# Biblio

Advanced Persistent Threat (APT) is a stealthy, continuous and sophisticated method of network attacks, which can cause serious privacy leakage and millions of dollars losses. In this paper, we introduce a new game-theoretic framework of the interaction between a defender who uses limited Security Resources(SRs) to harden network and an attacker who adopts a multi-stage plan to attack the network. The game model is derived from Stackelberg games called a Multi-stage Maze Network Game (M2NG) in which the characteristics of APT are fully considered. The possible plans of the attacker are compactly represented using attack graphs(AGs), but the compact representation of the attacker's strategies presents a computational challenge and reaching the Nash Equilibrium(NE) is NP-hard. We present a method that first translates AGs into Markov Decision Process(MDP) and then achieves the optimal SRs allocation using the policy hill-climbing(PHC) algorithm. Finally, we present an empirical evaluation of the model and analyze the scalability and sensitivity of the algorithm. Simulation results exhibit that our proposed reinforcement learning-based SRs allocation is feasible and efficient.

The emergence of Cyber-Physical Systems (CPSs) is a potential paradigm shift for the usage of Information and Communication Technologies (ICT). From predominantly a facilitator of information and communication services, the role of ICT in the present age has expanded to the management of objects and resources in the physical world. Thus, it is imperative to devise mechanisms to ensure the trustworthiness of data to secure vulnerable devices against security threats. This work presents an analytical framework based on non-cooperative game theory to evaluate the trustworthiness of individual sensor nodes that constitute the CPS. The proposed game-theoretic model captures the factors impacting the trustworthiness of CPS sensor nodes. Further, the model is used to estimate the Nash equilibrium solution of the game, to derive a trust threshold criterion. The trust threshold represents the minimum trust score required to be maintained by individual sensor nodes during CPS operation. Sensor nodes with trust scores below the threshold are potentially malicious and may be removed or isolated to ensure the secure operation of CPS.

This paper presents a novel game theoretic attack-defence decision making framework for cyber-physical system (CPS) security. Game theory is a powerful tool to analyse the interaction between the attacker and the defender in such scenarios. In the formulation of games, participants are usually assumed to be rational. They will always choose the action to pursuit maximum payoff according to the knowledge of the strategic situation they are in. However, in reality the capacity of rationality is often bounded by the level of intelligence, computational resources and the amount of available information. This paper formulates the concept of bounded rationality into the decision making process, in order to optimise the defender's strategy considering that the defender and the attacker have incomplete information of each other and limited computational capacity. Under the proposed framework, the defender can often benefit from deviating from the minimax Nash Equilibrium strategy, the theoretically expected outcome of rational game playing. Numerical results are presented and discussed in order to demonstrate the proposed technique.

This paper presents a control strategy for Cyber-Physical System defense developed in the framework of the European Project ATENA, that concerns Critical Infrastructure (CI) protection. The aim of the controller is to find the optimal security configuration, in terms of countermeasures to implement, in order to address the system vulnerabilities. The attack/defense problem is modeled as a multi-agent general sum game, where the aim of the defender is to prevent the most damage possible by finding an optimal trade-off between prevention actions and their costs. The problem is solved utilizing Reinforcement Learning and simulation results provide a proof of the proposed concept, showing how the defender of the protected CI is able to minimize the damage caused by his her opponents by finding the Nash equilibrium of the game in the zero-sum variant, and, in a more general scenario, by driving the attacker in the position where the damage she/he can cause to the infrastructure is lower than the cost it has to sustain to enforce her/his attack strategy.

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 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 the network connectivity in the presence of adversaries is a critical task for the infrastructure network operators. In this paper, we establish a three-player three-stage game-theoretic framework including two network operators and one attacker to capture the secure design of multi- layer 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 Internet of Battlefield Things (IoBT) to corroborate the obtained results.

With a large number of sensors and control units in networked systems, distributed support vector machines (DSVMs) play a fundamental role in scalable and efficient multi-sensor classification and prediction tasks. However, DSVMs are vulnerable to adversaries who can modify and generate data to deceive the system to misclassification and misprediction. This work aims to design defense strategies for DSVM learner against a potential adversary. We use a game-theoretic framework to capture the conflicting interests between the DSVM learner and the attacker. The Nash equilibrium of the game allows predicting the outcome of learning algorithms in adversarial environments, and enhancing the resilience of the machine learning through dynamic distributed algorithms. We develop a secure and resilient DSVM algorithm with rejection method, and show its resiliency against adversary with numerical experiments.

Large-scale infrastructures are critical to economic and social development, and hence their continued performance and security are of high national importance. Such an infrastructure often is a system of systems, and its functionality critically depends on the inherent robustness of its constituent systems and its defense strategy for countering attacks. Additionally, interdependencies between the systems play another critical role in determining the infrastructure robustness specified by its survival probability. In this paper, we develop game-theoretic models between a defender and an attacker for a generic system of systems using inherent parameters and conditional survival probabilities that characterize the interdependencies. We derive Nash Equilibrium conditions for the cases of interdependent and independent systems of systems under sum-form utility functions. We derive expressions for the infrastructure survival probability that capture its dependence on cost and system parameters, and also on dependencies that are specified by conditional probabilities. We apply the results to cyber-physical systems which show the effects on system survival probability due to defense and attack intensities, inherent robustness, unit cost, target valuation, and interdependencies.

We study the strategic considerations of miners participating in the bitcoin's protocol. We formulate and study the stochastic game that underlies these strategic considerations. The miners collectively build a tree of blocks, and they are paid when they create a node (mine a block) which will end up in the path of the tree that is adopted by all. Since the miners can hide newly mined nodes, they play a game with incomplete information. Here we consider two simplified forms of this game in which the miners have complete information. In the simplest game the miners release every mined block immediately, but are strategic on which blocks to mine. In the second more complicated game, when a block is mined it is announced immediately, but it may not be released so that other miners cannot continue mining from it. A miner not only decides which blocks to mine, but also when to release blocks to other miners. In both games, we show that when the computational power of each miner is relatively small, their best response matches the expected behavior of the bitcoin designer. However, when the computational power of a miner is large, he deviates from the expected behavior, and other Nash equilibria arise.

Game theory serves as a powerful tool for distributed optimization in multiagent systems in different applications. In this paper we consider multiagent systems that can be modeled as a potential game whose potential function coincides with a global objective function to be maximized. This approach renders the agents the strategic decision makers and the corresponding optimization problem the problem of learning an optimal equilibruim point in the designed game. In distinction from the existing works on the topic of payoff-based learning, we deal here with the systems where agents have neither memory nor ability for communication, and they base their decision only on the currently played action and the experienced payoff. Because of these restrictions, we use the methods of reinforcement learning, stochastic approximation, and learning automata extensively reviewed and analyzed in [3], [9]. These methods allow us to set up the agent dynamics that moves the game out of inefficient Nash equilibria and leads it close to an optimal one in both cases of discrete and continuous action sets.

The amount of personal information contributed by individuals to digital repositories such as social network sites has grown substantially. The existence of this data offers unprecedented opportunities for data analytics research in various domains of societal importance including medicine and public policy. The results of these analyses can be considered a public good which benefits data contributors as well as individuals who are not making their data available. At the same time, the release of personal information carries perceived and actual privacy risks to the contributors. Our research addresses this problem area. In our work, we study a game-theoretic model in which individuals take control over participation in data analytics projects in two ways: 1) individuals can contribute data at a self-chosen level of precision, and 2) individuals can decide whether they want to contribute at all (or not). From the analyst's perspective, we investigate to which degree the research analyst has flexibility to set requirements for data precision, so that individuals are still willing to contribute to the project, and the quality of the estimation improves. We study this tradeoffs scenario for populations of homogeneous and heterogeneous individuals, and determine Nash equilibrium that reflect the optimal level of participation and precision of contributions. We further prove that the analyst can substantially increase the accuracy of the analysis by imposing a lower bound on the precision of the data that users can reveal.