Stackelberg game in critical infrastructures from a network science perspective

Protecting critical infrastructure is a challenging task for security agencies all around the world, which is exacerbated by terrorism. Many infrastructures have network characteristics, such as transportation and communication systems. Therefore, it is necessary to study them from the perspective of network science. Game theory provides a suitable theoretical tool for the study of attack-defense confrontation between rational agents. Sequential game, which is more in line with the actual situation, can better analyze the confrontation in infrastructure protection. Previous models which combine network science with game theory only consider the attacker as a single type. However, in the real world, accurate information about the type of the attacker is not always available for the defender. In this paper, we apply Bayesian Stackelberg game to model the attack-defense confrontation in the case of uncertain attacker type.

With the development of various wireless personal area networks (WPANs), the issue of security has become a crucial problem for their applications. Jamming is one of the most important methods of attack to deprive or reduce the communication service of WPANs. Most existing jamming attacks can cause negative interference, but the attack strategies are usually not adjusted against the countermeasures that are currently taken. This paper proposes an effective dynamic jamming attack (EDJam) in an 802.15.4-compliant WPAN. In this attack, a jammer who is aware of a change in the network defense strategy, e.g. the use of a dynamic retransmission mechanism, may choose a better strategy to make more damage to the network with less cost. Similarly, a well-protected network can change its defense strategy against the EDJam. This procedure of competition between the EDJam attacker and defending networks is modeled and formulated as a Stackelberg game, and a unique Nash Equilibrium point is derived in analytical format. Based on an equilibrium analysis, we discuss the condition under which a defense strategy will increase the utility of the network and a dynamic retransmission mechanism defense strategy is proposed accordingly. The simulation results show that EDjam can be more cost-efficient than continuous, random and fixed-period jamming.

A variable neighborhood search based algorithm and game theory models for green supply chain design

Attack-defense game for critical infrastructure considering the cascade effect

Modern society relies heavily on complex infrastructures, such as power systems and communication systems, which makes it vulnerable to intentional attacks or unpredictable failures. Being able to locate critical components in such systems allows us to protect it from attacks or failures with minimal effort. From a network science perspective, two fundamental types of components in a system are its constituent nodes and edges. The importance of nodes recently attracts a lot of interests. However, edges are paid less attention to, although in the case of protection, edge targeted methods are less invasive and more flexible. In this brief, we address the issue of quantifying importance of edges. The importance of edges is defined as how their removal affects the connectivity of the network, since connectivity is the most important property that ensures the network’s function. The proposed importance measure, nearest-neighbor connectivity-based edge importance, can be used to quantify the importance of a single edge or a set of edges. The result on real-world network data shows that the proposed measure is more efficient than the most widely used measures. As another result, we show that the importance of a single edge is not necessarily positive correlated with the importance of incident nodes, which is widely assumed in literatures.

Free AccessAboutSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack CitationsPermissionsReprints ShareShare onFacebookTwitterLinked InEmail Go to SectionFree Access HomeINFORMS TutORials in Operations ResearchEmerging Theory, Methods, and Applications Analyzing the Vulnerability of Critical Infrastructure to Attack and Planning DefensesGerald G. Brown, W. Matthew Carlyle, Javier Salmerón, Kevin WoodGerald G. Brown, W. Matthew Carlyle, Javier Salmerón, Kevin WoodPublished Online:14 Oct 2014https://doi.org/10.1287/educ.1053.0018Abstract We describe new bilevel programming models to (1) help make the country's critical infrastructure more resilient to attacks by terrorists, (2) help governments and businesses plan those improvements, and (3) help influence related public policy on investment incentives, regulations, etc. An intelligent attacker (terrorists) and defender (us) are key features of all these models, along with information transparency: These are Stackelberg games, as opposed to two-person, zero-sum games. We illustrate these models with applications to electric power grids, subways, airports, and other critical infrastructure. For instance, one model identifies locations for a given set of electronic sensors that minimize the worst-case time to detection of a chemical, biological, or radiological contaminant introduced into the Washington, D.C. subway system. The paper concludes by reporting insights we have gained through forming “red teams,” each of which gathers open-source data on a real-world system, develops an appropriate attacker-defender or defender-attacker model, and solves the model to identify vulnerabilities in the system or to plan an optimal defense. This publication has no references to display. Your Access Options Login Options INFORMS Member Login Nonmember Login Purchase Options Save for later Item saved, go to cart Tutorials in OR, TutorialsNew $20.00 Add to cart Tutorials in OR, TutorialsNew Checkout Other Options Token Access Insert token number Claim access using a token Restore guest access Applies for purchases made as a guest Previous Back to Top Next FiguresReferencesRelatedInformationCited ByOn Time-Dependent Critical Platforms and Tracks in Metro SystemsJunwei Wang, Yue Gao, Yao Cheng18 February 2022 | Transportation Science, Vol. 56, No. 4Optimal Power Flow in Distribution Networks Under N – 1 Disruptions: A Multistage Stochastic Programming ApproachHaoxiang Yang, Harsha Nagarajan5 November 2021 | INFORMS Journal on Computing, Vol. 34, No. 2Modeling Defender-Attacker Problems as Robust Linear Programs with Mixed-Integer Uncertainty SetsJuan S. Borrero, Leonardo Lozano17 February 2021 | INFORMS Journal on Computing, Vol. 33, No. 4Mitigating Interdiction Risk with FortificationLe Thi Khanh Hien, Melvyn Sim, Huan Xu24 February 2020 | Operations Research, Vol. 68, No. 2Interdiction Games and Monotonicity, with Application to Knapsack ProblemsMatteo Fischetti, Ivana Ljubić, Michele Monaci, Markus Sinnl26 April 2019 | INFORMS Journal on Computing, Vol. 31, No. 2A Backward Sampling Framework for Interdiction Problems with FortificationLeonardo Lozano, J. Cole Smith21 December 2016 | INFORMS Journal on Computing, Vol. 29, No. 1 Emerging Theory, Methods, and ApplicationsSeptember 2005 Article Information Metrics Downloaded 239 times in the past 12 months Information Published Online:October 14, 2014 Copyright © 2005, INFORMSCite asGerald G. BrownW. Matthew CarlyleJavier SalmerónKevin Wood (2014) Analyzing the Vulnerability of Critical Infrastructure to Attack and Planning Defenses. INFORMS TutORials in Operations Research null(null):102-123. https://doi.org/10.1287/educ.1053.0018 Keywordscritical infrastructure protectionbilevel programmixed-integer programhomeland securityPDF download

Wireless virtualization is becoming a popular solution to resource sharing problems integral in providing access to future wireless networking applications by enabling access to the same physical wireless infrastructure by multiple virtual networks concurrently. This paper investigates cyber deception using game theory model for defining the deceptive interactions between a cyber attacker and the defender. We consider both the naive attacker who is not aware of the defender's strategy, and the rational (powerful) attacker who knows the defense strategy. In the Stackelberg game, the defender controls the observable configuration of the network when probed by an attacker. We show that the process for selecting an optimal defense strategy against a naive attacker is NP-hard. We also proposed an algorithm for computing optimal strategy for a naive attacker and a greedy based algorithm for selecting the optimal strategy against a powerful attacker. Results from extensive simulation runs show the scalability and effectiveness of the proposed approaches based on the run time in finding the optimum defense strategy as well as minimizing the attacker's utility are better than the approaches in state of the art literature.

This paper describes a two-person zero-sum game in function space concerning the optimal allocation of a homogenous defense force on different levels of readiness. The second player, the attacker, wants to determine the time for the attack such that the cost is minimized. As the defense is subject to attrition, a delay is preferable for the attacker. This is balanced, however, by a delay cost which increases with time. The existence of a solution consisting of a pure defense strategy and a mixed strategy for the attack time is proved elsewhere. This paper mainly treats an approximation of the game with a time-discrete version for which an algorithm is derived. Arbitrarily close upper and lower bounds of the value of the original game can be obtained by the algorithm, as well as feasible defense and attacker strategies that realize these value estimates. Computational results are given for two simple problems, one of which is also solved analytically.

Critical infrastructure systems are distributed environments in which the mixture of technologies and interdependencies between physical and logical components lead to complex interactions. Calculating the possible impacts of attacks and the success of proposed countermeasures in such environments represents a severe problem. We propose a process algebraic technique as a means of affecting such calculations. Our approach allows us to demonstrate equivalence w.r.t. attack and defense strategies respectively. It also forms a basis for determining the efficiency and effectiveness of countermeasures. In comparison with other methods, such as attack/defense trees and attack graphs, our approach allows us to relax assumptions regarding the ordering of events by applying structural reasoning to outcomes and reducing the state space for the analysis. An obvious application is to risk management.

This paper studies the problem of Stackelberg game based distributed power allocation for spectral coexisting multistatic radar and communication systems. The strategy aims to minimize the radiated power of each radar by optimizing transmit power allocation for a desired signal-to-interference-plus-noise ratio (SINR) meanwhile the communication base station (CBS) is protected from the interference of radar transmissions. We formulate this distributed power allocation process as a Stackelberg game, where the CBS is a leader and the radars are the followers. The Nash equilibrium (NE) for the formulated game is derived. Then, the existence of the NE and uniqueness of the solution are analytically proved. Moreover, an iterative algorithm is developed to solve the resulting problem. Finally, numerical results verify that the proposed scheme is effective on power allocation and CBS protection with reduced signaling overhead.

Leadership in singleton congestion games: What is hard and what is easy

Preamble slice orderly queue access scheme in cell-free dense communication systems

While blockchain technology offers promising solutions for malware detection through decentralized signature sharing, the strategic interactions between malicious actors and security agencies create complex adversarial dynamics that traditional viability assessment methods fail to capture. This paper presents a novel gametheoretic framework that combines multi-dimensional viability analysis with Stackelberg equilibrium theory to evaluate blockchain-based malware detection systems. We model the interaction between certified security agencies (leaders) and potential attackers (followers) as a two-stage Stackelberg game, where agencies strategically choose their signature publication policies while attackers respond by optimizing their malware deployment strategies. Our main contribution is the Blockchain Security Equilibrium Theorem, which proves the existence and uniqueness of Nash-Stackelberg equilibrium in this adversarial setting. Through theoretical analysis and empirical validation using the original multi-dimensional framework data, we demonstrate that our framework provides more accurate viability predictions compared to existing methodologies, offering critical insights for designing robust blockchain-based security solutions.

<title>Abstract</title> In the evolving cybernetic landscape, the development of highly responsive computational models constitutes a critical determinant of system resilience. As adversarial dynamics accelerate and become increasingly non-stationary, models must exhibit ultra-low-latency inference, adaptive contextualization, and autonomous self-optimization. Responsiveness transcends mere computational speed; it embodies algorithmic elasticity and epistemic agility, enabling systems to recalibrate their internal representations in real time under adversarial pressure. Hence, responsiveness emerges as the defining property that sustains homeostatic stability and operational continuity in self-regulating systems.In this study, we introduce a decision-theoretic algorithmic framework for the optimal selection of defensive strategies in safeguarding computational and information infrastructures against dynamic cyber adversaries. The proposed model synthesizes Epistemic Game Theory with the Stackelberg paradigm, facilitating an analytically grounded mechanism for equilibrating defensive efficacy, operational costs, and expected utility under adversarial uncertainty.The formulation models defender–attacker interactions as a Stackelberg game, wherein the defender assumes the role of the strategic leader. This construct is augmented with epistemic belief updating to capture multi-round adaptive behaviour and trace-driven adversarial modeling that reflects empirically observed attack trajectories. The defender dynamically revises probabilistic beliefs regarding the attacker’s typology and anticipated behavioural evolution, thereby enabling real-time adaptive and epistemically informed decision-making.A simulation conducted under empirically realistic conditions—focusing on defense mechanisms against Distributed Denial of Service (DDoS) attacks—demonstrates the operational viability of the framework. Additional evaluation using synthetic data traces encompassing a wider spectrum of attack archetypes substantiates the model’s generality. Results reveal that optimal defensive strategies emerge from the interplay between epistemic updating and the system’s intrinsic reward structure, underscoring the necessity of jointly modeling behavioural dynamics and incentive mechanisms within contemporary cybersecurity decision architectures.

Unmanned Aerial Vehicles, popularly known as UAVs, have been used in many applications, from healthcare services to military assignments with diverse capabilities such as data transmission, cellular service provisioning, and computational offloading tasks. UAV's have been recently used to provide Security as a Service (SaaS). SaaS involves technical solutions like anti-virus and anti-spam software, firewalls, using secure operating systems, etc. UAV's are resource-constrained devices, and thus they are connected to the base station (BS) so that they may avail the computational facilities of the BS. The UAV's connect themselves to the base station using cluster heads (intermediary devices). At times several UAVs cooperatively come together to serve a given region and such a group of UAVs is called a swarm of UAVs. In real-world scenarios, many stakeholders come together to form UAV swarm configuration proving services to users. Each stakeholder wants to maximize his gains. In this work, we propose a pricing Stackelberg game among UAVs, Cluster heads, and BS by formulating their behavioral utilities. Using particle swarm optimization on each entity's utility functions, we create an optimal price strategy for each entity to maximize their profit.