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Adversarial optimal transport has been proven useful as a mathematical formulation to model resource allocation problems to maximize the efficiency of transportation with an adversary, who modifies the data. It is often the case, however, that only the adversary knows which nodes are malicious and which are not. In this paper we formulate the problem of seeking adversarial optimal transport into Bayesian games. We construct the concept of Bayesian equilibrium and design a distributed algorithm that achieve those equilibria, making our model applicable to large-scale networks. Keywords: game theory, crime control, Markov games

The wide adoption of Internet of Things (IoT)-enabled energy devices improves the quality of life, but simultaneously, it enlarges the attack surface of the power grid system. The adversary can gain illegitimate control of a large number of these devices and use them as a means to compromise the physical grid operation, a mechanism known as the IoT botnet attack. This paper aims to improve the resiliency of cyber-physical power grids to such attacks. Specifically, we use an epidemic model to understand the dynamic botnet formation, which facilitates the assessment of the cyber layer vulnerability of the grid. The attacker aims to exploit this vulnerability to enable a successful physical compromise, while the system operator's goal is to ensure a normal operation of the grid by mitigating cyber risks. We develop a cross-layer game-theoretic framework for strategic decision-making to enhance cyber-physical grid resiliency. The cyber-layer game guides the system operator on how to defend against the botnet attacker as the first layer of defense, while the dynamic game strategy at the physical layer further counteracts the adversarial behavior in real time for improved physical resilience. A number of case studies on the IEEE-39 bus system are used to corroborate the devised approach.

In this work, we study policy poisoning through state manipulation, also known as sensor spoofing, and focus specifically on the case of an agent forming a control policy through batch learning in a linear-quadratic (LQ) system. In this scenario, an attacker aims to trick the learner into implementing a targeted malicious policy by manipulating the batch data before the agent begins its learning process. An attack model is crafted to carry out the poisoning strategically, with the goal of modifying the batch data as little as possible to avoid detection by the learner. We establish an optimization framework to guide the design of such policy poisoning attacks. The presence of bi-linear constraints in the optimization problem requires the design of a computationally efficient algorithm to obtain a solution. Therefore, we develop an iterative scheme based on the Alternating Direction Method of Multipliers (ADMM) which is able to return solutions that are approximately optimal. Several case studies are used to demonstrate the effectiveness of the algorithm in carrying out the sensor-based attack on the batch-learning agent in LQ control systems., Comment: First appearing in Systems, Optimization and Control at CISS 2023

The massive deployment of Internet of Things (IoT) devices, including sensors and actuators, is ushering in smart and connected communities of the future. The massive deployment of Internet of Things (IoT) devices, including sensors and actuators, is ushering in smart and connected communities of the future. The availability of real-time and high-quality sensor data is crucial for various IoT applications, particularly in healthcare, energy, transportation, etc. However, data collection may have to be outsourced to external service providers (SPs) due to cost considerations or lack of specialized equipment. Hence, the data market plays a critical role in such scenarios where SPs have different quality levels of available data, and IoT users have different application-specific data needs. The pairing between data available to the SP and users in the data market requires an effective mechanism design that considers the SPs' profitability and the quality-of-service (QoS) needs of the users. We develop a generic framework to analyze and enable such interactions efficiently, leveraging tools from contract theory and mechanism design theory. It can enable and empower emerging data sharing paradigms such as Sensing-as-a-Service (SaaS). The contract design creates a pricing structure for on-demand sensing data for IoT users. By considering a continuum of user types, we capture a diverse range of application requirements and propose optimal pricing and allocation rules that ensure QoS provisioning and maximum profitability for the SP. Furthermore, we provide analytical solutions for fixed distributions of user types to analyze the developed approach. For comparison, we consider the benchmark case assuming complete information of the user types and obtain optimal contract solutions. Finally, a case study is presented to demonstrate the efficacy of the proposed contract design framework., Comment: This paper has been accepted for publication in the IEEE Internet of Things Journal

Optimal transport (OT) is a framework that can guide the design of efficient resource allocation strategies in a network of multiple sources and targets. To ease the computational complexity of large-scale transport design, we first develop a distributed algorithm based on the alternating direction method of multipliers (ADMM). However, such a distributed algorithm is vulnerable to sensitive information leakage when an attacker intercepts the transport decisions communicated between nodes during the distributed ADMM updates. To this end, we propose a privacy-preserving distributed mechanism based on output variable perturbation by adding appropriate randomness to each node's decision before it is shared with other corresponding nodes at each update instance. We show that the developed scheme is differentially private, which prevents the adversary from inferring the node's confidential information even knowing the transport decisions. Finally, we corroborate the effectiveness of the devised algorithm through case studies., Comment: 6 pages, 4 images, 1 algorithm, IEEE GLOBECOMM 2022

The emerging Internet of Things (IoT) applications that leverage ubiquitous connectivity and big data are facilitating the realization of smart everything initiatives. IoT-enabled infrastructures have naturally a multi-layer system architecture with an overlaid or underlaid device network and its coexisting infrastructure network. The connectivity between different components in these two heterogeneous interdependent networks plays an important role in delivering real-time information and ensuring a high-level situational awareness. However, IoT-enabled infrastructures face cyber threats due to the wireless nature of communications. Therefore, maintaining network connectivity in the presence of adversaries is a critical task for infrastructure network operators. In this paper, we establish a three-player three-stage dynamic game-theoretic framework including two network operators and one attacker to capture the secure design of multi-layer interdependent infrastructure networks by allocating limited resources. We use subgame perfect Nash equilibrium (SPE) to characterize the strategies of players with sequential moves. In addition, we assess the efficiency of the equilibrium network by comparing with its team optimal solution counterparts in which two network operators can coordinate. We further design a scalable algorithm to guide the construction of the equilibrium IoT-enabled infrastructure networks. Finally, we use case studies on the emerging paradigm of the Internet of Battlefield Things (IoBT) to corroborate the obtained results., Comment: This paper has been accepted for publication in IEEE Transactions on Network Science and Engineering

Optimal transport (OT) is a framework that can be used to guide the optimal allocation of a limited amount of resources. The classical OT paradigm does not consider malicious attacks in its formulation and thus the designed transport plan lacks resiliency to an adversary. To address this concern, we establish an OT framework that explicitly accounts for the adversarial and stealthy manipulation of participating nodes in the network during the transport strategy design. Specifically, we propose a game-theoretic approach to capture the strategic interactions between the transport planner and the deceptive attacker. We analyze the properties of the established two-person zero-sum game thoroughly. We further develop a fully distributed algorithm to compute the optimal resilient transport strategies, and show the convergence of the algorithm to a saddle-point equilibrium. Finally, we demonstrate the effectiveness of the designed algorithm using case studies., Comment: Long version of paper of the same title in Control System Letters (L-CSS)

Renewable energy-based microgrids play a critical role in future smart grids. Due to the uncertainties of renewable generations, the microgrids face potential risk of load shedding during operation. To address this problem, we propose a contract-based approach to enhance the resilience of microgrids. Specifically, in the framework, the microgrids who may not be self-efficient to meet their local demands can purchase the needed power from their connected microgrids by signing a contract that specifies the power price in advance. We leverage a principal-agent model to capture the energy trading relationships between the microgrids through a resilience as a service (RaaS) paradigm. By focusing on the incentive compatible and individual rational constraints of the service requester, the service provider designs the optimal contracts for the transactive resilience that yields the largest payoff despite the incomplete information. We characterize analytical solutions of the optimal contracts for several scenarios where the service requester has various options on its hidden actions. Numerical simulations are used to illustrate and corroborate the obtained results.

In this paper, we consider a linear-quadratic-Gaussian defending assets differential game (DADG) where the attacker and the defender do not know each other's state information while they know the trajectory of a moving asset. Both players can choose to observe the other player's state information by paying a cost. The defender and the attacker have to craft both control strategies and observation strategies. We obtain a closed-form feedback solution that characterizes the Nash control strategies. We show that the trajectory of the asset does not affect both players' observation choices. Moreover, we show that the observation choices of the defender and the attacker can be decoupled and the Nash observation strategies can be found by solving two independent optimization problems. A set of necessary conditions is developed to characterize the optimal observation instances. Based on the necessary conditions, an effective algorithm is proposed to numerically compute the optimal observation instances. A case study is presented to demonstrate the effectiveness of the optimal observation instances.

Optimal curing strategy of suppressing competing epidemics spreading over complex networks is a critical issue. In this paper, we first establish a framework to capture the coupling between two epidemics, and then analyze the system's equilibrium states by categorizing them into three classes, and deriving their stability conditions. The designed curing strategy globally optimizes the trade-off between the curing cost and the severity of epidemics in the network. In addition, we provide structural results on the predictability of epidemic spreading by showing the existence and uniqueness of the solution. We also demonstrate the robustness of curing strategy by showing the continuity of epidemic severity with respect to the applied curing effort. A gradient descent algorithm based on a fixed-point iterative scheme is proposed to find the optimal curing strategy. Depending on the system parameters, the curing strategy can lead to switching between equilibria of the epidemic network as the control cost varies. Finally, we use case studies to corroborate and illustrate the obtained theoretical results., Comment: 15 pages

Network games have been instrumental in understanding strategic behaviors over networks for applications such as critical infrastructure networks, social networks, and cyber-physical systems. One critical challenge of network games is that the behaviors of the players are constrained by the underlying physical laws or safety rules, and the players may not have complete knowledge of network-wide constraints. To this end, this paper proposes a game framework to study constrained games on networks, where the players are locally aware of the constraints. We use \textit{awareness levels} to capture the scope of the network constraints that players are aware of. We first define and show the existence of generalized Nash equilibria (GNE) of the game, and point out that higher awareness levels of the players would lead to a larger set of GNE solutions. We use necessary and sufficient conditions to characterize the GNE, and propose the concept of the dual game to show that one can convert a locally-aware constrained game into a two-layer unconstrained game problem. We use linear quadratic games as case studies to corroborate the analytical results, and in particular, show the duality between Bertrand games and Cournot games.%, where each layer comprises an unconstrained game.

In this paper, we study the stabilization of two interdependent Markov jump linear systems (MJLSs) with partial information, where the interdependency arises as the transition of the mode of one system depends on the states of the other system. First, we formulate a framework for the two interdependent MJLSs to capture the interactions between various entities in the system, where the modes of the system cannot be observed directly. Instead, a signal which contains information of the modes can be obtained. Then, depending on the scope of the available system state information (global or local), we design centralized and distributed controllers, respectively, that can stochastically stabilize the overall interdependent MJLS. In addition, the sufficient stabilization conditions for the system under both types of information structure are derived. Finally, we provide a numerical example to illustrate the effectiveness of the designed controllers.

Mobile autonomous system (MAS) becomes pervasive especially in the vehicular and robotic networks. Multiple heterogeneous MAS networks can be integrated together as a multi-layer MAS network to offer holistic services. The network connectivity of multi-layer MAS plays an important role in the information exchange between agents within and across different layers of the network. In this paper, we establish a games-in-games framework to capture the uncoordinated nature of decision makings under adversarial environment at different layers. Specifically, each network operator controls the mobile agents in his own subnetwork and designs a secure strategy to maximize the global network connectivity by considering the behavior of jamming attackers that aim to disconnect the network. The solution concept of meta-equilibrium is proposed to characterize the system-of-systems behavior of the autonomous agents. For online implementation of the control, we design a resilient algorithm that improves the network algebraic connectivity iteratively. We show that the designed algorithm converges to a meta-equilibrium asymptotically. Finally, we use case studies of a two-layer MAS network to corroborate the security and agile resilience of the network controlled by the proposed strategy., Comment: 12 pages. To appear in IEEE Transactions on Control of Network Systems

Modern control systems are featured by their hierarchical structure composing of cyber, physical, and human layers. The intricate dependencies among multiple layers and units of modern control systems require an integrated framework to address cross-layer design issues related to security and resilience challenges. To this end, game theory provides a bottom-up modeling paradigm to capture the strategic interactions among multiple components of the complex system and enables a holistic view to understand and design cyber-physical-human control systems. In this review, we first provide a multi-layer perspective toward increasingly complex and integrated control systems and then introduce several variants of dynamic games for modeling different layers of control systems. We present game-theoretic methods for understanding the fundamental tradeoffs of robustness, security, and resilience and developing a clean-slate cross-layer approach to enhance the system performance in various adversarial environments. This review also includes three quintessential research problems that represent three research directions where dynamic game approaches can bridge between multiple research areas and make significant contributions to the design of modern control systems. The paper is concluded with a discussion on emerging areas of research that crosscut dynamic games and control systems., Comment: 12 pages, 8 figures

The interconnectivity of cyber and physical systems and Internet of things has created ubiquitous concerns of cyber threats for enterprise system managers. It is common that the asset owners and enterprise network operators need to work with cybersecurity professionals to manage the risk by remunerating them for their efforts that are not directly observable. In this paper, we use a principal-agent framework to capture the service relationships between the two parties, i.e., the asset owner (principal) and the cyber risk manager (agent). Specifically, we consider a dynamic systemic risk management problem with asymmetric information where the principal can only observe cyber risk outcomes of the enterprise network rather than directly the efforts that the manager expends on protecting the resources. Under this information pattern, the principal aims to minimize the systemic cyber risks by designing a dynamic contract that specifies the compensation flows and the anticipated efforts of the manager by taking into account his incentives and rational behaviors. We formulate a bi-level mechanism design problem for dynamic contract design within the framework of a class of stochastic differential games. We show that the principal has rational controllability of the systemic risk by designing an incentive compatible estimator of the agent's hidden efforts. We characterize the optimal solution by reformulating the problem as a stochastic optimal control program which can be solved using dynamic programming. We further investigate a benchmark scenario with complete information and identify conditions that yield zero information rent and lead to a new certainty equivalence principle for principal-agent problems. Finally, case studies over networked systems are carried out to illustrate the theoretical results obtained., Comment: 32 pages

Infrastructure networks are vulnerable to both cyber and physical attacks. Building a secure and resilient networked system is essential for providing reliable and dependable services. To this end, we establish a two-player three-stage game framework to capture the dynamics in the infrastructure protection and recovery phases. Specifically, the goal of the infrastructure network designer is to keep the network connected before and after the attack, while the adversary aims to disconnect the network by compromising a set of links. With costs for creating and removing links, the two players aim to maximize their utilities while minimizing the costs. In this paper, we use the concept of subgame perfect equilibrium (SPE) to characterize the optimal strategies of the network defender and attacker. We derive the SPE explicitly in terms of system parameters. We further investigate the resilience planning of the defender and the strategic timing of attack of the adversary. Finally, we use case studies of UAV-enabled communication networks for disaster recovery to corroborate the obtained analytical results., Comment: 13 pages; To appear in IEEE T-IFS. arXiv admin note: substantial text overlap with arXiv:1707.07054

This paper presents a games-in-games approach to provide design guidelines for mosaic command and control that enables the secure and resilient multi-domain operations. Under the mosaic design, pieces or agents in the network are equipped with flexible interoperability and the capability of self-adaptability, self-healing, and resiliency so that they can reconfigure their responses to achieve the global mission in spite of failures of nodes and links in the adversarial environment. The proposed games-in-games approach provides a system-of-systems science for mosaic distributed design of large-scale systems. Specifically, the framework integrates three layers of design for each agent including strategic layer, tactical layer, and mission layer. Each layer in the established model corresponds to a game of a different scale that enables the integration of threat models and achieve self-mitigation and resilience capabilities. The solution concept of the developed multi-layer multi-scale mosaic design is characterized by Gestalt Nash equilibrium (GNE) which considers the interactions between agents across different layers. The developed approach is applicable to modern battlefield networks which are composed of heterogeneous assets that access highly diverse and dynamic information sources over multiple domains. By leveraging mosaic design principles, we can achieve the desired operational goals of deployed networks in a case study and ensure connectivity among entities for the exchange of information to accomplish the mission., Comment: 10 pages