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Sharma, Prince, Shukla, Shailendra, Vasudeva, Amol.  2020.  Trust-based Incentive for Mobile Offloaders in Opportunistic Networks. 2020 International Conference on Smart Electronics and Communication (ICOSEC). :872—877.
Mobile data offloading using opportunistic network has recently gained its significance to increase mobile data needs. Such offloaders need to be properly incentivized to encourage more and more users to act as helpers in such networks. The extent of help offered by mobile data offloading alternatives using appropriate incentive mechanisms is significant in such scenarios. The limitation of existing incentive mechanisms is that they are partial in implementation while most of them use third party intervention based derivation. However, none of the papers considers trust as an essential factor for incentive distribution. Although few works contribute to the trust analysis, but the implementation is limited to offloading determination only while the incentive is independent of trust. We try to investigate if trust could be related to the Nash equilibrium based incentive evaluation. Our analysis results show that trust-based incentive distribution encourages more than 50% offloaders to act positively and contribute successfully towards efficient mobile data offloading. We compare the performance of our algorithm with literature based salary-bonus scheme implementation and get optimum incentive beyond 20% dependence over trust-based output.
Hatti, Daneshwari I., Sutagundar, Ashok V..  2020.  Trust Induced Resource Provisioning (TIRP) Mechanism in IoT. 2020 4th International Conference on Computer, Communication and Signal Processing (ICCCSP). :1–5.
Due to increased number of devices with limited resources in Internet of Things (IoT) has to serve time sensitive applications including health monitoring, emergency response, industrial applications and smart city etc. This has incurred the problem of solving the provisioning of limited computational resources of the devices to fulfill the requirement with reduced latency. With rapid increase of devices and heterogeneity characteristic the resource provisioning is crucial and leads to conflict of trusting among the devices requests. Trust is essential component in any context for communicating or sharing the resources in the network. The proposed work comprises of trusting and provisioning based on deadline. Trust quantity is measured with concept of game theory and optimal strategy decision among provider and customer and provision resources within deadline to execute the tasks is done by finding Nash equilibrium. Nash equilibrium (NE) is estimated by constructing the payoff matrix with choice of two player strategies. NE is obtained in the proposed work for the Trust- Respond (TR) strategy. The latency aware approach for avoiding resource contention due to limited resources of the edge devices, fog computing leverages the cloud services in a distributed way at the edge of the devices. The communication is established between edge devices-fog-cloud and provision of resources is performed based on scalar chain and Gang Plank theory of management to reduce latency and increase trust quantity. To test the performance of proposed work performance parameter considered are latency and computational time.
Solovey, R., Lavrova, D..  2020.  Game-Theoretic Approach to Self-Regulation of Dynamic Network Infrastructure to Protect Against Cyber Attacks. 2020 International Scientific and Technical Conference Modern Computer Network Technologies (MoNeTeC). :1–7.
The paper presents the concept of applying a game theory approach in infrastructure of wireless dynamic networks to counter computer attacks. The applying of this approach will allow to create mechanism for adaptive reconfiguration of network structure in the context of implementation various types of computer attacks and to provide continuous operation of network even in conditions of destructive information impacts.
Khoury, J., Nassar, M..  2020.  A Hybrid Game Theory and Reinforcement Learning Approach for Cyber-Physical Systems Security. NOMS 2020 - 2020 IEEE/IFIP Network Operations and Management Symposium. :1—9.
Cyber-Physical Systems (CPS) are monitored and controlled by Supervisory Control and Data Acquisition (SCADA) systems that use advanced computing, sensors, control systems, and communication networks. At first, CPS and SCADA systems were protected and secured by isolation. However, with recent industrial technology advances, the increased connectivity of CPSs and SCADA systems to enterprise networks has uncovered them to new cybersecurity threats and made them a primary target for cyber-attacks with the potential of causing catastrophic economic, social, and environmental damage. Recent research focuses on new methodologies for risk modeling and assessment using game theory and reinforcement learning. This paperwork proposes to frame CPS security on two different levels, strategic and battlefield, by meeting ideas from game theory and Multi-Agent Reinforcement Learning (MARL). The strategic level is modeled as imperfect information, extensive form game. Here, the human administrator and the malware author decide on the strategies of defense and attack, respectively. At the battlefield level, strategies are implemented by machine learning agents that derive optimal policies for run-time decisions. The outcomes of these policies manifest as the utility at a higher level, where we aim to reach a Nash Equilibrium (NE) in favor of the defender. We simulate the scenario of a virus spreading in the context of a CPS network. We present experiments using the MiniCPS simulator and the OpenAI Gym toolkit and discuss the results.
Zhang, H., Liu, H., Liang, J., Li, T., Geng, L., Liu, Y., Chen, S..  2020.  Defense Against Advanced Persistent Threats: Optimal Network Security Hardening Using Multi-stage Maze Network Game. 2020 IEEE Symposium on Computers and Communications (ISCC). :1—6.

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.

Jithish, J., Sankaran, S., Achuthan, K..  2020.  Towards Ensuring Trustworthiness in Cyber-Physical Systems: A Game-Theoretic Approach. 2020 International Conference on COMmunication Systems NETworkS (COMSNETS). :626–629.

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.

Razin, Yosef, Feigh, Karen.  2019.  Toward Interactional Trust for Humans and Automation: Extending Interdependence. 2019 IEEE SmartWorld, Ubiquitous Intelligence Computing, Advanced Trusted Computing, Scalable Computing Communications, Cloud Big Data Computing, Internet of People and Smart City Innovation (SmartWorld/SCALCOM/UIC/ATC/CBDCom/IOP/SCI). :1348–1355.
Trust in human-automation interaction is increasingly imperative as AI and robots become ubiquitous at home, school, and work. Interdependence theory allows for the identification of one-on-one interactions that require trust by analyzing the structure of the potential outcomes. This paper synthesizes multiple, formerly disparate research approaches by extending Interdependence theory to create a unified framework for outcome-based trust in human-automation interaction. This framework quantitatively contextualizes validated empirical results from social psychology on relationship formation, stability, and betrayal. It also contributes insights into trust-related concepts, such as power and commitment, which help further our understanding of trustworthy system design. This new integrated interactional approach reveals how trust and trustworthiness machines from merely reliable tools to trusted teammates working hand-in-actuator toward an automated future.
Elliott, Sean.  2019.  Nash Equilibrium of Multiple, Non-Uniform Bitcoin Block Withholding Attackers. 2019 2nd International Conference on Data Intelligence and Security (ICDIS). :144—151.
This research analyzes a seemingly malicious behavior known as a block withholding (BWH) attack between pools of cryptocurrency miners in Bitcoin-like systems featuring blockchain distributed databases. This work updates and builds on a seminal paper, The Miner's Dilemma, which studied a simplified scenario and showed that a BWH attack can be rational behavior that is profitable for the attacker. The new research presented here provides an in-depth profit analysis of a more complex and realistic BWH attack scenario, which includes mutual attacks between multiple, non-uniform Bitcoin mining pools. As a result of mathematical analysis and MATLAB modeling, this paper illustrates the Nash equilibrium conditions of a system of independent mining pools with varied mining rates and computes the equilibrium rates of mutual BWH attack. The analysis method quantifies the additional profit the largest pools extract from the system at the expense of the smaller pools. The results indicate that while the presence of BWH is a net negative for smaller pools, they must participate in BWH to maximize their remaining profits, and the results quantify the attack rates the smaller pools must maintain. Also, the smallest pools maximize profit by not attacking at all-that is, retaliation is not a rational move for them.
Yang, Shiman, Shi, Yijie, Guo, Fenzhuo.  2019.  Risk Assessment of Industrial Internet System By Using Game-Attack Graphs. 2019 IEEE 5th International Conference on Computer and Communications (ICCC). :1660–1663.
In this paper, we propose a game-attack graph-based risk assessment model for industrial Internet system. Firstly, use non-destructive asset profiling to scan components and devices included in the system and their open services and communication protocols. Further compare the CNVD and CVE to find the vulnerability through the search engine keyword segment matching method, and generate an asset threat list. Secondly, build the attack rule base based on the network information, and model the system using the attribute attack graph. Thirdly, combine the game theory with the idea of the established model. Finally, optimize and quantify the analysis to get the best attack path and the best defense strategy.
Sahabandu, Dinuka, Moothedath, Shana, Bushnell, Linda, Poovendran, Radha, Aller, Joey, Lee, Wenke, Clark, Andrew.  2019.  A Game Theoretic Approach for Dynamic Information Flow Tracking with Conditional Branching. 2019 American Control Conference (ACC). :2289–2296.
In this paper, we study system security against Advanced Persistent Threats (APTs). APTs are stealthy and persistent but APTs interact with system and introduce information flows in the system as data-flow and control-flow commands. Dynamic Information Flow Tracking (DIFT) is a promising detection mechanism against APTs which taints suspicious input sources in the system and performs online security analysis when a tainted information is used in unauthorized manner. Our objective in this paper is to model DIFT that handle data-flow and conditional branches in the program that arise from control-flow commands. We use game theoretic framework and provide the first analytical model of DIFT with data-flow and conditional-branch tracking. Our game model which is an undiscounted infinite-horizon stochastic game captures the interaction between APTs and DIFT and the notion of conditional branching. We prove that the best response of the APT is a maximal reachability probability problem and provide a polynomial-time algorithm to find the best response by solving a linear optimization problem. We formulate the best response of the defense as a linear optimization problem and show that an optimal solution to the linear program returns a deterministic optimal policy for the defense. Since finding Nash equilibrium for infinite-horizon undiscounted stochastic games is computationally difficult, we present a nonlinear programming based polynomial-time algorithm to find an E-Nash equilibrium. Finally, we perform experimental analysis of our algorithm on real-world data for NetRecon attack augmented with conditional branching.
He, Fei, Chandrasekar, Santhosh, Rao, Nageswara S. V., Ma, Chris Y. T..  2019.  Effects of Interdependencies on Game-Theoretic Defense of Cyber-Physical Infrastructures. 2019 22th International Conference on Information Fusion (FUSION). :1–8.
Resilience and security of infrastructures depend not only on their constituent systems but also on interdependencies among them. This paper studies how these interdependencies in infrastructures affect the defense effort needed to counter external attacks, by formulating a simultaneous game between a service provider (i.e., defender) and an attacker. Effects of interdependencies in three basic topological structures, namely, bus, star and ring, are considered and compared in terms of the game-theoretic defense strategy. Results show that in a star topology, the attacker's and defender's pure strategies at Nash Equilibrium (NE) are sensitive to interdependency levels whereas in a bus structure, the interdependencies show little impact on both defender's and attacker's pure strategies. The sensitivity estimates of defense and attack strategies at NE with respect to target valuation and unit cost are also presented. The results provide insights into infrastructure design and resource allocation for reinforcement of constituent systems.
Pirani, Mohammad, Nekouei, Ehsan, Sandberg, Henrik, Johansson, Karl Henrik.  2019.  A Game-theoretic Framework for Security-aware Sensor Placement Problem in Networked Control Systems. 2019 American Control Conference (ACC). :114–119.
This paper studies the sensor placement problem in a networked control system for improving its security against cyber-physical attacks. The problem is formulated as a zero-sum game between an attacker and a detector. The attacker's decision is to select f nodes of the network to attack whereas the detector's decision is to place f sensors to detect the presence of the attack signals. In our formulation, the attacker minimizes its visibility, defined as the system L2 gain from the attack signals to the deployed sensors' outputs, and the detector maximizes the visibility of the attack signals. The equilibrium strategy of the game determines the optimal locations of the sensors. The existence of Nash equilibrium for the attacker-detector game is studied when the underlying connectivity graph is a directed or an undirected tree. When the game does not admit a Nash equilibrium, it is shown that the Stackelberg equilibrium of the game, with the detector as the game leader, can be computed efficiently. Our results show that, under the optimal sensor placement strategy, an undirected topology provides a higher security level for a networked control system compared with its corresponding directed topology.
Zhu, Ziming.  2019.  Game theoretic framework for cyber-physical system security incorporating bounded rationality. 2019 International Conference on Wireless and Mobile Computing, Networking and Communications (WiMob). :360–365.

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.

Shirasaki, Yusuke, Takyu, Osamu, Fujii, Takeo, Ohtsuki, Tomoaki, Sasamori, Fumihito, Handa, Shiro.  2018.  Consideration of security for PLNC with untrusted relay in game theoretic perspective. 2018 IEEE Radio and Wireless Symposium (RWS). :109–112.
A physical layer network coding (PLNC) is a highly efficient scheme for exchanging information between two nodes. Since the relay receives the interfered signal between two signals sent by two nodes, it hardly decodes any information from received signal. Therefore, the secure wireless communication link to the untrusted relay is constructed. The two nodes optimize the transmit power control for maximizing the secure capacity but these depend on the channel state information informed by the relay station. Therefore, the untrusted relay disguises the informed CSI for exploiting the information from two nodes. This paper constructs the game of two optimizations between the legitimate two nodes and the untrusted relay for clarifying the security of PLNC with untrusted relay.
Chen, Jing, Du, Ruiying.  2009.  Fault Tolerance and Security in Forwarding Packets Using Game Theory. 2009 International Conference on Multimedia Information Networking and Security. 2:534–537.
In self-organized wireless network, such as ad hoc network, sensor network or mesh network, nodes are independent individuals which have different benefit; Therefore, selfish nodes refuse to forward packets for other nodes in order to save energy which causes the network fault. At the same time, some nodes may be malicious, whose aim is to damage the network. In this paper, we analyze the cooperation stimulation and security in self-organized wireless networks under a game theoretic framework. We first analyze a four node wireless network in which nodes share the channel by relaying for others during its idle periods in order to help the other nodes, each node has to use a part of its available channel capacity. And then, the fault tolerance and security problem is modeled as a non-cooperative game in which each player maximizes its own utility function. The goal of the game is to maximize the utility function in the giving condition in order to get better network efficiency. At last, for characterizing the efficiency of Nash equilibria, we analyze the so called price of anarchy, as the ratio between the objective function at the worst Nash equilibrium and the optimal objective function. Our results show that the players can get the biggest payoff if they obey cooperation strategy.
Rani, Rinki, Kumar, Sushil, Dohare, Upasana.  2019.  Trust Evaluation for Light Weight Security in Sensor Enabled Internet of Things: Game Theory Oriented Approach. IEEE Internet of Things Journal. 6:8421–8432.
In sensor-enabled Internet of Things (IoT), nodes are deployed in an open and remote environment, therefore, are vulnerable to a variety of attacks. Recently, trust-based schemes have played a pivotal role in addressing nodes' misbehavior attacks in IoT. However, the existing trust-based schemes apply network wide dissemination of the control packets that consume excessive energy in the quest of trust evaluation, which ultimately weakens the network lifetime. In this context, this paper presents an energy efficient trust evaluation (EETE) scheme that makes use of hierarchical trust evaluation model to alleviate the malicious effects of illegitimate sensor nodes and restricts network wide dissemination of trust requests to reduce the energy consumption in clustered-sensor enabled IoT. The proposed EETE scheme incorporates three dilemma game models to reduce additional needless transmissions while balancing the trust throughout the network. Specially: 1) a cluster formation game that promotes the nodes to be cluster head (CH) or cluster member to avoid the extraneous cluster; 2) an optimal cluster formation dilemma game to affirm the minimum number of trust recommendations for maintaining the balance of the trust in a cluster; and 3) an activity-based trust dilemma game to compute the Nash equilibrium that represents the best strategy for a CH to launch its anomaly detection technique which helps in mitigation of malicious activity. Simulation results show that the proposed EETE scheme outperforms the current trust evaluation schemes in terms of detection rate, energy efficiency and trust evaluation time for clustered-sensor enabled IoT.
Panfili, M., Giuseppi, A., Fiaschetti, A., Al-Jibreen, H. B., Pietrabissa, A., Priscoli, F. Delli.  2018.  A Game-Theoretical Approach to Cyber-Security of Critical Infrastructures Based on Multi-Agent Reinforcement Learning. 2018 26th Mediterranean Conference on Control and Automation (MED). :460-465.

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.

Guo, Y., Gong, Y., Njilla, L. L., Kamhoua, C. A..  2018.  A Stochastic Game Approach to Cyber-Physical Security with Applications to Smart Grid. IEEE INFOCOM 2018 - IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS). :33-38.
This paper proposes a game-theoretic approach to analyze the interactions between an attacker and a defender in a cyber-physical system (CPS) and develops effective defense strategies. In a CPS, the attacker launches cyber attacks on a number of nodes in the cyber layer, trying to maximize the potential damage to the underlying physical system while the system operator seeks to defend several nodes in the cyber layer to minimize the physical damage. Given that CPS attacking and defending is often a continual process, a zero-sum Markov game is proposed in this paper to model these interactions subject to underlying uncertainties of real-world events and actions. A novel model is also proposed in this paper to characterize the interdependence between the cyber layer and the physical layer in a CPS and quantify the impact of the cyber attack on the physical damage in the proposed game. To find the Nash equilibrium of the Markov game, we design an efficient algorithm based on value iteration. The proposed general approach is then applied to study the wide-area monitoring and protection issue in smart grid. Extensive simulations are conducted based on real-world data, and results show the effectiveness of the defending strategies derived from the proposed approach.
Chen, J., Touati, C., Zhu, Q..  2017.  Heterogeneous Multi-Layer Adversarial Network Design for the IoT-Enabled Infrastructures. GLOBECOM 2017 - 2017 IEEE Global Communications Conference. :1–6.

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.

Zhang, R., Zhu, Q..  2017.  A game-theoretic defense against data poisoning attacks in distributed support vector machines. 2017 IEEE 56th Annual Conference on Decision and Control (CDC). :4582–4587.

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.

Pass, Rafael, Shi, Elaine.  2017.  FruitChains: A Fair Blockchain. Proceedings of the ACM Symposium on Principles of Distributed Computing. :315–324.
Nakamoto's famous blockchain protocol enables achieving consensus in a so-called permissionless setting—anyone can join (or leave) the protocol execution, and the protocol instructions do not depend on the identities of the players. His ingenious protocol prevents "sybil attacks" (where an adversary spawns any number of new players) by relying on computational puzzles (a.k.a. "moderately hard functions") introduced by Dwork and Naor (Crypto'92). Recent work by Garay et al (EuroCrypt'15) and Pass et al (manuscript, 2016) demonstrate that this protocol provably achieves consistency and liveness assuming a) honest players control a majority of the computational power in the network, b) the puzzle-hardness is appropriately set as a function of the maximum network delay and the total computational power of the network, and c) the computational puzzle is modeled as a random oracle. Assuming honest participation, however, is a strong assumption, especially in a setting where honest players are expected to perform a lot of work (to solve the computational puzzles). In Nakamoto's Bitcoin application of the blockchain protocol, players are incentivized to solve these puzzles by receiving rewards for every "block" (of transactions) they contribute to the blockchain. An elegant work by Eyal and Sirer (FinancialCrypt'14), strengthening and formalizing an earlier attack discussed on the Bitcoin forum, demonstrates that a coalition controlling even a minority fraction of the computational power in the network can gain (close to) 2 times its "fair share" of the rewards (and transaction fees) by deviating from the protocol instructions. In contrast, in a fair protocol, one would expect that players controlling a φ fraction of the computational resources to reap a φ fraction of the rewards. We present a new blockchain protocol—the FruitChain protocol—which satisfies the same consistency and liveness properties as Nakamoto's protocol (assuming an honest majority of the computing power), and additionally is δ-approximately fair: with overwhelming probability, any honest set of players controlling a φ fraction of computational power is guaranteed to get at least a fraction (1-δ)φ of the blocks (and thus rewards) in any Ω(κ/δ) length segment of the chain (where κ is the security parameter). Consequently, if this blockchain protocol is used as the ledger underlying a cryptocurrency system, where rewards and transaction fees are evenly distributed among the miners of blocks in a length κ segment of the chain, no coalition controlling less than a majority of the computing power can gain more than a factor (1+3δ) by deviating from the protocol (i.e., honest participation is an n/2-coalition-safe 3δ-Nash equilibrium). Finally, the FruitChain protocol enables decreasing the variance of mining rewards and as such significantly lessens (or even obliterates) the need for mining pools.
He, F., Rao, N. S. V., Ma, C. Y. T..  2017.  Game-Theoretic Analysis of System of Systems with Inherent Robustness Parameters. 2017 20th International Conference on Information Fusion (Fusion). :1–9.

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.

Kiayias, Aggelos, Koutsoupias, Elias, Kyropoulou, Maria, Tselekounis, Yiannis.  2016.  Blockchain Mining Games. Proceedings of the 2016 ACM Conference on Economics and Computation. :365–382.

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.

Tatarenko, T..  2015.  1-recall reinforcement learning leading to an optimal equilibrium in potential games with discrete and continuous actions. 2015 54th IEEE Conference on Decision and Control (CDC). :6749–6754.

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.

Chessa, M., Grossklags, J., Loiseau, P..  2015.  A Game-Theoretic Study on Non-monetary Incentives in Data Analytics Projects with Privacy Implications. 2015 IEEE 28th Computer Security Foundations Symposium. :90–104.

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.