text: With the increasing connectivity enabled by the Internet of Things (IoT), security becomes a critical concern, and users should invest to secure their IoT applications. Due to the massive devices in the IoT network, users cannot be aware of the security policies taken by all its connected neighbors. Instead, a user makes security decisions based on the cyber risks that he perceives by observing a selected number of nodes. To this end, we propose a model which incorporates the limited attention or bounded rationality nature of players in the IoT. Specifically, each individual builds a sparse cognitive network of nodes to respond to. Based on this simplified cognitive network representation, each user then determines his security management policy by minimizing his own real-world security cost. The bounded rational decision-makings of players and their cognitive network formations are interdependent and thus should be addressed in a holistic manner. We establish a games-in-games framework and propose a Gestalt Nash equilibrium (GNE) solution concept to characterize the decisions of agents and quantify their risk of bounded perception due to the limited attention. In addition, we design a proximal-based iterative algorithm to compute the GNE. With case studies of smart communities, the designed algorithm can successfully identify the critical users whose decisions need to be taken into account by the other users during the security management.
  @cite_30: 
  @cite_35: The increasing connectivity between critical infrastructures creates a network of networks in which the interdependencies between the networks play an important role in understanding the emerging functions and performances. To this end, this paper aims to establish a game-theoretic framework to capture the interactions between two system designers who aim to maximize individual network utilities. In particular, we use the game model to investigate the decentralized interdependent network for maximizing the algebraic connectivity of the global network. We develop an alternating play algorithm, and show its convergence to a Nash equilibrium network after a finite number of iterations. We corroborate our results through case studies of power and communication networks, and compare the Nash equilibrium solutions with their constrained team solution counterparts. The experimental results provide design guidelines and insights to increase the efficiency of the interdependent network formation games.
  @cite_22: Network connectivity plays an important role in the information exchange between different agents in the multi-level networks. In this paper, we establish a game-theoretic framework to capture the uncoordinated nature of the decision-making at different layers of the multi-level networks. Specifically, we design a decentralized algorithm that aims to maximize the algebraic connectivity of the global network iteratively. In addition, we show that the designed algorithm converges to a Nash equilibrium asymptotically and yields an equilibrium network. To study the network resiliency, we introduce three adversarial attack models and characterize their worst-case impacts on the network performance. Case studies based on a two-layer mobile robotic network are used to corroborate the effectiveness and resiliency of the proposed algorithm and show the interdependency between different layers of the network during the recovery processes.
  @cite_7: We provide an overview and synthesis of the literatures analyzing games in which players are connected via a network structure. We discuss, in particular, the impact of the structure of the network on individuals’ behaviors. We focus on game theoretic modeling, but also include some discussion of analyses of peer effects, as well as applications to diffusion, employment, crime, industrial organization, and education.
  @cite_28: The integration of modern information and communication technologies (ICTs) into critical infrastructures (CIs) improves its connectivity and functionalities yet also brings cyber threats. It is thus essential to understand the risk of ICTs on CIs holistically as a cyber-physical system and design efficient security hardening mechanisms. To this end, we capture the system behaviors of the CIs under malicious attacks and the protection strategies by a zero-sum game. We further propose a computationally tractable approximation for large-scale networks which builds on the factored graph that exploits the dependency structure of the nodes of CIs and the approximate dynamic programming tools for stochastic Markov games. This work focuses on a localized information structure and the single-controller game solvable by linear programming. Numerical results illustrate the proper tradeoff of the approximation accuracy and computation complexity in the new design paradigm and show the proactive security at the time of unanticipated attacks.
  @cite_9: Traditional intrusion detection systems (IDSs) work in isolation and can be easily compromised by unknown threats. An intrusion detection network (IDN) is a collaborative IDS network intended to overcome this weakness by allowing IDS peers to share detection knowledge and experience, and hence improve the overall accuracy of intrusion assessment. In this work, we design an IDN system, called GUIDEX, using game-theoretic modeling and trust management for peers to collaborate truthfully and actively. We first describe the system architecture and its individual components, and then establish a game-theoretic framework for the resource management component of GUIDEX. We establish the existence and uniqueness of a Nash equilibrium under which peers can communicate in a reciprocal incentive compatible manner. Based on the duality of the problem, we develop an iterative algorithm that converges geometrically to the equilibrium. Our numerical experiments and discrete event simulation demonstrate the convergence to the Nash equilibrium and the security features of GUIDEX against free riders, dishonest insiders and DoS attacks.
  @cite_43: 
  @cite_27: This paper develops a simple model in which a social hierarchy emerges endogenously when agents form a network for complementary interaction ( activity''). Specifically, we assume that agents are ex ante identical and their best response activity, as well as their value function, increases (strictly) concavely in the total activity of their neighbours in the network. There exists a unique and stable positive activity equilibrium on exogenous networks under mild conditions. When we endogenise network formation, equilibria become strongly structured: more active players have more neighbours, i.e. a higher degree, but tend to sponsor fewer links. Additionally, in strict equilibria agents separate themselves into groups characterised by the symmetric activity of their members. The characteristic activity decreases in group size and the network is a complete multipartite graph.
  @cite_20: Enhancing the security and resilience of interdependent infrastructures is crucial. In this paper, we establish a theoretical framework based on Markov decision processes (MDPs) to design optimal resiliency mechanisms for interdependent infrastructures. We use MDPs to capture the dynamics of the failure of constituent components of an infrastructure and their cyber-physical dependencies. Factored MDPs and approximate linear programming are adopted for an exponentially growing dimension of both state and action spaces. Under our approximation scheme, the optimally distributed policy is equivalent to the centralized one. Finally, case studies in a large-scale interdependent system demonstrate the effectiveness of the control strategy to enhance the network resilience to cascading failures.
  @cite_17: The complex interconnections between various critical infrastructure sectors make the system of systems (SoS) vulnerable to failures and highlight the importance of robustness and resilience. To this end, we first establish holistic probabilistic networks to model the interdependencies between infrastructure components. To capture the underlying failure and recovery dynamics, we further propose a Markov decision processes (MDP) model in which the response policy determines a long-term performance. To address the challenge of a large dimensionality, we exploit the sparsity of the network interconnections and solve an approximate linear program by the variable elimination, which leads to a distributed control policy under mild assumptions. Finally, we use a case study of the interdependent power and subway systems to corroborate the results and show that the optimal resilience resource planning and allocation can reduce the failure probability and mitigate the impact of failures caused by natural or artificial disasters.
summary: Games over networks have caught a lot of attention recently especially from the economics perspective @cite_7 @cite_43 @cite_27 . The couplings between players in the network can be either in a strategic exclusive or strategic complement manner. Based on the features of security management in IoT, our problem falls into the latter class. For the engineering applications, the authors in @cite_22 @cite_35 have studied the resource allocation game over interdependent critical infrastructures where both players aim to increase the connectivity of the network. Huang @cite_28 @cite_20 @cite_17 @cite_30 have adopted a stochastic Markov game model to design resilient operating strategies for multilayer networks. Zhu @cite_9 have proposed a game-theoretic framework for collaborative intrusion detection systems through resource management to mitigate network cyber threats. Our work differs from @cite_9 in that we take into account the cognitive factors of human behaviors during decision making.