) different targets exhibit different types of dependencies based on the assets being protected (e.g., protection of critical infrastructure, network security, etc.). However, little is known about the computational complexity of these problems, especially when there exist dependencies among the targets. Moreover, previous security game models do not in general scale well. In this paper, we investigate a general security game where the utility function is defined on a collection of subsets of all targets, and provide a novel theoretical framework to show how to compactly represent such a game, efficiently compute the optimal (minimax) strategies, and characterize the complexity of this problem. We apply our theoretical framework to the network security game. We characterize settings under which we find a polynomial time algorithm for computing optimal strategies. In other settings we prove the problem is NP-hard and provide an approximation algorithm.

Multidefender Security Games

Stackelberg security game models and associated computational tools have seen deployment in a number of high-consequence security settings, such as LAX canine patrols and Federal Air Marshal Service. These models focus on isolated systems with only one defender, despite being part of a more complex system with multiple players. Furthermore, many real systems such as transportation networks and the power grid exhibit interdependencies between targets and, consequently, between decision makers jointly charged with protecting them. To understand such multidefender strategic interactions present in security, we investigate game theoretic models of security games with multiple defenders. Unlike most prior analysis, we focus on the situations in which each defender must protect multiple targets, so that even a single defender's best response decision is, in general, highly non-trivial. We start with an analytical investigation of multidefender security games with independent targets, offering an equilibrium and price-of-anarchy analysis of three models with increasing generality. In all models, we find that defenders have the incentive to over-protect targets, at times significantly. Additionally, in the simpler models, we find that the price of anarchy is unbounded, linearly increasing both in the number of defenders and the number of targets per defender. Considering interdependencies among targets, we develop a novel mixed-integer linear programming formulation to compute a defender's best response, and make use of this formulation in approximating Nash equilibria of the game. We apply this approach towards computational strategic analysis of several models of networks representing interdependencies, including real-world power networks. Our analysis shows how network structure and the probability of failure spread determine the propensity of defenders to over- or under-invest in security.

Power-Efficient Secure Transmission Against Full-Duplex Active Eavesdropper: A Game-Theoretic Framework

Information security is of paramount importance yet significant challenge for wireless communications. In this paper, we investigate the power-efficient transmissions with security concerns in the presence of a full-duplex (FD) active eavesdropper. With FD capability, the eavesdropper can launch jamming attacks while eavesdropping, which affects the legitimate transmissions, such that the legitimate power allocation becomes more favorable for eavesdropping. However, the jamming attacks require additional power consumption and result in self-interference at the eavesdropper itself. The legitimate user intends for a power-efficient manner to effectively guarantee the secure transmissions to defend against the simultaneous eavesdropping and jamming attacks. We formulate the problem within a Stackelberg game framework, where the eavesdropper takes action first as the leader and the legitimate user acts as the follower. We analyze the security game model for both single-channel and multi-channel cases. Furthermore, by exploring the properties of the game equilibrium, we propose the optimal transmission strategy and jamming strategy for the legitimate transmission and eavesdropping, respectively. Finally, we provide extensive simulation results to corroborate our theoretical analysis and evaluate the security performance.

Stackelberg Security Games: Models, Applications and Computational Aspects

Stackelberg games are non-symmetric games where one player or specified group of players have the privilege position and make decision before the other players. Such games are used in telecommunication and computational systems for supporting administrative decisions. Recently Stackleberg games became useful also in the systems where security issues are the crucial decision criteria. In this paper authors briefly survey the most popular Stackelberg security game models and provide the analysis of the model properties illustrated in the realistic use cases.

A Security Game Combining Patrolling and Alarm-Triggered Responses Under Spatial and Detection Uncertainties

Motivated by a number of security applications, among which border patrolling, we study, to the best of our knowledge, the first Security Game model in which patrolling strategies need to be combined with responses to signals raised by an alarm system, which is spatially uncertain (i.e., it is uncertain over the exact location the attack is ongoing) and is affected by false negatives (i.e., the missed detection rate of an attack may be positive). Ours is an infinite-horizon patrolling scenario on a graph, where a single patroller moves. We study the properties of the game model in terms of computational issues and form of the optimal strategies and we provide an approach to solve it. Finally, we provide an experimental analysis of our techniques.

Security Games with Protection Externalities

Stackelberg security games have been widely deployed in recent years to schedule security resources. An assumption in most existing security game models is that one security resource assigned to a target only protects that target. However, in many important real-world security scenarios, when a resource is assigned to a target, it exhibits protection externalities: that is, it also protects other “neighbouring” targets. We investigate such Security Games with Protection Externalities (SPEs). First, we demonstrate that computing a strong Stackelberg equilibrium for an SPE is NP-hard, in contrast with traditional Stackelberg security games which can be solved in polynomial time. On the positive side, we propose a novel column generation based approach—CLASPE—to solve SPEs. CLASPE features the following novelties: 1) a novel mixed-integer linear programming formulation for the slave problem; 2) an extended greedy approach with a constant-factor approximation ratio to speed up the slave problem; and 3) a linear-scale linear programming that efficiently calculates the upper bounds of target-defined subproblems for pruning. Our experimental evaluation demonstrates that CLASPE enable us to scale to realistic-sized SPE problem instances.

Exploring Information Asymmetry in Two-Stage Security Games

Stackelberg security games have been widely deployed to protect real-word assets. The main solution concept there is the Strong Stackelberg Equilibrium (SSE), which optimizes the defender's random allocation of limited security resources. However, solely deploying the SSE mixed strategy has limitations. In the extreme case, there are security games where the defender is able to defend all the assets ``almost perfectly" at the SSE, but she still sustains significant loss. In this paper, we propose an approach for improving the defender's utility in such scenarios. Perhaps surprisingly, our approach is to strategically reveal to the attacker information about the sampled pure strategy. Specifically, we propose a two-stage security game model, where in the first stage the defender allocates resources and the attacker selects a target to attack, and in the second stage the defender strategically reveals local information about that target, potentially deterring the attacker's attack plan. We then study how the defender can play optimally in both stages. We show, theoretically and experimentally, that the two-stage security game model allows the defender to gain strictly better utility than SSE.

Security Games for Risk Minimization in Automatic Generation Control

The power grid is a critical infrastructure that must be protected against potential threats. While modern technologies at the center of the ongoing smart grid evolution increase its operational efficiency, they also make it more susceptible to malicious attacks such as false data injection to electronic monitoring systems. This paper presents a game-theoretic approach to smart grid security by combining quantitative risk management techniques with decision making on protective measures. The consequences of data injection attacks are quantified using a risk assessment process where the well-known conditional value-at-risk (CVaR) measure provides an estimate of the defender's loss due to load shed in simulated scenarios. The calculated risks are then incorporated into a stochastic security game model as input parameters. The decisions on defensive measures are obtained by solving the game using dynamic programming techniques which take into account resource constraints. Thus, the formulated security game provides an analytical framework for choosing the best response strategies against attackers and minimizing potential risks. The theoretical results obtained are demonstrated through numerical examples. Simulation results show that different risk measures lead to different defense strategies, but the CVaR measure prioritizes high-loss tail events.