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.
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.
@cite_30 @cite_35 @cite_22 @cite_7 @cite_28 @cite_9 @cite_43 @cite_27 @cite_20 @cite_17
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Due to the dynamic, distributed, and heterogeneous nature of today's networks, intrusion detection systems (IDSs) have become a necessary addition to the security infrastructure and are widely deployed as a complementary line of defense to classical security approaches. In this paper, we address the intrusion detection problem in heterogeneous networks consisting of nodes with different noncorrelated security assets. In our study, two crucial questions are: What are the expected behaviors of rational attackers? What is the optimal strategy of the defenders (IDSs)? We answer the questions by formulating the network intrusion detection as a noncooperative game and performing an in-depth analysis on the Nash equilibrium and the engineering implications behind. Based on our game theoretical analysis, we derive the expected behaviors of rational attackers, the minimum monitor resource requirement, and the optimal strategy of the defenders. We then provide guidelines for IDS design and deployment. We also show how our game theoretical framework can be applied to configure the intrusion detection strategies in realistic scenarios via a case study. Finally, we evaluate the proposed game theoretical framework via simulations. The simulation results show both the correctness of the analytical results and the effectiveness of the proposed guidelines. 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. We study the dynamics of network selection in heterogeneous wireless networks (HetNets). Users in such networks selfishly select the best radio access technology (RAT) with the objective of maximizing their own throughputs. We propose two general classes of throughput models that capture the basic properties of random access (e.g., Wi-Fi) and scheduled access (e.g., WiMAX, LTE, 3G) networks. Next, we formulate the problem as a non-cooperative game, and study its convergence, efficiency, and practicality. Our results reveal that: (i) Singleclass RAT selection games converge to Nash equilibria, while an improvement path can be repeated infinitely with a mixture of classes. We next introduce a hysteresis mechanism in RAT selection games, and prove that with appropriate hysteresis policies, convergence can still be guaranteed; (ii) We analyze the Pareto-efficiency of the Nash equilibria of these games. We derive the conditions under which Nash equilibria are Paretooptimal, and we quantify the distance of Nash equilibria with respect to the set of Pareto-dominant points when the conditions are not satisfied; (iii) Finally, with extensive measurement-driven simulations we show that RAT selection games converge to Nash equilibria in a small number of steps, and hence are amenable to practical implementation. We also investigate the impact of noisy throughput measurements, and propose solutions to handle them. In this paper, a novel framework is proposed for optimizing the operation and performance of a large-scale multi-hop millimeter wave (mmW) backhaul within a wireless small cell network having multiple mobile network operators (MNOs). The proposed framework enables the small base stations to jointly decide on forming the multi-hop, mmW links over backhaul infrastructure that belongs to multiple, independent MNOs, while properly allocating resources across those links. In this regard, the problem is addressed using a novel framework based on matching theory composed of two, highly inter-related stages: a multi-hop network formation stage and a resource management stage. One unique feature of this framework is that it jointly accounts for both wireless channel characteristics and economic factors during both network formation and resource management. The multi-hop network formation stage is formulated as a one-to-many matching game, which is solved using a novel algorithm, that builds on the so-called deferred acceptance algorithm and is shown to yield a stable and Pareto optimal multi-hop mmW backhaul network. Then, a one-to-many matching game is formulated to enable proper resource allocation across the formed multi-hop network. This game is then shown to exhibit peer effects and, as such, a novel algorithm is developed to find a stable and optimal resource management solution that can properly cope with these peer effects. Simulation results show that, with manageable complexity, the proposed framework yields substantial gains, in terms of the average sum rate, reaching up to 27 and 54 , respectively, compared with a non-cooperative scheme in which inter-operator sharing is not allowed and a random allocation approach. The results also show that our framework improves the statistics of the backhaul sum rate and provides insights on how to manage pricing and the cost of the cooperative mmW backhaul network for the MNOs. In this paper, the cross-layer design problem of joint multiuser detection and power control is studied, using a game-theoretic approach that focuses on energy efficiency. The uplink of a direct-sequence code-division multiple-access data network is considered, and a noncooperative game is proposed in which users in the network are allowed to choose their uplink receivers as well as their transmit powers to maximize their own utilities. The utility function measures the number of reliable bits transmitted by the user per joule of energy consumed. Focusing on linear receivers, the Nash equilibrium for the proposed game is derived. It is shown that the equilibrium is one where the powers are signal-to-interference-plus-noise ratio-balanced with the minimum mean-square error (MMSE) detector as the receiver. In addition, this framework is used to study power-control games for the matched filter, the decorrelator, and the MMSE detector; and the receivers' performance is compared in terms of the utilities achieved at equilibrium (in bits joule). The optimal cooperative solution is also discussed and compared with the noncooperative approach. Extensions of the results to the case of multiple receive antennas are also presented. In addition, an admission-control scheme based on maximizing the total utility in the network is proposed. We consider in this chapter a class of two-player nonzero-sum stochastic games with incomplete information, which is inspired by recent applications of game theory in network security. We develop fully distributed reinforcement learning algorithms, which require for each player a minimal amount of information regarding the other player. At each time, each player can be in an active mode or in a sleep mode. If †This material is based upon work supported in part by the U.S. Air Force Office of Scientific Research (AFOSR) under grant number AFOSR MURI FA9550-09-1-0249. D R A F T October 2, 2011, 1:59am D R A F T 2 HYBRID LEARNING IN STOCHASTIC GAMES AND ITS APPLICATION IN NETWORK SECURITY a player is in an active mode, she updates her strategy and estimates of unknown quantities using a specific pure or hybrid learning pattern. The players’ intelligence and rationality are captured by the weighted linear combination of different learning patterns. We use stochastic approximation techniques to show that, under appropriate conditions, the pure or hybrid learning schemes with random updates can be studied using their deterministic ordinary differential equation (ODE) counterparts. Convergence to state-independent equilibria is analyzed for special classes of games, namely, games with two actions, and potential games. Results are applied to network security games between an intruder and an administrator, where the noncooperative behaviors are well characterized by the features of distributed hybrid learning. We consider multi-player repeated games involving a large number of players with large strategy spaces and enmeshed utility structures. In these ldquolarge-scalerdquo games, players are inherently faced with limitations in both their observational and computational capabilities. Accordingly, players in large-scale games need to make their decisions using algorithms that accommodate limitations in information gathering and processing. This disqualifies some of the well known decision making models such as ldquoFictitious Playrdquo (FP), in which each player must monitor the individual actions of every other player and must optimize over a high dimensional probability space. We will show that Joint Strategy Fictitious Play (JSFP), a close variant of FP, alleviates both the informational and computational burden of FP. Furthermore, we introduce JSFP with inertia, i.e., a probabilistic reluctance to change strategies, and establish the convergence to a pure Nash equilibrium in all generalized ordinal potential games in both cases of averaged or exponentially discounted historical data. We illustrate JSFP with inertia on the specific class of congestion games, a subset of generalized ordinal potential games. In particular, we illustrate the main results on a distributed traffic routing problem and derive tolling procedures that can lead to optimized total traffic congestion. This paper addresses the problem of joint resource block (RB) and uplink transmission power allocation in a Device to Device (D2D) underlay cellular network via a game theoretic approach. In contrast to the majority of previous research works in this area, the proposed framework aims mainly at interference mitigation and energy efficiency. We do not restrict a priori the number of D2D pairs which can reuse a RB allocated to a cellular link. However, this is determined dynamically by the objective of interference minimization. To address the resource allocation problem under consideration and deal with its inherent complexity, a two-step distributed approach is proposed. At first the RB allocation process is modeled as an exact potential game which is shown to minimize the total interference in the network. Second a non-cooperative game theoretic model for the uplink transmission power allocation process is proposed. For both stages of the proposed framework, efficient and distributed algorithms for the computation of the desired Nash Equilibrium (NE) point of each game are introduced. The efficiency of the overall proposed framework is evaluated through modeling and simulation, while comparative numerical results are presented that demonstrate the superiority of our methodology against other state of the art approaches. The field of convention emergence studies how agents involved in repeated coordination games can reach consensus through only local interactions. The literature on this topic is vast and is motivated by human societies, mainly addressing coordination problems between human agents, such as who gets to redial after a dropped telephone call. In contrast, real-world engineering problems, such as coordination in wireless sensor networks, involve agents with limited resources and knowledge and thus pose certain restrictions on the complexity of the coordination mechanisms. Due to these restrictions, strategies proposed for human coordination may not be suitable for engineering applications and need to be further explored in the context of real-world application domains. In this article we take the role of designers of large decentralized multi-agent systems. We investigate the factors that speed up the convergence process of agents arranged in different static and dynamic topologies and under different interaction models, typical for engineering applications. We also study coordination problems both under partial observability and in the presence of faults (or noise). The main contributions of this article are that we propose an approach for emergent coordination, motivated by highly constrained devices, such as wireless nodes and swarm bots, in the absence of a central entity and perform extensive theoretical and empirical studies. Our approach is called Win-Stay Lose-probabilistic-Shift, generalizing two well-known strategies in game theory that have been applied in other domains. We demonstrate that our approach performs well in different settings under limited information and imposes minimal system requirements, due to its simplicity. Moreover, our technique outperforms state-of-the-art coordination mechanisms, guarantees full convergence in any topology and has the property that all convention states are absorbing. Wireless Heterogeneous Sensor Network (WHSN) facilitates ubiquitous information acquisition for Ambient Intelligence (AmI) systems. It is of great importance of power management and topology control for WHSN to achieve desirable network performances, such as clustering properties, connectivity and power efficiency. This paper proposes a game theoretic model of topology control to analyze the decentralized interactions among heterogeneous sensors. We study the utility function for nodes to achieve desirable frame success rate and node degree, while minimizing the power consumption. Specifically, we propose a static complete-information game formulation for power scheduling and then prove the existence of the Nash equilibrium with simultaneous move. Because the heterogeneous sensors typically react to neighboring environment based on local information and the states of sensors are evolving over time, the power-scheduling problem in WHSN is further formulated into a more realistic incomplete-information dynamic game model with sequential move. We then analyze the separating equilibrium, one of the perfect Bayesian equilibriums resulted from the dynamic game, with the sensors revealing their operational states from their actions. The sufficient and necessary conditions for the existence of separating equilibrium are derived for the dynamic Bayesian game, which provide theoretical basis to the proposed power scheduling algorithms, NEPow and BEPow. The primary contributions of this paper include applying game theory to analyze the distributed decision-making process of individual sensor nodes and to analyze the desirable utilities of heterogeneous sensor nodes. Simulations are presented to validate the proposed algorithms and the results show their ability of maintaining reliable connectivity, reducing power consumption, while achieving desirable network performances. The security game is a basic model for resource allocation in adversarial environments. Here there are two players, a defender and an attacker. The defender wants to allocate her limited resources to defend critical targets and the attacker seeks his most favorable target to attack. In the past decade, there has been a surge of research interest in analyzing and solving security games that are motivated by applications from various domains. Remarkably, these models and their game-theoretic solutions have led to real-world deployments in use by major security agencies like the LAX airport, the US Coast Guard and Federal Air Marshal Service, as well as non-governmental organizations. Among all these research and applications, equilibrium computation serves as a foundation. This paper examines security games from a theoretical perspective and provides a unified view of various security game models. In particular, each security game can be characterized by a set system E which consists of the defender's pure strategies; The defender's best response problem can be viewed as a combinatorial optimization problem over E. Our framework captures most of the basic security game models in the literature, including all the deployed systems; The set system E arising from various domains encodes standard combinatorial problems like bipartite matching, maximum coverage, min-cost flow, packing problems, etc. Our main result shows that equilibrium computation in security games is essentially a combinatorial problem. In particular, we prove that, for any set system @math , the following problems can be reduced to each other in polynomial time: (0) combinatorial optimization over E; (1) computing the minimax equilibrium for zero-sum security games over E; (2) computing the strong Stackelberg equilibrium for security games over E; (3) computing the best or worst (for the defender) Nash equilibrium for security games over E. Therefore, the hardness [polynomial solvability] of any of these problems implies the hardness [polynomial solvability] of all the others. Here, by "games over E" we mean the class of security games with arbitrary payoff structures, but a fixed set E of defender pure strategies. This shows that the complexity of a security game is essentially determined by the set system E. We view drawing these connections as an important conceptual contribution of this paper. We investigate the problem of resource block (RB) and power allocation jointly and in a distributed manner using game theoretic learning solutions, in an underlay device-to-device network where device pairs communicate directly with each other by reusing the spectrum allocated to the cellular users. We formulate the joint RB and power allocation as multi-agent learning problems with discrete strategy sets; and suggest partially distributed and fully distributed learning algorithms to determine the RB and power level to be used by each device pair. The partially distributed algorithms, viz., Fictitious Play and its variant Fading Memory Joint Strategy Fictitious Play with Inertia, achieve Nash Equilibrium (NE) of the sum-rate maximization game in a static wireless environment. The completely distributed and uncoupled Stochastic Learning Algorithm converges to pure strategy NE of the interference mitigation game in a time-varying radio environment. We provide proofs for the existence of NE and convergence of the learning algorithms to the NE. Performance of the proposed schemes are evaluated in log-normal, Rayleigh and Nakagami fading environments and compared with an existing hybrid scheme and a centralized scheme. The simulation results show that the partially distributed schemes give the same performance as the centralized scheme, and the fully distributed scheme gives similar performance as the hybrid scheme but with much reduced signaling and computation overhead. Security breaches and attacks are critical problems in today’s networking. A key-point is that the security of each host depends not only on the protection strategies it chooses to adopt but also on those chosen by other hosts in the network. The spread of Internet worms and viruses is only one example. This class of problems has two aspects. First, it deals with epidemic processes, and as such calls for the employment of epidemic theory. Second, the distributed and autonomous nature of decision-making in major classes of networks (e.g., P2P, adhoc, and most notably the Internet) call for the employment of game theoretical approaches. Accordingly, we propose a unified framework that combines the N-intertwined, SIS epidemic model with a noncooperative game model. We determine the existence of a Nash equilibrium of the respective game and characterize its properties. We show that its quality, in terms of overall network security, largely depends on the underlying topology. We then provide a bound on the level of system inefficiency due to the noncooperative behavior, namely, the “price of anarchy” of the game. We observe that the price of anarchy may be prohibitively high, hence we propose a scheme for steering users towards socially efficient behavior. We study the problem of allocating limited security countermeasures to protect network data from cyber-attacks, for scenarios modeled by Bayesian attack graphs. We consider multi-stage interactions between a network administrator and cybercriminals, formulated as a security game. This formulation is capable of representing security environments with significant dynamics and uncertainty, and very large strategy spaces. For the game model, we propose parameterized heuristic strategies for both players. Our heuristics exploit the topological structure of the attack graphs and employ different sampling methodologies to overcome the computational complexity in determining players' actions. Given the complexity of the game, we employ a simulation-based methodology, and perform empirical game analysis over an enumerated set of these heuristic strategies. Finally, we conduct experiments based on a variety of game settings to demonstrate the advantages of our heuristics in obtaining effective defense strategies which are robust to the uncertainty of the security environment. 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. In the traffic assignment problem, first proposed by Wardrop in 1952, commuters select the shortest available path to travel from their origins to their destinations. We study a generalization of this problem in which competitors, who may control a nonnegligible fraction of the total flow, ship goods across a network. This type of games, usually referred to as atomic games, readily applies to situations in which the competing freight companies have market power. Other applications include intelligent transportation systems, competition among telecommunication network service providers, and scheduling with flexible machines. Our goal is to determine to what extent these systems can benefit from some form of coordination or regulation. We measure the quality of the outcome of the game without centralized control by computing the worst-case inefficiency of Nash equilibria. The main conclusion is that although self-interested competitors will not achieve a fully efficient solution from the system's point of view, the loss is not too severe. We show how to compute several bounds for the worst-case inefficiency that depend on the characteristics of cost functions and on the market structure in the game. In addition, building upon the work of Catoni and Pallotino, we show examples in which market aggregation (or collusion) adversely impacts the aggregated competitors, even though their market power increases. For example, Nash equilibria of atomic network games may be less efficient than the corresponding Wardrop equilibria. When competitors are completely symmetric, we provide a characterization of the Nash equilibrium using a potential function, and prove that this counterintuitive phenomenon does not arise. Finally, we study a pricing mechanism that elicits more coordination from the players by reducing the worst-case inefficiency of Nash equilibria. We study competition between wireless devices with incomplete information about their opponents. We model such interactions as Bayesian interference games. Each wireless device selects a power profile over the entire available bandwidth to maximize its data rate. Such competitive models represent situations in which several wireless devices share spectrum without any central authority or coordinated protocol. In contrast to games where devices have complete information about their opponents, we consider scenarios where the devices are unaware of the interference they cause to other devices. Such games, which are modeled as Bayesian games, can exhibit significantly different equilibria. We first consider a simple scenario of simultaneous move games, where we show that the unique Bayes-Nash equilibrium is where both devices spread their power equally across the entire bandwidth. We then extend this model to a two-tiered spectrum sharing case where users act sequentially. Here one of the devices, called the primary user, is the owner of the spectrum and it selects its power profile first. The second device (called the secondary user) then responds by choosing a power profile to maximize its Shannon capacity. In such sequential move games, we show that there exist equilibria in which the primary user obtains a higher data rate by using only a part of the bandwidth. In a repeated Bayesian interference game, we show the existence of reputation effects: an informed primary user can bluff to prevent spectrum usage by a secondary user who suffers from lack of information about the channel gains. The resulting equilibrium can be highly inefficient, suggesting that competitive spectrum sharing is highly suboptimal. In this paper, we introduce and analyze the properties of a class of games, the atomic congestion games on graphs (ACGGs), which is a generalization of the classical congestion games. In particular, an ACGG captures the spatial information that is often ignored in a classical congestion game. This is useful in many networking problems, e.g., wireless networks where interference among the users heavily depends on the spatial information. In an ACGG, a player's payoff for using a resource is a function of the number of players who interact with it and use the same resource. Such spatial information can be captured by a graph. We study fundamental properties of the ACGGs: under what conditions these games possess a pure strategy Nash equilibrium (PNE), or the finite improvement property (FIP), which is sufficient for the existence of a PNE. We show that a PNE may not exist in general, but that it does exist in many important special cases including tree, loop, or regular bipartite networks. The FIP holds for important special cases including systems with two resources or identical payoff functions for each resource. Finally, we present two wireless network applications of ACGGs: power control and channel contention under IEEE 802.11. This paper introduces a novel framework for modeling interacting humans in a multi-stage game environment by combining concepts from game theory and reinforcement learning. The proposed model has the following desirable characteristics: (1) Bounded rational players, (2) strategic (i.e., players account for one another’s reward functions), and (3) is computationally feasible even on moderately large real-world systems. To do this we extend level-K reasoning to policy space to, for the first time, be able to handle multiple time steps. This allows us to decompose the problem into a series of smaller ones where we can apply standard reinforcement learning algorithms. We investigate these ideas in a cyber-battle scenario over a smart power grid and discuss the relationship between the behavior predicted by our model and what one might expect of real human defenders and attackers. The spread of epidemics and malware is commonly modeled by diffusion processes on networks. Protective interventions such as vaccinations or installing anti-virus software are used to contain their spread. Typically, each node in the network has to decide its own strategy of securing itself, and its benefit depends on which other nodes are secure, making this a natural game-theoretic setting. There has been a lot of work on network security game models, but most of the focus has been either on simplified epidemic models or homogeneous network structure. We develop a new formulation for an epidemic containment game, which relies on the characterization of the SIS model in terms of the spectral radius of the network. We show in this model that pure Nash equilibria (NE) always exist, and can be found by a best response strategy. We analyze the complexity of finding NE, and derive rigorous bounds on their costs and the Price of Anarchy or PoA (the ratio of the cost of the worst NE to the optimum social cost) in general graphs as well as in random graph models. In particular, for arbitrary power-law graphs with exponent β > 2, we show that the PoA is bounded by O(T2(β -1))), where T = γ α is the ratio of the recovery rate to the transmission rate in the SIS model. We prove that this bound is tight up to a constant factor for the Chung-Lu random power-law graph model. We study the characteristics of Nash equilibria empirically in different real communication and infrastructure networks, and find that our analytical results can help explain some of the empirical observations.